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CVPR/2025/Leveraging SD Map to Augment HD Map-based Trajectory Prediction/full.md

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+# Leveraging SD Map to Augment HD Map-based Trajectory Prediction
+
+Zhiwei Dong Ran Ding Wei Li* Peng Zhang Guobin Tang Jia Guo Riemann Lab, 2012 Laboratories, Huawei Technologies.
+
+kivee@foxmail.com liwei.levi@huawei.com
+
+# Abstract
+
+Trajectory prediction models in real-world autonomous driving often rely on online High-Definition (HD) maps to understand road environments, but online HD maps suffer from perception errors and feature redundancy, which hinder the performance of these models. To address this issue, we introduce a framework, termed SD map-Augmented Trajectory Prediction (SATP), which leverages Standard-Definition (SD) maps to enhance HD map-based trajectory prediction models. First, we propose an SD-HD fusion approach to leverage SD maps across the diverse range of HD map-based trajectory prediction models. Second, we design a novel AlignNet to align the SD map with the HD map, further improving the effectiveness of SD maps. Experiments on real-world autonomous driving benchmarks demonstrate that SATP not only improves the performance of HD map-based trajectory prediction up to  $25\%$  in real-world scenarios using online HD maps but also brings benefits in ideal scenarios with ground-truth HD maps.
+
+# 1. Introduction
+
+Trajectory prediction is a fundamental and critical task in autonomous driving, and it aims to predict the future trajectories of traffic participants (hereafter referred to as agents). To make more precise predictions, it is essential to accurately understand the road environment.
+
+HD maps serve as a crucial input for the accurate understanding of the road environment in recent trajectory prediction research [2, 5, 7, 14, 20, 27, 28, 38, 39], albeit with high associated construction and maintenance costs. Therefore, most deployed autonomous systems [11, 12, 26] use online HD maps instead. Online HD maps are constructed in real-time from inexpensive onboard sensor data [4, 15-17, 32, 34, 40], such as RGB images, making low-cost HD maps available at any location on the earth. However, online HD maps introduce perception errors and also retain the inherent feature redundancy of HD maps (as shown in
+
+![](images/6aad41102fc4ed151d7e8c9631a68a7004b9833dda0f04d2d01804f57988d3b3.jpg)  
+Figure 1. Left: Due to limitations in sensors or algorithms, online HD maps inevitably contain errors, while SD maps accurately capture the road skeleton. Right: Online HD maps require numerous elements to precisely describe road details, lacking a compact description, which is a characteristic of SD maps. These two problems of online HD maps hinder the performance of trajectory prediction models, while SD maps could be used to address them.
+
+Figure 1), both of which hinder the performance of trajectory prediction models in deployed autonomous driving systems. The method proposed in [8] tries to address the problem of perception errors by producing and leveraging online HD map uncertainty, but it ignores the inherent feature redundancy of HD maps. We notice that simple SD maps used for road-level navigation can help address these two problems of complex online HD maps in trajectory prediction (as shown in Figure 1): (1) Perception errors: Although SD maps only provide road-level skeletons, they are generated manually offline, so their accuracy is reliable. When errors arise in online HD maps due to sensor limitations, occlusions, or other inherent factors, SD maps can offer corrective support. (2) Feature redundancy: The road skeletons provided by SD maps summarize the key features of detailed lane information in HD maps, which could provide more concise environmental clues for trajectory prediction models and improve their learning efficiency. Additionally, SD maps have global coverage and are freely available, making them an ideal complement to HD maps.
+
+Based on the above considerations, we propose a framework named SATP to effectively integrate SD maps into various online HD map-based trajectory prediction models (hereafter referred to as baseline models $^1$ ), along with an AlignNet designed to enhance the utilization of SD maps. Our goal is to improve trajectory prediction performance in real-world autonomous driving scenarios that rely on online HD maps through leveraging SD maps.
+
+Specifically, we develop an SD-HD fusion approach by abstracting the HD map utilization process of different baseline models. HD map-based trajectory prediction models typically contain HD map encoding and HD feature extraction, and these two steps incorporate HD information into the features used for regressing trajectory coordinates. These features have different names across various baseline models, such as agent tokens [28, 38], goal queries [7, 36], or mode queries [25, 39], which we collectively refer to as "queries" for simplicity. Considering the compact feature of SD maps and feature consistency between SD and HD maps, we scale down the HD map encoding and feature extraction modules in baseline models to create SD map encoding and feature extraction modules. Finally, the HD-informed and SD-informed queries are adaptively fused for trajectory prediction.
+
+Furthermore, we design AlignNet to address the misalignment between SD and HD maps as illustrated in Figure 1. This problem is caused by vehicle positioning errors or SD map precision limitations and weakens the effectiveness of the SD map utilization. AlignNet extracts the structural features of SD and HD maps through 2D point transformers and explicitly predicts a relative pose to transform SD maps to better align with HD maps. Since the map elements contained in SD maps and HD maps do not correspond one-to-one, and perception errors exist in online HD maps, it is not feasible to compute an accurate ground-truth relative pose to directly supervise the AlignNet's output. Instead, we rely on the final trajectory prediction loss to allow it to learn the relative pose adaptively.
+
+Our contributions can be summarized as follows:
+
+- We find that simple SD maps can help address perception errors and feature redundancy in online HD maps, and thus propose an SD-HD fusion framework to integrate SD maps into various HD map-based trajectory prediction models.  
+- We propose AlignNet to explicitly align SD maps with HD maps, enhancing the effectiveness of SD maps in augmenting HD map-based trajectory prediction.  
+- We implement SATP on several representative trajectory prediction models and improve their performance on real-
+
+world trajectory prediction benchmarks up to  $25\%$  while keeping the increase of inference time within  $10\%$ .
+
+# 2. Related Work
+
+# 2.1. HD Map-Based Trajectory Prediction
+
+Trajectory prediction is challenging because the intentions of agents are uncertain. Intuitively, the road structure imposes certain restrictions on traffic participants' intentions, as cars are typically expected to drive within the lanes and not stray off the road. Therefore, researchers usually use HD maps to enhance trajectory prediction, as they contain precise information about road structures, such as lanes, pedestrian crossings, and traffic lights. Currently, there are two methods for using HD maps: rasterization and vectorization. The rasterization method [2, 14, 19, 20] is an earlier solution where researchers render elements of the HD map into a bird's-eye-view image (with different attributes occupying different channels) and then use well-established convolutional neural networks (CNNs) [10, 24] to extract features from the HD map. This method, benefiting from the development of CNNs, dominated the field in the early times. However, rasterization has many disadvantages. First, it is limited by the resolution, which cannot accurately represent the position of map elements, always leading to a loss of precision during the rasterization process. Second, it is restricted by the receptive field limitations of CNNs, which struggle to capture distant features well, resulting in lower accuracy of distant trajectory predictions. Third, many locations without map elements still need to be represented numerically, which is redundant and inefficient. To address the issues with rasterization, researchers proposed vectorized representation [7, 38, 39]. In vectorized representation, each element of the HD map is represented as a vector (including its position coordinates, category attributes, etc.), and then GNNs or Transformers are used to compute and extract features from the vectors directly. Due to the absence of information loss caused by rasterization and the limitations of the receptive field, vectorized representations achieve much better results than rasterized representations in various benchmarks [1, 3, 6, 29]. To fully exploit the potential of SD maps in trajectory prediction, we also adopt the vectorized representation.
+
+# 2.2. Utilization of SD Maps in Autonomous Driving
+
+HD maps provide high-precision and detailed road information to support precise perception, localization, and planning for autonomous driving systems. However, due to the high cost of HD maps, many researchers are exploring how to use SD maps to advance the development of autonomous driving. In terms of perception, P-MapNet [13], BLOSBEV [31], and SMERF [18] have significantly improved accuracy by incorporating SD map priors to assist in the
+
+![](images/585a13665c714d1c57cfe0151ab94170cf6c3cf05d177c8ecdc89f3e47bf8dc9.jpg)  
+Figure 2. Overview of SATP. The gray part is the baseline model. SATP uses AlignNet to align SD with HD and uses SD-HD Fusion to get fused features, which are used for trajectory prediction.
+
+construction of online HD maps. In localization, OrienterNet [21] and MapLocNet [30] have achieved good accuracy by matching real-world images with SD maps, allowing autonomous vehicles to perform visual localization based on free SD maps in areas without HD maps. In trajectory prediction, due to the high cost and low coverage of HD maps, the method in [22] attempts to use SD maps instead of HD maps as the map input for trajectory prediction and enhance the performance of the SD map-based trajectory prediction model under conditions where ground-truth HD maps are available through knowledge distillation, but the accuracy is still lower than that based on ground-truth HD maps. This work demonstrates that SD maps can be used to assist trajectory prediction, but it also has flaws. First, it does not achieve accuracy comparable to using ground-truth HD maps. Second, it does not consider the problem of map misalignment. Additionally, it still relies on expensive ground-truth HD maps for knowledge distillation during training, which would further reduce the accuracy of trajectory prediction if not performed. Our method leverages SD maps to promote trajectory prediction as well, and it could achieve performance comparable to using expensive ground-truth HD maps by combining SD maps with imperfect but inexpensive online HD maps.
+
+# 3. Methodology
+
+# 3.1. Overview
+
+As shown in Figure 2, SATP is a framework that directly integrates SD map information into HD map-based trajectory prediction models. In SATP, SD map information is independently encoded and extracted outside the baseline model and then fused with HD information before the prediction head. This SD-HD fusion strategy allows SATP to be easily applied to different types of trajectory prediction models without modifying their internal modules. To ensure the consistency between SD and HD features, SATP applies model downscaling to create modules for SD map encoding and SD feature extraction. The proposed AlignNet predicts a relative pose between the SD and HD maps and better aligns these two types of maps, which is important for effectively utilizing SD maps.
+
+# 3.2. Preparation of SD Maps
+
+OpenStreetMap² [9] provides global SD maps for free, and we use it as our source of SD maps. For each scenario in the nuScenes [1] and Argoverse2 [29] datasets, we extract the corresponding SD map as follows:
+
+1. Ego-vehicle positioning: We first obtain the latitude and longitude of the ego vehicle based on the original latitude and longitude of the city provided by the dataset and the ground-truth relative pose of the ego vehicle.  
+2. SD map retrieval: Using the ego vehicle's pose, we retrieve the SD map within a certain range centered on the ego vehicle (the specific range is consistent with the HD map range of nuScenes and Argoverse2)  
+3. Road skeleton extraction: The original SD maps contain elements of many attributes, including roads and buildings. For autonomous driving purposes, we extract multilinear string elements that contain the highway field, such as highway:primary. These elements represent roads that vehicles can travel on. We then perform equidistant sampling at the 1-meter intervals on these vector elements to accurately capture their shapes.
+
+Moreover, it is worth mentioning that the pose of each scene's ego vehicle obtained by the method above is very accurate, as the dataset provides precise GPS coordinates of the city's origin, and the relative pose of the ego vehicle is highly accurate after complex offline post-processing. However, in practical application, real-time positioning technology often involves larger errors. Since SATP is aimed at real-world autonomous driving, we add random Gaussian noise to the ego vehicle's pose during the SD map retrieval to simulate positioning errors in real scenarios.
+
+# 3.3. SD-HD Fusion
+
+Our approach to leveraging SD maps is rooted in the following principle: SD maps should be integrated into trajectory prediction in the same way that the baseline model utilizes HD maps. Therefore, we need to abstract the framework for utilizing HD maps across different baseline models and apply this framework to SD map usage. As illustrated in Figure 3(a), we observe that most recent trajectory prediction models [7, 23, 25, 28, 33, 36, 38, 39] commonly employ a two-step approach when incorporating HD maps: HD map encoding and HD feature extraction.
+
+1. HD Map Encoding: Since HD map elements are generally polylines with specific traffic attributes, they must first be encoded into the feature space to interact with agent motion features and support trajectory predictions effectively. Typically, this step involves applying MLPs [23, 38] to encode the geometric information and traffic attributes of the map elements or, in more complex approaches, using self-attention mechanisms to capture
+
+![](images/66f67c98788e588d9687949112ffa79e6152538489c0db80d158059d7273a933.jpg)  
+(a) SD-HD fusion framework
+
+![](images/ccea7efd12f7da235001b65f122fcbc64708b8f9312af250ea8f4356d4744572.jpg)  
+(b) HiVT with SD-HD fusion
+
+![](images/8cc6bc821ff3d33297a15af9ad4038fd9729c0b08336ff9f8d5c4e78dddcc7d9.jpg)  
+(c) DenseTNT with SD-HD fusion
+
+![](images/647a338f06eaf9ecf46a957a716b395e7a304d3ad26120cf0ae5a1a29011f73f.jpg)  
+(d) QCNet with SD-HD fusion  
+Figure 3. Description of SD-HD fusion and its implementations on three baseline models. We downscale the HD map encoding and feature extraction modules to create modules for SD map encoding and feature extraction. The SD map encoding module takes SD maps as input, and its outputs serve as key/value inputs for SD feature extraction. Q, K, and V represent the query, key, and value used for attention.
+
+more comprehensive global map features [7, 36, 39].
+
+2. HD Feature Extraction: To combine HD map features with agent motion features and subsequently generate trajectory predictions, recent models usually rely on cross-attention mechanisms. In these models, HD features serve as key/value inputs, while agent features are used as queries [28, 38], or learnable queries are employed [7, 25, 36], or a combination of both [39].
+
+Thus, for each type of baseline model, we reduce the layers and channels of the HD encoding and extraction modules in the baseline model to generate the structure of the SD encoding and extraction modules, which we call model downscaling. There are two main reasons for employing model downscaling to create new modules for SD maps: (1) Feature Consistency: To ensure compatibility between SD and HD features, using similar structures for encoding and extraction is optimal. (2) Fewer Parameters: Since SD maps contain only essential road skeleton information, they include far fewer map element vectors than HD maps, allowing for a smaller model size.
+
+Finally, we adopt an adaptive approach to fuse the two sets of queries, each containing HD and SD features, respectively. The fusion process is defined by:
+
+$$
+\begin{array}{l} w _ {i} = \operatorname {S i g m o i d} \left(M L P \left(\operatorname {C o n c a t} \left(Q _ {i} ^ {H}, Q _ {i} ^ {S}\right)\right)\right), \tag {1} \\ Q _ {i} ^ {F} = \left(1 - w _ {i}\right) \cdot Q _ {i} ^ {H} + w _ {i} \cdot Q _ {i} ^ {S}, \\ \end{array}
+$$
+
+where  $Q_{i}^{H}, Q_{i}^{S}$  and  $Q_{i}^{F}$  represent the map-informed queries derived from the initial query  $i$ , incorporating HD features, SD features, and SD-HD fusion features, respectively. Here,  $Q_{i}^{F}$  is used for subsequent trajectory prediction, while baseline HD map-based models use  $Q_{i}^{H}$  directly for trajectory prediction, as illustrated in Figure 3(a).
+
+Based on the above principles, we demonstrate specific SATP implementations on three representative trajectory prediction models: HiVT [38], DenseTNT [7], and QCNet [39]. We choose these baseline models because they represent three typical ways of HD feature extraction: agent query, learnable query, and a combination of them.
+
+HiVT with SATP In HiVT (Figure 3(b)), an HD Map Encoder composed of MLPs is used for HD map encoding, so we downscale it to create an SD Map Encoder for SD map encoding. Next, HiVT performs HD feature extraction through cross-attention in the Agent-Lane Interaction module, passing HD features to agent queries. Accordingly, we scale down the Agent-Lane Interaction module to create an Agent-SD Interaction module for SD feature extraction. Finally, we fuse the two sets of queries containing different map information.
+
+DenseTNT with SATP DenseTNT (Figure 3(c)) utilizes a Context Encoder for HD map encoding, which takes both map element polylines and agent trajectories as inputs, applying hierarchical self-attention within and between instances. We scale down the Context Encoder to create an SD Context Encoder. However, we input only the polylines from the SD map into the SD Context Encoder for efficiency. For HD feature extraction, the Dense Goal Encoder uses dense goals sampled from the HD map as queries and employs the Context Encoder output as key/value inputs. To adapt this process, we downscale the Dense Goal Encoder to create a Dense Goal-SD Encoder for SD feature extraction, which takes the output of the SD Context Encoder as key/value inputs and dense goal as queries.
+
+![](images/ffaa859d4312c7c8c0881298d1b8134c6dc618beaed59429fdb1209fa39b5481.jpg)  
+Figure 4. Structure of the AlignNet.
+
+QCNet with SATP QCNet's HD Map Encoder employs hierarchical attention for HD map encoding, which we scale down to create an SD Map Encoder. As shown in Figure 3(d), QCNet has two modules for HD feature extraction: the Agent-Lane Encoder and Mode-Map Cross-Attention. By downscaling these modules, we obtain the Agent-SD Encoder and Mode-SD Cross-Attention for SD feature extraction. The Agent-SD Encoder uses agent features as query inputs and SD features as key/value inputs to perform cross-attention. Mode-SD Cross-Attention, on the other hand, uses learnable mode queries as the query inputs for cross-attention. The Agent-Lane Encoder and the Agent-SD Encoder pass HD and SD features, respectively, to the agent queries. The learnable mode queries then acquire features from these agent queries through cross-attention. Finally, HD and SD features are directly injected into the mode queries via the Mode-Map Encoder and Mode-SD Encoder, respectively, enabling them to predict trajectories.
+
+# 3.4. AlignNet
+
+The cropped local SD map from OpenStreetMap based on real-time vehicle positioning results generally has misalignment with the corresponding HD map, whether it is an online HD map estimated in the ego vehicle's coordinate system or an offline constructed ground-truth HD map. As illustrated in Figure 4, there are two reasons: (1) The poor precision of SD maps leads to misalignment with the centerlines of roads. (2) The vehicle's positioning results based on GPS/IMU or other technologies have inherent errors. Directly using the misaligned SD maps increases the learning difficulty for the trajectory prediction model due to conflicting information between misaligned SD and HD maps. Therefore, we design AlignNet to align these two kinds of maps, aiming at improving the effectiveness of SD maps. AlignNet extracts structural features from both the HD map and the SD map, then concatenates these features to predict the translation  $t$  and rotation angle  $\theta$  of the SD map relative to the HD map, and finally applies  $(\theta, t)$  to transform the SD map for alignment with the HD map.
+
+In AlignNet, we first sample sparse and key points from the input HD and SD maps to preserve maps' structures but
+
+decrease the computational cost of the point transformer. Specifically, for each vector element in the map, we sample at a 5-meter interval and preserve those corner points. Then, a shared light-weighted 2D Point Transformer, which is a variation of the Point Transformer [37], is used as the map encoder. The 2D Point Transformer embeds the coordinates of each point as initial features, then performs self-vector attention [35] within its K-Nearest Neighbor (KNN) neighborhood to extract local structural features, followed by local max pooling. After multiple iterations of feature extraction and local max pooling, global average pooling is used to obtain the global features. The structural features of HD and SD maps are concatenated, and then an MLP is used to predict the rotation angle  $\theta$  and transformation  $t$  of the SD map relative to the HD map. Finally, we compute rotation matrix  $R = \begin{bmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{bmatrix}$  and the following formula is used to obtain the aligned SD Map:
+
+$$
+S _ {\text {a l i g n e d}} = R \cdot S ^ {T} + t, \tag {2}
+$$
+
+where  $S$  and  $S_{\text{aligned}}$  are map element vectors of the SD map. In this paper,  $\theta$  and  $t$  are not directly supervised but are optimized by the trajectory prediction loss. To ease the learning process, we use sigmoid activation on the output of the MLP and multiply it by the  $\pi$ , limiting  $-\pi \leq \theta \leq \pi$ .
+
+# 4. Experiments
+
+Dataset nuScenes [1] is a popular real-world autonomous driving dataset, which includes 1,000 driving scenarios over 20 seconds. It provides agent trajectories, offline ground-truth HD maps, and sensor data (RGB images). We apply the methodology in [8] to upsample nuScenes' data frequency to fit trajectory prediction models, which aim to predict 3-second future trajectories based on 2-second historical motion information. Argoverse2 [29] is the latest large-scale trajectory prediction dataset from six cities, totaling 250,000 scenarios. It provides 5-second historical trajectories of various agents sampled at  $10\mathrm{Hz}$  and HD maps. The models need to predict a 6-second future trajectory for each agent.
+
+<table><tr><td colspan="2">Map Input</td><td colspan="3">HiVT</td><td colspan="3">DenseTNT</td><td colspan="3">QCNet</td></tr><tr><td>Method</td><td>mAP↑</td><td>ADE↓</td><td>FDE↓</td><td>MR↓</td><td>ADE↓</td><td>FDE↓</td><td>MR↓</td><td>ADE↓</td><td>FDE↓</td><td>MR↓</td></tr><tr><td>SD</td><td>N/A</td><td>0.454</td><td>0.89</td><td>0.107</td><td>1.379</td><td>2.255</td><td>0.444</td><td>0.401</td><td>0.871</td><td>0.091</td></tr><tr><td>MapTRv2</td><td>53.49</td><td>0.399</td><td>0.832</td><td>0.095</td><td>1.174</td><td>2.191</td><td>0.403</td><td>0.385</td><td>0.801</td><td>0.087</td></tr><tr><td>+ SATP</td><td>53.49</td><td>0.37</td><td>0.731</td><td>0.075</td><td>1.023</td><td>2.08</td><td>0.393</td><td>0.371</td><td>0.698</td><td>0.071</td></tr><tr><td>+ SATP + [8]</td><td>55.12</td><td>0.366</td><td>0.715</td><td>0.071</td><td>1.017</td><td>1.92</td><td>0.379</td><td>0.362</td><td>0.673</td><td>0.069</td></tr><tr><td>HRMapNet</td><td>74.16</td><td>0.397</td><td>0.82</td><td>0.091</td><td>0.907</td><td>1.671</td><td>0.218</td><td>0.371</td><td>0.796</td><td>0.083</td></tr><tr><td>+ SATP</td><td>74.16</td><td>0.365</td><td>0.722</td><td>0.071</td><td>0.732</td><td>1.406</td><td>0.183</td><td>0.358</td><td>0.637</td><td>0.062 (-25%)</td></tr><tr><td>+ SATP + [8]</td><td>74.91</td><td>0.362</td><td>0.72</td><td>0.07</td><td>0.709</td><td>1.397</td><td>0.181</td><td>0.346</td><td>0.625</td><td>0.062</td></tr><tr><td>GT HD</td><td>GT</td><td>0.371</td><td>0.736</td><td>0.072</td><td>0.852</td><td>1.475</td><td>0.199</td><td>0.36</td><td>0.632</td><td>0.062</td></tr><tr><td>GT HD + SATP</td><td>GT</td><td>0.336</td><td>0.672</td><td>0.065</td><td>0.724</td><td>1.388</td><td>0.175</td><td>0.327</td><td>0.615 (-3%)</td><td>0.06</td></tr></table>
+
+Table 1. Performance of SATP on nuScenes. GT means ground-truth. A larger mAP means a better online HD map. We highlight the maximum (25%) and minimum (3%) improvements brought by SATP for combinations of different map inputs and baseline models.
+
+Metrics For trajectory prediction, we follow the official metrics of Argoverse2, which include  $\text{minFDE}_6$ ,  $\text{minADE}_6$ ,  $MR_6$ . These metrics are calculated based on the best one out of 6 predicted trajectories. FDE refers to the L2 distance between the predicted trajectory and the ground-truth trajectory at the last frame, while ADE is the average L2 error across all predicted time steps. MR (Miss Rate) refers to the proportion of predicted trajectories with an FDE larger than 2 meters. In our tables, we just use ADE, FDE, and MR to represent  $\text{minFDE}_6$ ,  $\text{minADE}_6$ , and  $MR_6$  for simplicity. For end-to-end autonomous driving, we follow [12] and use the L2 displacement error and collision rate as metrics. L2 displacement error measures the average L2 distance between the planning trajectory and the ground truth. The collision rate represents the frequency of collisions with other agents using the planning trajectory.
+
+Model Training First, we train the latest online HD map construction models MapTRv2 [16] and HRMapNet [34] on the nuScenes dataset and perform inference with the mapping models to generate the online HD maps for the trajectory prediction scenarios. Then, we train the trajectory prediction models with SATP, using the generated online HD maps without inference with HD map construction models. All training configurations for the online HD mapping models and trajectory prediction models are consistent with their official implementations. All trajectory prediction models are trained and tested on a single V100 GPU.
+
+# 4.1. Performance on nuScenes
+
+Quantitative Results Table 1 shows the experimental results of deploying SATP on the three latest trajectory prediction models, utilizing the state-of-the-art MapTRv2 and HRMapNet for online HD map construction. First, Table 1 demonstrates that STAP significantly enhances the performance of these online HD map-based baseline models by integrating SD maps. This is reasonable because perception errors in online HD maps can lead to an imprecise understanding of the road environment, and SD maps can
+
+correct these errors to some degree. Second, we combine SATP with the ground-truth HD map and find that it can still bring stable improvements to baseline models. The reason is that SD maps contain only the concise and key information of road environment, which could alleviate the feature redundancy problem and improve the training efficiency of baseline models. Overall, across the combinations of different map inputs and baseline models, SATP brings an average improvement of  $9\%$ ,  $13\%$ , and  $17\%$  in terms of ADE, FDE, and MR, respectively. These results demonstrate the value of SATP in real-world autonomous driving applications: (1) When only defective online HD maps are available, SATP can significantly improve the performance of HD map-based trajectory prediction models, achieving results comparable to those using perfect ground-truth HD maps. (2) SATP can also play an important role when offline ground-truth HD maps are available in some areas or when significant advancements are made in the future online HD map construction technology. The method proposed in [8] enhances the performance of online HD Map-based trajectory prediction models by predicting uncertainty for online HD Maps. We combine it with SATP, and experiment results indicate that these two approaches can jointly improve the performance of trajectory prediction models based on online HD Maps.
+
+Qualitative Results In Figure 5, we draw the results of HiVT on the nuScenes dataset with different map inputs. First, it illustrates that SATP effectively utilizes SD maps, achieving predictions superior to those using only online HD maps and comparable to those using precise ground-truth HD maps. This highlights SATP's value in most real-world scenarios, where ground-truth HD maps are difficult to obtain. Additionally, Figure 5 shows that our AlignNet could align SD maps with HD maps to some extent.
+
+# 4.2. Performance on Argoverse2
+
+We conduct experiments on the larger and more complex real-world Argoverse2 dataset. The Argoverse2 trajectory
+
+![](images/39ef479ef5321d898b62ff9cd951421c7230baff59822330c1171a348fa62fb9.jpg)  
+(a) T-shaped intersection
+
+![](images/b81eee4ef56ebeaa250f1e1776326f731a0287e52afd2803586ea7510a357c36.jpg)  
+(b) Normal intersection
+
+![](images/e8d39209b3d977406467882f89a3a2536ae8e1fc2857e17b0bb7c46013ef75f7.jpg)  
+(c) Straight road  
+Figure 5. Qualitative results. In each subfigure, left: online HD map (MapTRv2), mid: online HD map + SATP, right: GT HD map. For simplicity, we only show three front-viewed images, but we use six surround-viewed images to construct online HD maps in experiments.
+
+<table><tr><td rowspan="2">Map Input</td><td colspan="3">QCNet</td></tr><tr><td>ADE↓</td><td>FDE↓</td><td>MR↓</td></tr><tr><td>SD</td><td>1.105</td><td>2.316</td><td>0.238</td></tr><tr><td>GT HD + Noise</td><td>0.884</td><td>1.525</td><td>0.206</td></tr><tr><td>GT HD + Noise + SATP</td><td>0.752</td><td>1.306</td><td>0.164</td></tr><tr><td>GT HD</td><td>0.741</td><td>1.293</td><td>0.162</td></tr><tr><td>GT HD + SATP</td><td>0.708</td><td>1.236</td><td>0.152</td></tr></table>
+
+prediction dataset does not provide RGB images or LiDAR data for HD map construction, and there is minimal overlap between it and the Argoverse2 HD map construction dataset. So, we simulate perception errors in online HD maps by adding noise and randomly dropping map elements of ground-truth HD maps in the Argoverse2 trajectory prediction dataset. As shown in Table 2, the performance of QCNet using simulated online HD maps declines compared to using ground-truth HD maps as input, indicating that our simulation is effective. Subsequently, we leverage SD maps using SATP, and QCNet's performance improves to be comparable to that using ground-truth HD maps, demonstrating the effectiveness of SATP. Finally, we introduce SATP on top of ground-truth HD maps, which brings performance improvement as well, indicating that SATP leverages the concise and key map elements in SD maps to enhance the learning efficiency of the trajectory prediction model.
+
+# 4.3. Ablation Study
+
+We conduct ablation experiments on HiVT to validate the effectiveness and rational design of each module of SATP.
+
+First, we remove AlignNet, not aligning SD maps with HD maps. Although this still yields slightly better predictions than using online HD maps alone, the results are significantly inferior to those using aligned SD maps, demonstrating the necessity of aligning SD maps with HD maps in practical application. Additionally, we implement AlignNet using a CNN-based approach, rasterizing both SD and HD
+
+Table 2. Performance of SATP on Argoverse2. We add noise to ground-truth HD maps to simulate online HD maps with errors.  
+
+<table><tr><td>Method</td><td>ADE↓</td><td>FDE↓</td><td>MR↓</td></tr><tr><td>HiVT + MapTRv2</td><td>0.399</td><td>0.832</td><td>0.095</td></tr><tr><td>+ SATP</td><td>0.37</td><td>0.731</td><td>0.075</td></tr><tr><td>+ SATP/without AlignNet</td><td>0.391</td><td>0.818</td><td>0.089</td></tr><tr><td>+ SATP/with CNN align</td><td>0.388</td><td>0.807</td><td>0.082</td></tr><tr><td>+ SATP/with SD→HD</td><td>0.393</td><td>0.81</td><td>0.093</td></tr><tr><td>+ SATP/with HD→SD</td><td>0.396</td><td>0.823</td><td>0.091</td></tr></table>
+
+Table 3. Ablation study of SATP on HiVT.
+
+maps and employing ResNet-18 [10] as a backbone to extract map features and predict translation and rotation. The CNN-based alignment performs less effectively compared to using a 2D Point Transformer. This may be due to CNNs' limitations in accurately determining the precise positions of map elements, whereas the calculation of relative pose requires precise input of location coordinates.
+
+Finally, we replace our SD-HD fusion with an alternative method, sequential fusion. In the sequential fusion, the SD and HD feature extraction modules work sequentially. The two variants with different orders of extraction SD and HD features are labeled as  $\mathrm{SD} \rightarrow \mathrm{HD}$  and  $\mathrm{HD} \rightarrow \mathrm{SD}$ . Table 3 shows that sequential fusion methods perform worse than our standard method. We hypothesize that SD maps and HD maps each have their own advantages, and a fixed order might cause features at the beginning of the pipeline to be somewhat forgotten. In contrast, parallel fusion can select appropriate map features more adaptively.
+
+# 4.4. Efficiency Study
+
+Since we introduce additional modules for SD maps, it is crucial to study the impact of these additional computations on the overall efficiency of baseline models. Table 4 shows that SATP does not add a significant amount of parameters to the baseline model, nor does it noticeably decrease their inference speed. There are two reasons for this result: (1) Although we introduce SD map encoding and SD feature extraction modules, these modules have reduced depth and
+
+<table><tr><td>Model</td><td>Param(M)↓</td><td>Latency(ms)↓</td></tr><tr><td>HiVT</td><td>2.6</td><td>36</td></tr><tr><td>HiVT + SATP</td><td>2.9 (+0.3M)</td><td>39 (+8%)</td></tr><tr><td>DenseTNT</td><td>1.6</td><td>317</td></tr><tr><td>DenseTNT + SATP</td><td>1.8 (+0.2M)</td><td>335 (+6%)</td></tr><tr><td>QCNet</td><td>7.7</td><td>142</td></tr><tr><td>QCNet + SATP</td><td>8.1 (+0.4M)</td><td>153 (+8%)</td></tr></table>
+
+![](images/99a2b3e392a87f1453b3a0d24f7dda9e5ca05ec2068648df66661d9a2df41c81.jpg)  
+Figure 6. Training process of HiVT on nuScenes.
+
+width compared to the corresponding modules in the baseline model. (2) The number of vector elements in SD maps is significantly lower than that in HD maps, which further reduces the computational load. On the contrary, Figure 6 shows that whether using online or ground-truth HD maps, SATP improves the training efficiency and enables the baseline model to converge more quickly and better. We believe this is because the concise road skeletons provided by SD maps alleviate the feature redundancy in HD maps and make the model's learning process easier.
+
+# 4.5. End-to-End Autonomous Driving
+
+To further validate the effectiveness of SATP, we integrate it with the advanced end-to-end autonomous driving model, VAD [12] and validate on the nuScenes [1] val dataset. In VAD, the planning transformer uses a set of learnable ego queries to extract the HD map features by treating the online HD map tokens as keys and values, similar to QCNet. Therefore, we implement SATP on VAD in a manner akin to that used with QCNet. Table 5 shows that SATP significantly improves various metrics of VAD. An interesting observation is that SATP brings greater improvements over a longer time horizon. This is reasonable, as online HD map construction has smaller errors closer to the vehicle than farther away, so the enhancements brought by SD maps are
+
+Table 4. Efficiency study of SATP.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="4">L2(m)↓</td><td colspan="4">Collision Rate(%)↓</td></tr><tr><td>1s</td><td>2s</td><td>3s</td><td>Avg.</td><td>1s</td><td>2s</td><td>3s</td><td>Avg.</td></tr><tr><td>VAD-tiny</td><td>0.46</td><td>0.76</td><td>1.12</td><td>0.78</td><td>0.21</td><td>0.35</td><td>0.58</td><td>0.38</td></tr><tr><td>+ SATP</td><td>0.39</td><td>0.62</td><td>0.94</td><td>0.65</td><td>0.14</td><td>0.21</td><td>0.42</td><td>0.26</td></tr></table>
+
+Table 5. Performance of SATP on end-to-end autonomous driving.  
+
+<table><tr><td>Method</td><td>\( \mathbf{{mAP}} \uparrow \)</td><td>ADE↓</td><td>FDE↓</td><td>MR↓</td></tr><tr><td>HiVT + MapTRv2</td><td>53.49</td><td>0.399</td><td>0.832</td><td>0.095</td></tr><tr><td>+ SATP</td><td>53.49</td><td>0.37</td><td>0.731</td><td>0.075</td></tr><tr><td>+ P-MapNet</td><td>61.24</td><td>0.395</td><td>0.826</td><td>0.093</td></tr><tr><td>+ P-MapNet + SATP</td><td>61.24</td><td>0.371</td><td>0.723</td><td>0.073</td></tr></table>
+
+Table 6. Comparison with SD-Enhanced online HD map.
+
+less obvious near the vehicle than at greater distances.
+
+# 4.6. SD-Enhanced Online HD Map Comparison
+
+As SD maps can be used to enhance the construction of online HD maps, an intuitive idea is to use SD map-enhanced online HD maps to improve trajectory prediction performance. To explore the differences between this method and SATP, we incorporate the SD map fusion module from PMapNet[13] into MapTRv2 for experiments. As shown in Table 6, adding SD maps improves the HD map construction quality of MapTRv2, which slightly enhances HiVT, though not as significantly as SATP. We also combine SATP with MapTRv2-PMapNet, and SATP still leads to better trajectory prediction results. We believe that reasons are twofold: (1) Using SD maps to enhance HD map construction, rather than directly for trajectory prediction, results in greater information loss. (2) Although SD map-enhanced online HD maps have fewer perception errors, this way cannot address the feature redundancy of HD maps.
+
+# 5. Conclusion
+
+In this paper, we propose SATP, a framework that integrates SD maps into HD map-based trajectory prediction. This addresses the performance degradation of HD map-only trajectory prediction caused by perception errors and feature redundancy in online HD maps in real-world autonomous driving systems. Our experiments show that SATP yields up to  $25\%$  improvement for various representative trajectory prediction models in real-world scenarios while keeping the increase in parameter size and inference time within  $10\%$ , which suggests the practical value of SATP for autonomous driving applications. While SATP demonstrates promising results for augmenting HD map-based trajectory prediction, some limitations remain. For instance, we do not account for errors caused by delayed updates of SD maps. In future work, we will focus on addressing such issues by combining real-time sensor data with SD maps or leveraging traffic flow monitoring.
+
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+# Leveraging Temporal Cues for Semi-Supervised Multi-View 3D Object Detection
+
+Jinhyung Park<sup>1</sup> Navyata Sanghvi<sup>1</sup> Hiroki Adachi<sup>1</sup> Yoshihisa Shibata<sup>2</sup> Shawn Hunt<sup>3</sup> Shinya Tanaka<sup>3</sup> Hironobu Fujiyoshi<sup>2</sup> Kris Kitani<sup>1</sup>
+
+$^{1}$ Carnegie Mellon University  $^{2}$ DENSO Corporation  $^{3}$ DENSO International America, Inc.
+
+# Abstract
+
+While recent advancements in camera-based 3D object detection demonstrate remarkable performance, they require thousands or even millions of human-annotated frames. This requirement significantly inhibits their deployment in various locations and sensor configurations. To address this gap, we propose a performant semi-supervised framework that leverages unlabeled RGB-only driving sequences - data easily collected with cost-effective RGB cameras - to significantly improve temporal, camera-only 3D detectors. We observe that the standard semi-supervised pseudo-labeling paradigm underperforms in this temporal, camera-only setting due to poor 3D localization of pseudo-labels. To address this, we train a single 3D detector to handle RGB sequences both forward and backward in time, then ensemble both its forwards and backwards pseudo-labels for semi-supervised learning. We further improve the pseudo-label quality by leveraging 3D object tracking to infill missing detections and by eschewing simple confidence thresholding in favor of using the auxiliary 2D detection head to filter 3D predictions. Finally, to enable the backbone to learn directly from the unlabeled data itself, we introduce an object-query conditioned masked reconstruction objective. Our framework demonstrates remarkable performance improvement on large-scale autonomous driving datasets nuScenes and nuPlan.
+
+# 1. Introduction
+
+Camera-driven 3D object detection [17, 28, 46, 67] has seen remarkable improvement in recent years, even achieving close to LiDAR-based 3D detection [56, 78, 84] performance. Improvements in 2D backbones [15, 41], advancements in query-driven 3D detection [28, 34, 67], and emphasis on temporal modeling of objects [16, 30, 36, 46] have fueled these detectors, making camera-only pipelines an indispensable component of an autonomous driving stack due to their cost efficiency and semantically accurate predictions. However, these detectors heavily depend on labor-intensive human annotations of thousands or millions of
+
+![](images/fb6dbd9a9b634961915c9d8ab871ebc8acd84d774f4b27ed162bd167508fc20b.jpg)  
+Figure 1. Our proposed semi-supervised learning framework for temporal camera-driven 3D detection substantially improves over labeled-only training and a strong pseudo-labeling baseline.
+
+frames [7, 8, 60], which hinders their widespread deployment to new cities and sensor configurations. For truly scalable development of autonomous driving, camera-driven 3D detectors must directly leverage unlabeled data for training in a semi-supervised pipeline.
+
+While prior work has explored semi-supervised learning for 2D and 3D detection in autonomous driving, the temporal aspect of camera-driven 3D object detection remains under-explored. Autonomous vehicles inherently capture RGB video sequences during operation, and since depth estimation is the main bottleneck for camera-based 3D detectors [43, 69], temporal RGB data offers valuable priors about the 3D world. To advance semi-supervised learning in this domain, it is crucial to fully leverage the temporal dimension of the problem. For instance, DPL [88] proposes a strong semi-supervised learning (SSL) pipeline for 3D object detection. However, they build on MonoFlex [91], a single-image 3D detector that does not use video, which places an upper bound on the performance the 3D detector can achieve. MVC-MonoDet [29] does leverage images from other timesteps during training for photometric con
+
+sistency loss, but it similarly only explores single-image 3D detectors. Other work [44, 48] use an additional LiDAR sensor to generate stronger pseudo-labels, but the requirement of an expensive LiDAR sensor hinders the scalability of this approach.
+
+In this work, we propose a novel SSL framework that focuses on performant, temporal 3D detectors, fully exploits the video sequence for semi-supervised learning, and works solely with cost-effective RGB cameras. Our method incorporates both pseudo-labeling on unlabeled data as well as a self-supervised loss term directly on the RGB images. To derive accurate pseudo-labels, we focus squarely on the problem of 3D localization, the most significant challenge of camera-driven 3D detectors. Observing that pseudolabeling errors are significantly higher for regions behind the ego-vehicle compared to regions ahead, we propose to train a single detector both on forward-running sequences as well as the reversed backward-running sequences. Without additional training costs, the detector, conditioned on consecutive timestamps, can effectively handle both directions. Using this detector for pseudo-labeling unlabeled data both forwards and backwards in time, we observe a remarkable performance improvement.
+
+We further improve our temporal pseudo-labeling pipeline by incorporating a lightweight tracking mechanism that fills in missing detections for tracked objects. Since tracking and pseudo-labeling heavily depend on the chosen quality metric for thresholding, we eschew standard 3D detection confidence thresholding in favor of extending a 2D-3D consistency metric developed by DetMatch [46]. More specifically, DetMatch leverages separate 2D and 3D detectors trained on RGB and LiDAR, respectively, and pseudolabels both modalities by matching 2D and 3D detections. Observing that camera-driven 3D detection is fundamentally a 2D detection task, with 3D localization and attribute prediction [68, 94], we leverage the auxiliary 2D detection head as our separate "2D detector" and match the temporal 3D predictions with the same model's 2D predictions. We find that such 2D-3D consistency, even within the same model, significantly improves pseudo-label quality.
+
+Finally, to allow our model to learn directly from the unlabeled data itself, we include a masked reconstruction task on the RGB images. However, directly adding the masked autoencoder (MAE) head worsens 3D detection performance due to conflict between the 3D detection and reconstruction tasks. Instead, we condition the masked tokens on the 3D detection object queries. Intuitively, the 3D object queries not only encode information about the scene and objects from this timestep, but also from previous timesteps, facilitating the reconstruction task. Conversely, to solve the reconstruction task, the object queries are encouraged to focus on scene elements for both current and past timesteps, which is complementary to the tempo
+
+ral 3D object detection task. We find that this module further boosts SSL performance. By fully exploiting temporal priors for pseudo-labeling and self-supervision, our SSL pipeline demonstrates significant improvements using unlabeled data.
+
+Our main contributions are as follows:
+
+- We propose a novel SSL pipeline focusing on improving the performance of strong temporal 3D detectors.  
+- Our pipeline leverages forward-backward training and assembling, 3D tracking, 2D-3D Hungarian Matching for pseudo-labeling, and an object-query conditioned masked reconstruction objective.  
+- We evaluate our method on nuScenes and nuPlan driving datasets, demonstrating improvement over a strong pseudo-labeling baseline as well as prior work.  
+- We extensively ablate each component of our pipeline.
+
+# 2. Related Work
+
+# 2.1. Camera-Driven 3D Object Detection
+
+Earlier works in RGB-only 3D object detection focus on the single-view problem, predicting 3D boxes directly from CNN feature maps [5, 6, 12, 39, 45, 51, 68, 75, 94]. Later works leverage CAD models [40], formulate 3D box prediction first as keypoint regression [27, 90], leverage depth predictions before performing 3D detection on the point cloud [14, 70, 71, 74, 85], or focus on disentangling 3D box attributes [57, 68]. Many works, especially those focusing on the multi-camera setup, extract features and detect directly in 3D space. A line of work follows the Lift-Splat-Shoot (LSS) [49] framework of predicting a probability distribution over depths, then processing the depth probability-weighted, outprojected image features in BEV [17, 24, 53]. Follow-up works have improved the efficiency of BEV pooling [25, 42] and introduced depth supervision for more accurate out-projection. Another line of work follows DETR3D [72] in instantiating 3D queries that attend to each other and image features before making 3D box predictions [11, 18, 28, 35]. While most of these methods effectively handle the ill-posed problem of single-image 3D detection, their lack of temporal information upper bounds their absolute performance in large-scale driving datasets [7, 8, 60].
+
+Recognizing that autonomous vehicles naturally capture video, follow-up works improve on the temporal aspect of camera-driven 3D detection. BEVFormer [28] and followup work [33, 79] use queries associated with BEV locations which attend to the image as well as past BEV features. BEVDet4D [16] proposes a BEV warping operation to fuse consecutive timesteps. BEVStereo [23] demonstrates the utility of stereo matching for depth prediction in 3D detection, and SOLOFusion [46] extends this work to incorporate long-term feature fusion. One line of
+
+![](images/1cc82c73535879be44a668ac925c12fba265126c0e70a895d94074096e16907d.jpg)  
+Figure 2. Our Proposed Semi-Supervised Learning Framework. Observing that temporal 3D object detectors consistently perform worse for objects ahead of it compared to objects behind it, we propose training a temporal 3D detector jointly on forwards-running and reversed backwards-running RGB sequences. To pseudo-label, we ensemble forwards & backwards predictions on unlabeled data, leverage 2D-3D hungarian matching to derive an accurate and 2D-consistent set of predictions, and perform 3D object tracking and label propagation. More details are in the text.
+
+work focuses specifically on temporal processing with object queries. PETRv2 [36] and Sparse4D [30] fuses multistep features into object queries through attention. Follow up works StreamPETR [73], Sparse4Dv2 [31], and Sparse4Dv3 [32] focus on recurrent feature propagation over time, dramatically accelerating inference speed. In this work, we use StreamPETR as our base model for its efficiency and strong performance, reducing the significant annotation costs of training a camera-based 3D detector.
+
+# 2.2. Semi-Supervised Learning
+
+To derive training signals from unlabeled data, SSL methods either enforce consistency between augmented variants of a single input [1, 19, 52, 55, 63] or leverage a network trained on a small amount of labeled data to pseudo-label the unlabeled data [2, 3, 20, 58, 62, 86]. While most semisupervised methods work with image classification, many recent methods have examined this problem for 2D detection and 3D LiDAR-based detection.
+
+In 2D detection, STAC [59] pre-trains a model on a small amount of labeled data, pseudo-labels offline, then trains the detector on the entire dataset. Instant-Teacher [93] examines augmentation strategies [4, 87], other works [22, 76, 77] modify the quality score of predictions to threshold on for pseudo labels, and a line of work focuses on exponential moving average (EMA) for predictions or the pseudo-labeler [37, 61, 82].
+
+Many works have extended SSL to 3D detection on point clouds. SESS [92] focuses on consistency over strong-weak
+
+augmentation, 3D IoUMatch [65] improves the thresholding metric for pseudo-labeling with an IoU score, ProficientTeachers [83] improves pseudo-labels by ensembling predictions from multiple LiDAR views, and PseudoAugment [21] proposes pseudo-labeling driven augmentation. Leveraging the temporal, 3D nature of the LiDAR-based detection setting, many works focus on offline labeling and detection [9, 26, 50, 66]. Notably [50] uses extensive test-time augmentation and LiDAR point cloud aggregation to derive pseudo-labels that approach human annotation quality. While our work is similar in leveraging multiple timesteps over a driving sequence, effective pseudolabeling in camera-driven 3D detection is a more difficult challenge due to the lack of reliable 3D signals.
+
+# 2.3. SSL for Camera-Driven 3D Detection
+
+Semi-supervised learning in camera-driven 3D detection is comparatively less explored. Mix-Teaching [81] uses a teacher network to assemble a database of background images and high-confidence object instances and trains a student network on mixed images. Other works seek additional sources of supervision such as LiDAR [44, 48, 89]. While demonstrating strong performance, these works rely on LiDAR to provide precise 3D cues that, in many cases, obviate the 3D location of an object. DPL [88] explicitly decouples the 3D and 2D attributes of pseudo-labels, and devises a homography estimation method for determining the quality of the 3D attributes. While DPL additionally identifies incorrect depth as a major issue in pseudo-labeling, their depth
+
+gradient projection method necessitates that the 3D detector separates 3D box prediction into attribute prediction and depth estimation, which is not the case for most query and BEV based methods. Furthermore, DPL is a single-view method, under-utilizing video frames naturally present in autonomous driving. MVC-MonoDet [29] proposes to use a photometric loss between consecutive frames as a depth supervision signal for objects. While demonstrating performance improvement, the base detector is a single-frame model. To the best of our knowledge, this is the first work to examine SSL in the context of temporal, camera-driven 3D object detection.
+
+# 3. Method
+
+Figure 2 provides an overview of our pseudo-labeling pipeline. In Section 3.1 we first describe the SSL problem setting and also provide an overview of our base 3D detector StreamPETR [67]. We then detail our forward-backward pseudo-labeling algorithm in Section 3.2, provide details on the 2D-3D Hungarian Matching in Section 3.3, and propose pseudo-label refinement via tracking in Section 3.4. Finally, we introduce our object query-conditioned masked reconstruction pipeline in Section 3.5
+
+# 3.1. Preliminaries
+
+Task Overview. In semi-supervised learning, we have a small dataset of labeled samples  $\mathcal{D}_l = \{(x_i^l,y_i^l)\}_{i = 1}^{N_l}$  and a larger dataset of unlabeled samples  $\mathcal{D}_u = \{x_i^u\}_{i = 1}^{N_u}$ , where  $N_{l} < N_{u}$ . In the temporal, camera-driven 3D detection task, the input  $x$  consists of RGB images at a single timestep  $I\in \mathbb{R}^{K\times H\times W\times 3}$ , where  $K$  is the number of cameras mounted on the ego-vehicle, the camera intrinsics, and the extrinsics  $e_t$  from an IMU or GPU sensor. The label  $y$  is a set of bounding boxes  $b\in \mathbb{R}^{M\times 9 + C}$ , where each box has 3D location, dimensions, rotation, BEV velocity, and a class label between 1 and  $C$ . The goal is to leverage a small amount of labeled data and a large amount of unlabeled data to scalably improve 3D detection performance.
+
+Overview of StreamPETR. A strong but efficient 3D detector, StreamPETR [67] propagates a set of object queries through the driving sequence, aggregating image features from each timestep to them before predicting 3D boxes. More specifically, StreamPETR consists of a CNN backbone and a custom DETR [10] head. At each timestep, given images  $I_{t}$ , the backbone extracts features  $f_{t} = \mathrm{CNN}(I_{t})$ . Then, the custom DETR head processes both image features from the current timestep  $f_{t}$ , object queries from the previous timestep  $q_{t-1}$ , and motion attributes between the timesteps (ego-movement, predicted object velocity, time difference) and yields refined object queries for the current timestep  $q_{t} = \mathrm{DETR}(f_{t}, q_{t-1})$ . Finally, an MLP predicts box parameters from the object queries  $\hat{y}_{t} = \mathrm{MLP}(y_{t})$ . StreamPETR achieves efficiency by prop
+
+![](images/4e68002a1cd0c8c7675ee0625fe8a55e7279a57dc793fc28b633e463f3561de5.jpg)  
+Figure 3. Histogram of 3D Detection Confidence Preserved After Hungarian Matching. The 2D-3D hungarian matching preserves a large number of low-confidence, yet accurate 3D detections that would have otherwise been discarded by a 0.4 pseudolabeling confidence threshold.
+
+agating temporal information exclusively through object queries rather than through past feature maps.
+
+# 3.2. Forward-Backward Pseudo-Labeling
+
+The dominant approach in semi-supervised learning is pseudo-labeling. However, for temporal 3D detection, we find that pseudo-labels for objects in front of the vehicle are consistently worse than those behind. This is because as the car moves forward and passes objects, the temporal detector has observed objects that are now behind it for a longer period of time and can draw from a wider multi-view stereo baseline for more precise 3D localization. Furthermore, this observation is symmetric over time - if the driving sequence is seen backwards in time, the detector would have observed objects originally in front of it for longer, potentially allowing it to better pseudo-label objects in front of it as well.
+
+Leveraging this insight, we propose to jointly train a detector on both forward-running and reversed backward-running sequences. As the temporal DETR head in StreamPETR takes as input the timestamp difference between consecutive timesteps, the detector can adaptively handle both temporal directions. After training the detector on the labeled data, we pseudo-label the unlabeled set by ensembling predictions from both a forward and backwards pass of the driving sequences. More specifically, we directly combine backward detections ahead of the ego-car and forward detections behind it. We find this intuitive method is enough to substantially improve performance — as shown in Figure 4, this achieves accurate pseudo-labels both in front and behind the vehicle.
+
+The detector is able to achieve this level of performance by effectively leveraging privileged information. The detector's performance on objects ahead of it — which it
+
+<table><tr><td># Labeled</td><td>Method</td><td>mAP ↑</td><td>NDS ↑</td><td>mATE ↓</td><td>mASE ↓</td><td>mAOE ↓</td><td>mAVE ↓</td><td>mAAE ↓</td></tr><tr><td rowspan="3">800</td><td>Labeled Only</td><td>0.151</td><td>0.234</td><td>0.924</td><td>0.177</td><td>1.132</td><td>1.263</td><td>0.317</td></tr><tr><td>Pseudo-Labeling</td><td>0.187</td><td>0.249</td><td>0.916</td><td>0.171</td><td>1.108</td><td>1.192</td><td>0.354</td></tr><tr><td>Ours</td><td>0.222</td><td>0.280</td><td>0.851</td><td>0.160</td><td>1.115</td><td>1.078</td><td>0.294</td></tr><tr><td rowspan="3">2000</td><td>Labeled Only</td><td>0.219</td><td>0.293</td><td>0.849</td><td>0.156</td><td>0.936</td><td>0.936</td><td>0.284</td></tr><tr><td>Pseudo-Labeling</td><td>0.269</td><td>0.314</td><td>0.803</td><td>0.151</td><td>0.947</td><td>1.051</td><td>0.300</td></tr><tr><td>Ours</td><td>0.271</td><td>0.330</td><td>0.810</td><td>0.150</td><td>0.934</td><td>0.868</td><td>0.292</td></tr><tr><td rowspan="3">4000</td><td>Labeled Only</td><td>0.291</td><td>0.384</td><td>0.807</td><td>0.140</td><td>0.765</td><td>0.693</td><td>0.210</td></tr><tr><td>Pseudo-Labeling</td><td>0.304</td><td>0.405</td><td>0.806</td><td>0.137</td><td>0.726</td><td>0.600</td><td>0.201</td></tr><tr><td>Ours</td><td>0.331</td><td>0.410</td><td>0.778</td><td>0.137</td><td>0.782</td><td>0.672</td><td>0.187</td></tr></table>
+
+Table 1. Comparison of methods on the nuPlan dataset [8] with different labeled sample sizes. Our framework achieves better 3D localization due to more accurate pseudo-labels.
+
+achieved by moving backwards in time — will always be ahead of the detector's forward performance on those regions. This low-cost addition substantially improves the performance of the final trained model.
+
+# 3.3. 2D-3D Hungarian Matching
+
+While generating pseudo labels by thresholding on detection confidence can achieve good performance [38, 47], we draw inspiration from DetMatch's Hungarian Matching-based pseudo-labeling to improve pseudo-label quality for free. DetMatch proposes to match 2D and 3D detections from separate RGB and LiDAR models, respectively, and threshold on their matching cost instead. While DetMatch had cited agreement between disparate models and modalities as the cause of this method's success, we find that using even 2D and 3D detections from the same model and modality can improve performance. More specifically, StreamPETR is equipped with an auxiliary 2D detection head for additional training-time supervision. We find that in terms of 2D detection performance, the 2D head's predictions achieve higher mAP compared to the projections of the 3D head (53.8 AP@50 vs 40.5 AP@50). Motivated by this discrepancy, we perform Hungarian Matching between these 2D and 3D detections, minimizing focal loss, GIoU [54], and 2D box parameter difference. Thresholding on the matching cost, we see a boost in pseudo-label quality, and this method retains low-confidence but accurate 3D detections that would otherwise have been discarded, as shown in Figure 3. We emphasize that this addition imposes no additional cost to training or inference, and it adds negligible runtime to the pseudo-labeling procedure.
+
+# 3.4. 3D Tracking and Label Propagation
+
+While the detector is able to maintain most objects through time, in the presence of uncertainty, distance, or significant occlusion, we see object detections disappear between frames. Such missing detections negatively influence the final trained model and exacerbates the problem of object impermanence. To address this issue, we pro
+
+pose a straightforward but effective object tracking-based fix. More specifically, we use a predicted velocity-based tracking pipeline [84], where each tracklet from the previous timestep is matched with the current prediction moved backwards its predicted velocity. Notably, unlike LiDAR where object locations, and hence velocities, are more 3D accurate, camera-based predictions have more significant per-frame velocity errors. To alleviate this, we maintain a velocity of each tracklet which we set as the exponential moving average (EMA) of its associated predictions' center location changes over time. Then, to match past tracklets and current detections, we use velocity estimates to move tracklets forward and detections backwards a half-timestep. This robustly handles static initialization and uncertain velocity predictions. We use a greedy, multi-object, distance-based tracker [84] for its good 3D performance.
+
+# 3.5. Object Query-Conditioned Masked Reconstruction
+
+In addition to our pseudo-labeling framework, we also enable the network to learn directly from unlabeled samples. More specifically, we formulate an object query-conditioned masked reconstruction loss. First, we uniformly randomly mask patches in the input images and process it with a CNN once more:
+
+$$
+f _ {t} ^ {\text {m a s k}} = \operatorname {C N N} (M \odot I _ {t}) \tag {1}
+$$
+
+At this stage,  $f_{t}^{mask}$  encodes information about the visible part of the input image. While prior work directly input  $f_{t}^{mask}$  into a masked decoder for pre-training, we find that doing so significantly hurts the performance of our 3D detector. The network focuses on optimizing the auxiliary loss at the expense of the main task loss. To more explicitly tie the detector to the reconstruction, we update the masked features  $f_{t}^{mask}$  by attending onto the object queries output from the temporal DETR head  $q_{t}$ . More specifically:
+
+$$
+\tilde {f} _ {t} ^ {\text {m a s k}} = \operatorname {T r a n s f o r m e r D e c o d e r} \left(f _ {t} ^ {\text {m a s k}}, q _ {t}, q _ {t}\right) \tag {2}
+$$
+
+<table><tr><td># Labeled</td><td>Method</td><td>mAP ↑</td><td>NDS ↑</td><td>mATE ↓</td><td>mASE ↓</td><td>mAOE ↓</td><td>mAVE ↓</td><td>mAAE ↓</td></tr><tr><td rowspan="3">800</td><td>Labeled Only</td><td>0.103</td><td>0.191</td><td>0.953</td><td>0.352</td><td>1.299</td><td>1.359</td><td>0.299</td></tr><tr><td>UniPAD + Pseudo.</td><td>0.116</td><td>0.198</td><td>0.954</td><td>0.359</td><td>1.216</td><td>1.075</td><td>0.286</td></tr><tr><td>Ours</td><td>0.137</td><td>0.221</td><td>0.940</td><td>0.340</td><td>1.339</td><td>0.940</td><td>0.258</td></tr><tr><td rowspan="3">2000</td><td>Labeled Only</td><td>0.157</td><td>0.242</td><td>0.894</td><td>0.318</td><td>0.988</td><td>0.916</td><td>0.250</td></tr><tr><td>UniPAD + Pseudo.</td><td>0.170</td><td>0.282</td><td>0.896</td><td>0.325</td><td>0.894</td><td>0.685</td><td>0.230</td></tr><tr><td>Ours</td><td>0.194</td><td>0.293</td><td>0.902</td><td>0.315</td><td>0.932</td><td>0.664</td><td>0.226</td></tr></table>
+
+Table 2. Comparison of methods on the nuScenes dataset [7]. Our framework significantly improves over both the Labeled-Only baseline as well as UniPAD [80].  
+
+<table><tr><td># Labeled</td><td>Method</td><td>mAP ↑</td><td>Car</td><td>Tru.</td><td>Bus</td><td>Trai.</td><td>Con.</td><td>Bic.</td><td>Mot.</td><td>Ped.</td><td>Traf.</td><td>Bar.</td></tr><tr><td rowspan="3">800</td><td>Labeled Only</td><td>0.103</td><td>0.247</td><td>0.054</td><td>0.048</td><td>0.018</td><td>0.003</td><td>0.035</td><td>0.019</td><td>0.116</td><td>0.278</td><td>0.208</td></tr><tr><td>UniPAD + Pseudo-Lab</td><td>0.116</td><td>0.267</td><td>0.061</td><td>0.026</td><td>0.016</td><td>0.007</td><td>0.040</td><td>0.013</td><td>0.138</td><td>0.318</td><td>0.270</td></tr><tr><td>Ours</td><td>0.137</td><td>0.284</td><td>0.060</td><td>0.075</td><td>0.023</td><td>0.008</td><td>0.074</td><td>0.041</td><td>0.182</td><td>0.351</td><td>0.271</td></tr><tr><td rowspan="3">2000</td><td>Labeled Only</td><td>0.157</td><td>0.346</td><td>0.091</td><td>0.124</td><td>0.020</td><td>0.007</td><td>0.085</td><td>0.080</td><td>0.184</td><td>0.336</td><td>0.299</td></tr><tr><td>UniPAD + Pseudo-Lab</td><td>0.170</td><td>0.359</td><td>0.098</td><td>0.089</td><td>0.030</td><td>0.005</td><td>0.102</td><td>0.079</td><td>0.188</td><td>0.382</td><td>0.367</td></tr><tr><td>Ours</td><td>0.194</td><td>0.384</td><td>0.101</td><td>0.134</td><td>0.030</td><td>0.006</td><td>0.137</td><td>0.122</td><td>0.239</td><td>0.420</td><td>0.371</td></tr></table>
+
+Table 3. mAP of methods across 10 classes on the nuScenes dataset [7]. Our method consistently outperforms prior work over both easy and difficult classes.
+
+where TransformerDecoder  $(f_{t}^{mask}, q_{t}, q_{t})$  performs self-attention between the masked features  $f_{t}^{mask}$  and then performs cross-attention, pulling information from  $q_{t}$  to refine  $f_{t}^{mask}$ . By conditioning the masked reconstruction on the predicted object queries, this enables gradient flow from the reconstruction loss to influence the temporal DETR head directly. To minimize the reconstruction loss, the object queries need to retain information about scene elements from both current and past timesteps, which is complementary to the main detection task. We find that this self-supervised objective improves performance in conjunction with our pseudo-labeling method.
+
+# 4. Experiments
+
+# 4.1. Datasets and Evaluation Metrics
+
+The nuScenes Dataset. nuScenes [7] includes 1000 scenes split into 700, 150, and 150 sequence for training, validation, and online testing. Each sequence is 20s long and is annotated at  $2\mathrm{Hz}$ , resulting in 28130 total training frames. The ego-vehicle has 6 high-resolution  $900 \times 1600$  cameras which cover the entire  $360^{\circ}$  field-of-view. The annotation covers 10 classes: car, truck, bus, trailer, construction vehicle, pedestrian, motorcycle, bicycle, barrier, and traffic cone, and methods are evaluated with mean Average Precision (mAP), Average Translation Error (ATE), Average Scale Error (ASE), Average Orientation Error (AOE), Average Velocity Error (AVE), Average Attribute Error (AAE), and a combined metric Nuscenes Detection Score (NDS). For semi-supervised learning, we split the training set into either 800 or 2000 labeled frames, and take the remainder as the unlabeled set. Note that as we work in the temporal 3D detection setting, we sample frames at the sequence level in
+
+chunks of 40 consecutive frames.
+
+The nuPlan Dataset. nuPlan [8] is a large-scale planning dataset that releases sensor data (RGB videos) and 3D box annotations for 120 hours of driving. This dataset contains 1065 driving logs, which totals 590,499 frames across four regions — Las Vegas with 455k frames, Boston with 64k, Pittsburgh with 51k, and Singapore with 19k. Each frame contains 8 high-resolution RGB images at  $1080 \times 1920$  resolution, as well as 3D bounding box labels. We use the most common car and pedestrian classes on this dataset. We choose this dataset to demonstrate the scalability of our method leveraging a large amount of unlabeled data.
+
+In our work, we leverage 800, 2000, or 4000 labeled frames, keeping the rest as unlabeled data to learn from. Considering the uneven distribution of frames from each city, we evenly split the labeled data frames across the four cities. Notably, we select sequences at the log level, which, on average, has 600 frames (5 minutes) of driving data. We do this to mimic realistic data collection scenarios where annotators label 3D boxes continuously through time. We use the same metrics as in nuScenes.
+
+# 4.2. Implementation Details
+
+We develop our SSL pipeline on the performant temporal 3D detector StreamPETR [67]. For the backbone, we use the ConvNeXt-S [41] backbone with 50M parameters pretrained by SparK [64]. As SparK pretrains the backbone on ImageNet-1k [13] for masked reconstruction, we adopt its pretrained decoder as our masked reconstruction head as well, affording the backbone a continuous transition in supervision. We split our training two stages. First, the detector is trained on the small amount of labeled data until convergence. Then, we leverage our pseudo-labeling pipeline
+
+<table><tr><td></td><td>Method</td><td>mAP ↑</td><td>NDS ↑</td><td>mATE ↓</td></tr><tr><td>(a)</td><td>Labeled-Only</td><td>0.155</td><td>0.232</td><td>0.938</td></tr><tr><td>(b)</td><td>+ Pseudo-Labeling</td><td>0.182</td><td>0.247</td><td>0.924</td></tr><tr><td>(c)</td><td>+ Fw-Bw</td><td>0.208</td><td>0.267</td><td>0.855</td></tr><tr><td>(d)</td><td>+ Masked Recon</td><td>0.209</td><td>0.265</td><td>0.862</td></tr><tr><td>(e)</td><td>+ Masked Recon &amp; Query Cond.</td><td>0.209</td><td>0.271</td><td>0.847</td></tr><tr><td>(f)</td><td>+ 3D Tracking</td><td>0.215</td><td>0.275</td><td>0.848</td></tr><tr><td>(g)</td><td>+ Hung. Matching</td><td>0.219</td><td>0.278</td><td>0.850</td></tr></table>
+
+Table 4. Ablation study of the major components of our framework. Results are on nuPlan with 800 labeled and 60k unlabeled samples.
+
+to annotate the unlabeled data offline. Finally, we continue training our network on both the labeled and unlabeled data, evenly sampling between them. For our final models in the second stage, we disable the forwards-backwards flipping to allow the model to focus solely on the deployment setting. We use a masking ratio of 0.3. Additional implementation details can be found in the supplementary.
+
+# 4.3. Results on nuPlan
+
+We present results on the large-scale nuPlan dataset in Table 1. As we are the first to address the problem of SSL for temporal 3D object detection, we develop a straightforward but strong pseudo-labeling baseline based on confidence thresholding. We note that this baseline already significantly improves performance over the labeled-only baseline. Our proposed pipeline, by generating higher-quality pseudo-labels and leveraging a self-supervised objective, further improves results in for all # of labeled samples. The performance gain is especially notable for the low-resource setting of just 800 labeled samples, where we see a substantial  $+3.5$  mAP and  $+3.1$  NDS.
+
+# 4.4. Results on nuScenes
+
+We also evaluate our pipeline on the 10 detection classes in the nuScenes dataset. For comparison, we include UniPAD [80], a self-supervised pre-training method designed for nuScenes. Specifically, UniPAD builds on the camera-based 3D detector [24], pre-training its 2D backbone using an RGB and depth rendering loss. Although this approach leverages privileged information (e.g., depth from LiDAR), it does not rely on human annotations during the pre-training phase. To enhance this baseline, we further train UniPAD on the limited labeled dataset, use it to pseudo-label the unlabeled data, and then continue training. We note that UniPAD also uses the ConvNeXt-S [41] initially pre-trained by SparK [64].
+
+The results are in Table 2. While both UniPAD and our method significantly improve over the labeled-only baseline, our pipeline consistently demonstrates stronger per
+
+formance. We further examine mAP over each of the 10 classes in nuScenes in Table 3 and observe a similar trend. While all methods struggle on rare classes like trailer and construction vehicle, our method significantly improves on common classes (car and pedestrian) as well as on classes that are difficult to localize in 3D (bicycle, motorcycle).
+
+# 4.5. Ablations and Analysis
+
+# 4.5.1. Ablation of Components
+
+We carefully ablate the major components of our framework in Table 4. In this table, we focus on three metrics - mAP, which captures overall detection performance, NDS, which balances detection with attribute prediction, and mATE, which examines localization of the object center. Starting with the Labeled-Only baseline (a), adding pseudo-labeling (b) improves mAP substantially, but mATE does not improve significantly. This is due to pseudo-labeling expanding the semantic boundary of the classes and enabling the model to detect previously uncertain objects. Despite this, the 3D localization of such objects remains poor due to the suboptimal 3D localization of the pseudo-labels themselves. Adding our forwards-backwards ensembling approach (c), however, substantially boosts mATE in addition to mAP and NDS. By allowing the model to adopt a more diverse multiview stereo baseline, the resulting pseudo-labels have more precise 3D center estimation.
+
+We then add the self-supervised objective masked reconstruction loss (d) as an independent decoder head as is done in SparK [64]. We find that this hurts performance due to the backbone alone handling reconstruction in addition to 3D detection. However, by conditioning the masked reconstruction on object queries predicted from the detection head (e), mATE improves further. This demonstrates that by looping in the detection head, the reconstruction task is now complementary to 3D detection. Adding 3D tracking (f) further improves performance by ensuring pseudo-labels remain more consistent over time, and replacing confidence thresholding with the cost-free Hungarian Matching (g) further improves both mAP and NDS. We hypothesize that tracking and Hungarian Matching improve mAP as opposed to mATE because these modules mainly focus on reducing false positives and false negatives as opposed to refining the 3D location of pseudo-labels.
+
+# 4.5.2. Qualitative Analysis of Pseudo-Labels
+
+We also show qualitative results of our pseudo-labeling algorithm with 800 labeled samples on nuPlan in Figure 4. Our framework more consistently captures difficult objects — those ahead of the vehicle and objects at a far depth. The more precise and consistent pseudo-labels in turn improve performance of the final trained model. Additional visualizations on pseudo-labels and reconstruction can be found in the supplementary.
+
+![](images/9cd2a9471cae73071e59ba7aed4e0263199cd6ea2183b709f30dd57903bc2713.jpg)  
+Figure 4. Qualitative results on pseudo-labeling. We visualize pseudo labels from confidence thresholding in orange and our framework in blue. Our pseudo labels capture distant objects with 2D-3D hungarian matching, achieve better performance in front of the vehicle due to forward-backward ensembling, and maintains persistency of past objects through tracking.
+
+# 5. Conclusion
+
+In this paper, we present a novel semi-supervised learning pipeline for temporal 3D object detection, designed to fully leverage the temporal dynamics of RGB video data. Our approach addresses the challenges of 3D localization in camera-driven detectors by introducing forward-backward ensembling for pseudo-labeling, leveraging 2D-3D Hungarian Matching for consistency, and enhancing self-supervised learning with an object-query
+
+conditioned masked reconstruction task. Through extensive evaluation on nuScenes and nuPlan datasets, we demonstrate that our method achieves significant performance gains over a strong pseudo-labeling baseline, highlighting the value of temporal modeling in semi-supervised 3D detection. Our framework paves the way for scalable, cost-effective deployment of camera-based 3D detection systems, leveraging easy-to-collect unlabeled data to develop accurate 3D detectors.
+
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CVPR/2025/LeviTor_ 3D Trajectory Oriented Image-to-Video Synthesis/full.md

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+# LeviTor: 3D Trajectory Oriented Image-to-Video Synthesis
+
+Hanlin Wang $^{1,2}$   
+Ka Leong Cheng $^{4,2}$
+
+Hao Ouyang² Qifeng Chen⁴
+
+Qiuyu Wang2 Yujun Shen2
+
+Wen Wang $^{3,2}$ , Limin Wang $^{1,\dagger}$
+
+$^{1}$ State Key Laboratory for Novel Software Technology, Nanjing University
+
+$^{2}$ Ant Group  $^{3}$ Zhejiang University  $^{4}$ The Hong Kong University of Science and Technology
+
+![](images/dc7ab3abe49cad1863b59244e23bb88169ff7f4749615d149bae7fdb3ee4f40b.jpg)  
+Figure 1. LeviTor is capable of generating videos with controlled occlusion, better depth changes, and complex 3D orbiting movement based on user inputs. Given an initial frame, users can easily draw 3D trajectory using our inference pipeline to represent their desired movements for designated area. We highly recommend viewing the supplementary materials for detailed video demonstrations.
+
+# Abstract
+
+The intuitive nature of drag-based interaction has led to its growing adoption for controlling object trajectories in image-to-video synthesis. Still, existing methods that perform dragging in the 2D space usually face ambiguity when handling out-of-plane movements. In this work, we augment the interaction with a new dimension, i.e., the depth dimension, such that users are allowed to assign a relative depth for each point on the trajectory. That way, our new interaction paradigm not only inherits the convenience from 2D dragging, but facilitates trajectory control in the 3D space, broadening the scope of creativity. We propose a pioneering method for 3D trajectory control in image-to-video synthesis by abstracting object masks
+
+into a few cluster points. These points, accompanied by the depth information and the instance information, are finally fed into a video diffusion model as the control signal. Extensive experiments validate the effectiveness of our approach, dubbed LeviTor, in precisely manipulating the object movements when producing photo-realistic videos from static images. Our code is available at: https://github.com/ant-research/LeviTor.
+
+# 1. Introduction
+
+Controlling object trajectories in video generation [49, 51, 58, 66] is a fundamental task with wide-ranging applications in computer graphics, virtual reality, and interactive media. Precise trajectory control allows for generation
+
+of dynamic scenes where objects move in desired paths, enabling creators to create realistic and compelling visual content. Such control is crucial for tasks like animating characters in a virtual environment, simulating physical phenomena, and developing advanced visual effects that require objects to interact seamlessly within a scene.
+
+Despite its importance, controlling object trajectories in video synthesis presents significant challenges. Traditional methods [51, 58, 66] often rely on 2D trajectory inputs drawn directly on images. While these approaches allow for motion representation to some extent, they inherently suffer from ambiguity and complexities associated with interpreting 2D motions in 3D space. Consider the example of animating a hot air balloon flowing over a building as illustrated in Fig. 1. A 2D trajectory drawn on the image cannot distinguish whether the balloon should pass in front of or behind the building. This ambiguity arises because a single 2D path can correspond to multiple 3D trajectories due to the lack of 3D information, making it insufficient for precise control over object movements in a 3D space. However, extracting accurate 3D trajectories poses additional difficulties, especially in scenes with occlusions or complex interactions between objects. For users, inputting valid 3D trajectories is also non-trivial. It often demands specialized knowledge and tools to define object paths accurately within a 3D space, which can be a barrier for artists and non-expert users aiming to create video content.
+
+To address these challenges, we propose LeviTor, a novel model that fine-tunes pre-trained video generation models to incorporate an efficient and effective 3D trajectory control mechanism. Our approach introduces an innovative representation of control signal by combining depth information with K-means clustered points of object masks in video. Such control signal can clearly indicate the occlusion and depth changes between objects through the aggregation or separation of clustered points and their depth. This fusion also captures essential 3D attributes of objects' trajectory without the need for explicit 3D trajectory estimation, thus simplifying the modeling of complex object motions and interactions. For training, we utilize the recently released high-quality Video Object Segmentation (VOS) dataset from SAM2 [37], which provides rich annotations conducive to our method. By integrating depth cues with clustered points, our representation effectively encodes the object's spatial movements and depth variations over time. This method not only enhances the model's ability to interpret and generate accurate 3D motions but also mitigates issues related to occlusions and depth ambiguities.
+
+We also design a user-friendly inference pipeline that lowers the barrier for users to input 3D trajectories. Users can simply draw trajectories on 2D images and adjust point depths interactively, which the system then interprets as 3D paths for object movements. This approach streamlines
+
+the process, making it accessible to users without extensive technical expertise in 3D modeling or animation.
+
+Our method demonstrates superior performance both quantitatively and qualitatively compared to existing approaches. We achieve accurate 3D trajectory control in image-to-video synthesis task where previous baselines fail. In summary, our contributions are as follows: We introduce LeviTor, a novel method for controlling 3D object trajectories in video synthesis by combining depth information with K-means clustered points without the need for explicit 3D trajectory tracking. We leverage the high-quality SA-V dataset for training, effectively capturing complex object motions and interactions in diverse scenes. We develop a user-friendly inference pipeline that simplifies the input of 3D trajectories, making it accessible to a broader range of users. To the best of our knowledge, this work is the first to introduce 3D object trajectory control in image-to-video synthesis, paving the way for more advanced and accessible video generation techniques.
+
+# 2. Related Work
+
+# 2.1. Video Diffusion Models
+
+Diffusion models [17, 41, 42] have demonstrated unprecedented power in video generation. Video Diffusion Models (VDMs) [18] are broadly categorized into Text-to-Video (T2V) and Image-to-Video (I2V) frameworks, aiming to generate video samples from text prompts or image prompts. T2V generation [5, 6, 8, 12, 13, 19, 24, 33, 40, 45, 50, 56] has been extensively studied in recent years, introducing text descriptions to control the content of video generation semantically. Previous works [6, 13, 15, 46, 48, 65] incorporate temporal layers into large pretrained text-to-image (T2I) diffusion models [38]. Subsequent studies [5, 6, 27, 56, 64] have expanded T2V capabilities by utilizing large text-video pairs, achieving improved results. Building upon T2V, I2V synthesis [5, 9, 30, 53, 56, 61, 64] has also been widely explored. Given a still image, I2V aims to animate it into a video clip that retains all visual content from the image and exhibits naturally suggested dynamics. Many recent works, such as SVD [5], VideoCrafter2 [9] and CogVideoX [56] support both T2V and I2V simultaneously.
+
+Despite producing high-quality videos, these models rely on text or image prompts, limiting fine-grained control and potentially leading to actions misaligned with user intentions. For precise control, some works [20-22, 32, 35, 47, 52, 54, 59, 62, 67, 68] employ multimodal video sequences as conditions, such as pose [20, 32, 35, 54, 62, 67], depth [16, 52, 68], or sound [22, 28, 29, 43], treating video generation as a video translation task. Although these models achieve precise control, they require per-frame dense control signals, which makes them cumbersome and not user-friendly in real-world applications. Therefore, sim
+
+![](images/b449f5bd4b47ef5f9130daf6abd8841fc20e26034503166e2db78808fe3e22bd.jpg)  
+Figure 2. An example of object movement and occlusion represented by K-means clustered points.
+
+![](images/13c426cb9f46ba357bd99d9c504e3a961f6b2f9e47d79ab0a8b9950a4b055811.jpg)
+
+![](images/e13b929f0056ad56962c0ef4d1318221bc78fe63d35b7170bd824407a03b8294.jpg)
+
+![](images/58555149c3acc2821b36c5bff773a85dde8867d000e840b48885738f82d8ab10.jpg)
+
+pler yet precise control mechanisms are needed. Trajectory-based control offers an effective method for manipulating video generation, combining simplicity with precision.
+
+# 2.2. Trajectory Control in Video Generation
+
+Controllable editing has gained advancements in the field of image editing due to its precise control information [2, 10, 34, 57]. For video synthesis, trajectory-controlled generation has recently gained popularity due to its ability to achieve precise motion control. Early works [1, 3, 4, 14] employed recurrent neural networks or optical flow to guide motion. Methods like TrailBlazer [31] utilize bounding boxes to direct subject motion in video generation. MotionCtrl [49] encodes trajectory coordinates into dense vector maps, and DragNUWA [58] transforms sparse strokes into dense flow spaces; both use these representations as guidance signals. Tora [63] employs a motion variational autoencoder [25] to embed trajectory vectors into the latent space, preserving motion information across frames.
+
+Although these methods facilitate trajectory control, they often lack semantic understanding of entities, making control over video generation less refined. To address this issue, DragAnything [51] combines entity representation extraction with a 2D Gaussian representation to achieve entity-level controllable video generation. TrackGo [66] uses user-provided free-form masks and arrows to define target regions and movement trajectories, serving as precise blueprints for video generation. However, all these methods consider 2D trajectories in image space, leading to ambiguities in real 3D environments. The recent 3DTrajMaster [11] manipulates multi-entity 3D motions with user-desired 6DoF pose sequences of entities for video generation. In this paper, we introduce an innovative control signal representation that combines depth information with K-means clustered points from object masks in video, achieving accurate entity-level and 3D trajectory control.
+
+# 3. Method
+
+# 3.1. Problem Formulation
+
+To learn realistic object motion, the training dataset should contain high-quality videos with accurate object motions.
+
+However, existing datasets that provide 3D motion trajectories are either limited in size or consist solely of synthetic data. The Video Object Segmentation (VOS) datasets [7, 37], particularly with the recent release of SAM2 [37], offer high-quality videos with precise object mask annotations, making it an appropriate choice for our purposes. Nevertheless, two primary challenges remain:
+
+1. The dataset lacks explicit 3D trajectory information, which is essential for training a model to understand and synthesize 3D motions. Therefore, we need to implicitly express the 3D motion information contained in the data.  
+2. The provided mask annotations are too detailed for practical user input, as users cannot be expected to supply such fine-grained masks or dense 3D trajectories for control. Thus it is necessary to design a representation of 3D trajectories that is easy for users to input.
+
+To address these issues, we propose using K-means points extracted from the object masks along with their depth information as control signals. Specifically, we apply K-means clustering to the pixels of the mask to obtain a set of representative control points:
+
+$$
+\left\{\left(x _ {t} ^ {i}, y _ {t} ^ {i}\right) \right\} _ {i = 1} ^ {N} = \mathrm {K - m e a n s} (M _ {t}, N), \tag {1}
+$$
+
+where  $M_{t}$  denotes all object masks at frame  $t$ ,  $N$  is the number of clusters (control points), and  $(x_{t}^{i},y_{t}^{i})$  is the 2D coordinate of control point  $i$  at frame  $t$ . These control points not only simplify user input but also encapsulate implicit 3D information. As illustrated in Figure 2, the spatial distribution and density of the K-means points reflect changes in the object's depth and motion. For example, as a motorbike moves closer to the camera, the points spread out due to perspective scaling, indicating depth changes. Similarly, during occlusions, the distribution of points on the car shifts, capturing the occlusion dynamics. Then we employ a depth estimation network, DepthAnythingV2 [55], to predict relative depth maps  $\{D_t\}_{t = 1}^L$  for frames in the dataset, where  $L$  is the video length. In this way, we avoid the need of absolutely accurate depth information, making it easier for users to interact. We sample the depth at each control point:
+
+$$
+d _ {t} ^ {i} = D _ {t} \left(x _ {t} ^ {i}, y _ {t} ^ {i}\right), \tag {2}
+$$
+
+where  $d_t^i$  is the depth value at control point  $i$  in frame  $t$ . This process enriches the control points with depth information, effectively providing approximate 3D coordinates without requiring explicit 3D annotations. By combining the 2D coordinates and the estimated depth values, we construct the control trajectories:
+
+$$
+\mathcal {T} = \left\{\left\{\left(x _ {t} ^ {i}, y _ {t} ^ {i}, d _ {t} ^ {i}\right) \right\} _ {t = 1} ^ {L} \right\} _ {i = 1} ^ {N}, \tag {3}
+$$
+
+This representation allows users to efficiently specify 3D trajectories by simply selecting points on a 2D image and
+
+![](images/ddae7e2db0d31ec0cd93fc38829d2563887f7b14596c48e77701bdb9f7120b5a.jpg)  
+Figure 3. Control signal generation process of LeviTor.
+
+adjusting depth values as needed. We thus design our training and inference pipeline as in Sec. 3.2 and Sec. 3.3.
+
+# 3.2. Training Pipeline
+
+Given a VOS format video  $V \in \mathbb{R}^{L \times H \times W \times 3}$ , it provides the ground truth masks of multiple objects in the video, represented as  $\{\{M_i^j\}_{i=1}^X\}_{j=1}^L$ , where  $X$  denotes the number of object masks in each frame. For each mask  $M_i^j$ , we conduct K-means algorithm to obtain  $k$  center points as control signal. Specifically, we first calculate the area ratio of  $M_i^j$  to the entire image and multiply a hyper-parameter  $\alpha$  to determine the approximate number of cluster points:
+
+$$
+k = \left(\frac {S _ {M _ {i} ^ {j}}}{H * W}\right) * \alpha \tag {4}
+$$
+
+Then we assess whether there is a significant change of  $S_{M^j}$ , which indicates 3D related situations such as the object being occluded, moving out of the frame, or changing distance from the lens. To achieve this, we go through all video frames and calculate the ratio of the maximum to minimum area of the  $i_{th}$  object. If the ratio exceeds 10, we ensure that the value of  $k$  is not less than 3 in order to better represent the changes of this object along the temporal dimension:
+
+$$
+k = \left\{ \begin{array}{l l} \max  (k, 3), & \text {i f} \frac {\max  \left(\left\{S _ {M _ {i} ^ {j}} \right\} _ {j = 1} ^ {L}\right)}{\min  \left(\left\{S _ {M _ {i} ^ {j}} \right\} _ {j = 1} ^ {L}\right)} > 1 0, \\ k, & \text {o t h e r w i s e}, \end{array} \right. \tag {5}
+$$
+
+We later ensure  $k \leq 8$  to avoid the issue of having too many control points. We perform K-means clustering with the calculated  $k$  value on  $M_{i}^{j}$  and use the resulting cluster centers as control points. After extracting key points for all objects in each frame, we obtain the 2D coordinate information of all control points and instance information that show which object the point belongs to.
+
+We then use DepthAnythingV2 [55] to estimate the relative depth of each frame. Thus we can assign depth value to the corresponding 2D coordinate trajectories to get 3D trajectories. Finally, we represent the 2D trajectories
+
+with Gaussian heatmap and concatenate the trajectories, instance points, and depth points to serve as control signal, which is injected into the Stable Video Diffusion (SVD) [5] using ControlNet [60] to generate a video that aligns with the 3D trajectory. Our control signal generation process is shown in Fig. 3.
+
+Our training process can be represented as:
+
+$$
+\mathcal {L} = \mathbb {E} _ {z _ {t}, z ^ {0}, t, \epsilon \sim \mathcal {N} (0, \mathbf {I})} \left[ \left\| \epsilon - \epsilon_ {\theta} ^ {c} \left(z _ {t}; t, z ^ {0}, c _ {t r a j}\right) \right\| ^ {2} \right], \tag {6}
+$$
+
+where  $z^0$  denotes VAE-encoded latent feature of the first frame,  $c_{traj}$  means the control signal and  $\epsilon_{\theta}^{c}$  is the combination of the denoising U-Net and the ControlNet branch.
+
+# 3.3. Inference Pipeline
+
+We have designed a user-friendly interactive system for inference and the overview is provided in Fig. 4. Take an image as input, the system first automatically extracts depth information and object masks from the image using DepthAnythingV2 and SAM. Then users can utilize the retrieval panel to select the masks of objects to be moved by simply clicking on the image. They can also get relative depth values of clicked points automatically. After that, the user can use the interactive panel to click on more points to form the object trajectory. At the same time, the user can refer to the relative depth values of previously obtained click positions to input depth information of points within the trajectory according to their needs, thereby providing the corresponding 3D trajectories.
+
+With the sparse 3D trajectories and selected masks provided by user as input, we need to convert it into corresponding multi-points control information. This is because requiring users to input multiple point trajectories that comply with physical laws to represent correct occlusions and depth changes is hard. Generally, they only input a single trajectory to indicate the movement of an object. Thus we need this conversion to represent the 3D movements of objects through the clustering or dispersion of control points. We achieve this by generating 3D rendered object masks then selecting control points with K-means, as illustrated in Fig. 5. Specifically, we first combine the 2D coordinates of pixels in the starting image with their depth values to obtain 3D spatial points, represented as  $\{P_i\}_{i=1}^n = \{x_i, y_i, d_i\}_{i=1}^n$ , where  $n$  means the number of pixels in selected masks. Then we transform these points into the camera coordinate system. We assume that all camera intrinsic parameters are all the same and the camera to be still, so the rotation matrix is an identity matrix. The first step of transformation is converting 2D pixel points with their depth value into the camera coordinate system and moving the points belonging to user selected masks in this transformed 3D space:
+
+$$
+\left[ X _ {i}, Y _ {i}, Z _ {i} \right] ^ {T} = \mathbf {K} ^ {- 1} \cdot \left[ x _ {i}, y _ {i}, 1 \right] ^ {T} \cdot d _ {i}, \tag {7}
+$$
+
+$$
+\left[ X _ {i} ^ {\prime}, Y _ {i} ^ {\prime}, Z _ {i} ^ {\prime} \right] ^ {T} = \left[ X _ {i}, Y _ {i}, Z _ {i} \right] ^ {T} + \mathbf {T},
+$$
+
+![](images/b04ce35881f87d074577086fa6a654c76fda43e068d7eda4a13829cfa922486c.jpg)  
+Figure 4. Inference pipeline of LeviTor, which consists of user retrieval panel, interactive panel, 3D rendered object masks generation and video synthesis. Users can easily draw 3D trajectories through our retrieval panel and interactive panel, and our system later use these inputs to generate user desired videos.
+
+![](images/190b0ec79b92a75e441690d92c3d41d317f17c813fd81296c0974bfab875e4fb.jpg)  
+Figure 5. 3D rendered object masks generation pipeline.
+
+here  $\mathbf{K}$  denotes the perspective projection matrix of camera and  $\mathbf{T}$  is the moving vectors assigned by users. After that, we render these points back to 2D images:
+
+$$
+\left[ x _ {i}, y _ {i} \right] ^ {T} = f \left(\left[ X _ {i} ^ {\prime}, Y _ {i} ^ {\prime}, Z _ {i} ^ {\prime} \right] ^ {T}, I D _ {i}\right), \tag {8}
+$$
+
+$f$  is a rendering function which we implement with renderer function in PyTorch3D [36] and  $ID_{i}$  is the instance that the  $i_{th}$  point belongs to. All the points are assigned the corresponding instance information, so rendering them back results in images with masks of different objects.
+
+In this way, we represent the movements, occlusion, and size changes due to forward and backward movements of objects only with the sparse trajectories input by the user. At the same time, the changes in 2D masks rendered from 3D space also fully comply with the laws of physics.
+
+By mapping points to 3D space and then rendering them back to 2D mask images, we convert sparse user controls into dense mask representations. These masks can accurately reflect the movement and occlusion of objects. Next, we compute cluster centers using K-means based on the masks obtained from rendering. By combining these with user-specified depth changes, we derive an appropriate number of control trajectories to generate the final video using our LeviTor. Further selecting control points with K-means is necessary because the movement process in 3D space cannot represent non-rigid transformations. If we directly use a dense mask for control, it will only result in a straightforward translation of the object, as demonstrated in Fig. 8. By converting the mask into a moderate number of trajectory control signals, the generative model can capture the motion variation of the object while also adding some details of non-rigid movements.
+
+# 4. Experiments
+
+# 4.1. Experiment Settings
+
+Implementation details. We use SVD [5] as our base model. During training, we sample 16 consecutive frames from videos at a spatial resolution of  $288 \times 512$ . Specifically, we center-crop the video to an aspect ratio of  $288 / 512$ , then resize the video frames to the resolution of  $288 \times 512$ . Our LeviTor is trained for 200K iterations using the AdamW optimizer with a learning rate of 1e-5. All training is conducted on 16 NVIDIA A100 GPUs with a total batch size equal to 16.
+
+![](images/0acd39c6d88d0fd9b4256442c9b8b75b11041a3e08add8caa4a47ab8de22201f.jpg)  
+Figure 6. Qualitative comparison with DragAnything [51] and DragNUWA [58]. LeviTor and DragAnything both support moving user-selected mask areas, whereas DragNUWA directly encodes trajectories as control signals and does not support user selection of operation areas. The top two rows show evaluation on control of mutual occlusion between objects. The left bottom images show comparison of forward and backward object movements control. The right bottom images show a case of complex motion implementation.
+
+Datasets. For training, we utilize the high-quality Video Object Segmentation (VOS) dataset Segment Anything Video (SA-V) [37], which consists of 51K diverse videos and 643K high-quality spatio-temporal segmentation masks. We conduct an evaluation on the DAVIS [7] dataset and split videos into clips with 16 frames for testing. Inspired by DragAnything [51], we apply K-means to the mask of each object in the start frame to select K points in each mask area as control points. Then, we employ Co-Tracker [23] to track these control points to generate corresponding point trajectories as the ground truth.
+
+Metrics. Following [49, 51], we adopt Frechet Video
+
+Distance [44] (FVD) to measure video quality and assess image quality using Frechet Inception Distance [39] (FID). For motion controllability evaluation, we leverage ObjMC [49], which computes the Euclidean distance between the generated and pre-defined trajectories. Trajectories of generated videos are extracted using Co-Tracker.
+
+# 4.2. Comparison with Other Approaches
+
+We compare our methods with DragNUWA [58] and DragAnything [51], which enable motion control on given images and have publicly available code. We conduct both qualitative and quantitative comparisons.
+
+Qualitative comparison. For qualitative analysis, we focus on verifying the crucial role of introducing 3D trajectories into video generation, which includes the following three aspects: 1) The control of mutual occlusion between objects; 2) Better control for forward and backward object movements in relation to the lens; 3) The implementation of complex motions (such as orbiting).
+
+Qualitative comparison results are shown in Fig. 6, where we input the same 2D control trajectory to all models. The top two rows of images show the verification results of occlusion control. In this case, we provide our LeviTor with different depth variations: the depth in the first row changes from far to near, while the depth in the second row only moves closer without being closer to the camera than the buildings on street side. The generated results perfectly meet our requirements, with the tornadoes progressing from far to near and gradually getting larger. Meanwhile, tornado in the first row sweeps across the front of the building, while in the second row it just passes behind the building. In contrast, the other two methods can only control the generation through 2D trajectories. It can be observed that DragAnything misinterprets the movement of the tornado as a forward movement of the camera, resulting in a blurry output. On the other hand, DragNUWA correctly understands that the tornado needs to be moved. However, since it lacks consideration of changes in depth, the size of the tornado hardly changes after the movement, which does not comply with perspective projection rules.
+
+Evaluation results on control for forward and backward object movements in relation to the lens are shown as the left-bottom images in Fig. 6. It is clear that 2D trajectory cannot provide depth information, so DragAnything and DragNUWA can only simulate planets motion that conforms to that trajectory, resulting in blurry videos. In contrast, LeviTor can generate accurate and clear movements of two planets based on user-specified inputs meanwhile conforming to perspective projection rules.
+
+Based on the information input by users, we can derive 3D trajectories to control the movement of objects, which represent users' desired object occlusions and size changes. Furthermore, we can simulate more complex motions, such as object orbiting. The right-bottom images in Fig. 6 shows an example and our model is able to accurately simulate the situation of a black bowl rotating around a vase and correctly handle the occlusion relationships. Instead, DragAnything cannot directly interpret the 2D trajectory to achieve our desired swirling effect. It only generates a video where the bowl moves from right to left and then back. During this movement, the bowl also undergoes distortion and blurring. DragNUWA treats this 2D input as a camera trajectory, resulting in a video that shows a stationary table and bowl filmed from different angles.
+
+The qualitative comparison results demonstrate that by
+
+Table 1. Quantitative comparison on DAVIS [7].  
+
+<table><tr><td>Settings</td><td>Methods</td><td>FID↓</td><td>FVD↓</td><td>ObjMC↓</td></tr><tr><td rowspan="3">Single-Point</td><td>DragAnything [51]</td><td>36.69</td><td>327.41</td><td>42.19</td></tr><tr><td>DragNUWA1.5 [58]</td><td>44.82</td><td>330.17</td><td>33.03</td></tr><tr><td>LeviTor (Ours)</td><td>28.79</td><td>226.45</td><td>37.39</td></tr><tr><td rowspan="3">Multi-Points</td><td>DragAnything [51]</td><td>36.04</td><td>324.95</td><td>38.86</td></tr><tr><td>DragNUWA 1.5 [58]</td><td>42.34</td><td>299.96</td><td>23.12</td></tr><tr><td>LeviTor (Ours)</td><td>25.41</td><td>190.44</td><td>25.97</td></tr></table>
+
+introducing 3D trajectory control which allows for easy input by users, our LeviTor can better manage the proximity changes of objects. It can also produce video results that cannot be generated with only 2D trajectories, such as controlling object occlusion and executing complex movements like orbiting. Additionally, since our pipeline includes all object masks automatically extracted by SAM [26], LeviTor ensures that only objects selected by users can be moved. This prevents interpreting object movement as camera movement. And camera movement can be implemented by moving the mask of the selected background (as shown in Fig. 7).
+
+Quantitative comparison. We evaluate the quantitative results with two input settings: Single-Point and Multi-Points. The setting of Single-Point is consistent with previous work [51], which means that only one point trajectory is selected for each mask as video generation condition. For Multi-Points setting, we select at most 8 points in each mask and use their trajectories as condition. Tab. 1 shows the quantitative comparison results of LeviTor with baselines on DAVIS. Using the same SVD as base model, our method achieves a significant advantage in both FID and FVD metrics, thanks to the consideration of 3D trajectory and training on high-quality SA-V dataset. Besides, increasing the number of control trajectories can effectively benefit DragNUWA and LeviTor. This indicates that considering object size changes over time and occlusion is effective. DragAnything is trained using a single trajectory with object mask semantic information in first frame, thus increasing the number of trajectories doesn't match the training and improvement is limited. LeviTor performs worse than DragNUWA on the ObjMC metric, which we attribute to the fact that we do not use tracking methods to obtain complete point trajectories and require the generated video to perfectly match these trajectories.
+
+# 4.3. Ablation Studies
+
+We conduct ablations to study how depth points, instance information and the number of control points for inference affect our synthesis results with the Multi-Points setting.
+
+Depth and instance information. Tab. 2 shows the results of training LeviTor without depth or object instance input, which suggest that both depth and instance information
+
+![](images/f5e8a99c865e05dc35e1a077eb710a00115d3c32a7a8963678d1f6746eda56f3.jpg)  
+Figure 7. Ablation on Instance and Depth information. Enlarged details are shown in red boxes. Zoom in for better viewing.
+
+![](images/a4ba4e2c075355790ecdaed3f311e6e9652bcc8c10da00e32b2959551850a60d.jpg)  
+Figure 8. Ablation on number of inference control points. 'Scale' means the value multiplied by the default number of control points.
+
+are helpful to our model learning. Compared to depth information, object instance is more important because it represents the objects corresponding to different control points. Without this information, model can easily confuse the control points of different objects, leading to blurred and unrealistic results. Depth information of objects is to some extent implicit in the degree of clustering of points, so its impact is relatively small. We also present a qualitative ablation result in Fig. 7, which suggests that without instance or depth information, the model can easily confuse occlusion relationship between objects, resulting in blurry and unrealistic generation results.
+
+Number of control points for inference. During inference,
+
+Table 2. Ablations on Object Instance and Depth information.  
+
+<table><tr><td>Depth</td><td>Instance</td><td>FID↓</td><td>FVD↓</td><td>ObjMC↓</td></tr><tr><td>X</td><td>X</td><td>27.83</td><td>227.58</td><td>29.82</td></tr><tr><td>✓</td><td>X</td><td>28.04</td><td>221.29</td><td>29.13</td></tr><tr><td>X</td><td>✓</td><td>25.45</td><td>199.44</td><td>25.40</td></tr><tr><td>✓</td><td>✓</td><td>25.41</td><td>190.44</td><td>25.97</td></tr></table>
+
+our model can choose different number of control points to strike a balance between motion amplitude and generation quality. Fig. 8 illustrates an example, where we multiply the initial number of control points by a scale to evaluate the impact of different numbers of control points on generation results. It can be seen that when there are few control points, the generated result exhibits significant movement amplitude, but the object may experience some deformation or blurring during the motion. However, too many control points can get close to the object's mask. Although taking these points as control ensures the reasonableness of the object's shape, it prevents the model from generating the result of its movement. As shown in the last row of Fig. 8, the puppy will translate directly from back to front. Users can therefore adjust the number of control points according to their needs to achieve the desired generation results.
+
+# 5. Conclusion
+
+In this paper, we have presented LeviTor, a novel model for implementing 3D object trajectory control in image-to-video synthesis. Taking depth information combined with K-means clustered points as control signal, our approach captures essential 3D attributes without the need for explicit 3D trajectory estimation. Our user-friendly inference pipeline allows users to input 3D trajectories by simply drawing on 2D images and adjusting point depths, making the synthesis process more accessible. Our model also has certain limitations. First, LeviTor is constrained by the segmentation results of SAM and trajectories provided by the user, and it does not understand physical laws to generate movements of objects without provided trajectory controls. Additionally, since LeviTor was not trained using tracking data, it cannot control the internal pose changes of objects. Finally, the current generation results are limited by the base model SVD. For future work, we aim to extend LeviTor by incorporating more advanced video base models capable of capturing deformable objects and intricate dynamics to better handle non-rigid motions.
+
+Acknowledgements: This work was supported by the National Key R&D Program of China (No. 2022ZD0160900), the Research Grant Council of the Hong Kong Special Administrative Region under grant number 16203122, Ant Group Research Intern Program, Jiangsu Frontier Technology Research and Development Program (No. BF2024076), and the Collaborative Innovation Center of Novel Software Technology and Industrialization.
+
+# References
+
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+# LiDAR-RT: Gaussian-based Ray Tracing for Dynamic LiDAR Re-simulation
+
+Chenxu Zhou<sup>1*</sup>
+
+Lvchang  $\mathrm{Fu}^{2*}$
+
+Sida Peng $^{1\dagger}$
+
+Yunzhi Yan
+
+Zhanhua Zhang
+
+Yong Chen<sup>3</sup> Jiazhi Xia<sup>2</sup>
+
+Xiaowei Zhou
+
+<sup>1</sup>Zhejiang University
+
+$^{2}$ Central South University
+
+<sup>3</sup>Geely Automobile Research Institute
+
+![](images/7cc939845fe6b93efe14051478f11e535920b450d401eb86086b2b4c39810efc.jpg)  
+Figure 1. Realistic and real-time rendering of LiDAR views in dynamic driving scenes. Our LiDAR-RT produces high-fidelity LiDAR views at 30 FPS (64×2650) within 2 hours of training. SOTA method [61] struggles to model the dynamic objects in complex scenes and suffers from high training and rendering costs (15 hours for training and 0.2 FPS for rendering a range image).
+
+![](images/c2c6bb04b452db49e6064ac6b8f7225031a442926330f01a05da11e33b203b85.jpg)
+
+# Abstract
+
+This paper targets the challenge of real-time LiDAR re-simulation in dynamic driving scenarios. Recent approaches utilize neural radiance fields combined with the physical modeling of LiDAR sensors to achieve high-fidelity re-simulation results. Unfortunately, these methods face limitations due to high computational demands in large-scale scenes and cannot perform real-time LiDAR rendering. To overcome these constraints, we propose LiDAR-RT, a novel framework that supports real-time, physically accurate LiDAR re-simulation for driving scenes. Our primary contribution is the development of an efficient and effective rendering pipeline, which integrates Gaussian primitives and hardware-accelerated ray tracing technology. Specifically, we model the physical properties of LiDAR sensors using Gaussian primitives with learnable parameters and incorporate scene graphs to handle scene dynamics. Building upon this scene representation, our framework first constructs a bounding volume hierarchy (BVH), then casts rays for each pixel and generates novel LiDAR views through a differentiable
+
+rendering algorithm. Importantly, our framework supports realistic rendering with flexible scene editing operations and various sensor configurations. Extensive experiments across multiple public benchmarks demonstrate that our method outperforms state-of-the-art methods in terms of rendering quality and efficiency. Our code and data are available at https://github.com/zju3dv/LiDAR-RT.
+
+# 1. Introduction
+
+Modeling dynamic urban scenes is of great importance for a variety of applications, such as digital twin simulation, autonomous driving, and virtual reality. Recent research has shown impressive results of novel view synthesis in driving scenarios [8, 9, 54, 62] with camera sensors, significantly enhancing the fidelity and diversity of data for downstream tasks and applications. However, the majority of current approaches overlook the re-simulation of LiDAR sensors, which are key components for many 3D perception algorithms, thereby restricting the scope of simulation applications. In contrast to cameras, the inherent physical properties of LiDAR sensors and sparsity of point clouds make it challenging to reconstruct and simulate, especially in dynamic scenes with complicated motions.
+
+Previous methods [20, 27] initially reconstruct 3D scenes from real-world data with explicit representations
+
+like dense point clouds or triangular meshes, which are utilized to render novel LiDAR views via ray-casting. Although these two-stage methods manage to produce acceptable results, they are hampered by geometric inaccuracies and struggle to model the physical properties of LiDAR sensors. Additionally, they are only capable of modeling static scenes and fail to handle dynamic objects.
+
+As neural scene representations advance, there have been some works [16, 44, 53, 59] that attempt to synthesize novel views of LiDAR with neural radiance fields [29]. These NeRF-based methods [16, 44, 53, 59] combine the rendering power of neural fields with the physical modeling process of LiDAR sensors, achieving physically realistic LiDAR rendering. By introducing 4D hybrid features or tracked bounding boxes, some recent works [49, 61] extend these methods to handle dynamic scenes. However, these approaches are constrained by high training costs and slow rendering speeds due to the large amount of network parameters, and struggle to model complex dynamic scenes with long-distance vehicle motion and occlusions.
+
+In this paper, we propose a novel framework, named LiDAR-RT, for novel LiDAR view synthesis of dynamic driving scenes. Our primary contribution is the development of an efficient and effective rendering pipeline for Gaussian-based [15, 17] LiDAR representation. Firstly, we enhance Gaussian primitives with additional learnable parameters to accurately model the physical characteristics of LiDAR sensors. Furthermore, to tackle the challenges of dynamic scenes, we integrate the scene graphs [31] into LiDAR representation, which provides flexible modeling capabilities under various environmental conditions.
+
+Building upon proposed scene representation, we extend a differentiable Gaussian-based ray tracer [30] to simulate the physical formation of LiDAR sensors. Specifically, our method constructs the corresponding proxy geometries for Gaussian primitives and inserts them into a bounding volume hierarchy (BVH). To compute the LiDAR radiance, we cast ray for each pixel from the sensor against the BVH to determine the intersections and store the information in a sorted buffer [3, 30]. Subsequently, we calculate the response of the intersected Gaussians and integrate the radiance along the ray via volumetric rendering techniques. [30] This process continues until all Gaussian primitives have been traversed or the accumulated transmittance reached a predefined threshold. Then the rendered properties are fused to generate novel LiDAR views. Compared to the vanilla tile-based Gaussian rasterizer [17], our method employs a physically accurate ray tracing process, which enhances both the realism and accuracy for LiDAR re-simulation. Thanks to the proposed components, our method not only reconstructs high fidelity LiDAR point clouds and achieves real-time rendering of novel LiDAR views, but also supporting flexible LiDAR manipulations.
+
+We evaluate the proposed method on Waymo Open (Waymo) [42] and KITTI-360 [21] datasets, which cover a wide range of complex dynamic scenes. Our method achieves state-of-the-art performance in terms of rendering quality and efficiency across all datasets. Moreover, our comprehensive experiments have confirmed that the components we proposed are highly adaptable for LiDAR re-simulation and maintain great performance under various editing manipulations.
+
+# 2. Related work
+
+LiDAR Simulation. Traditional self-driving simulators such as CARLA [10] or Airsim [41] do possess the ability to simulate LiDAR sensors, but suffer from the sim-to-real gap [22, 28] and costly manual effort in creating virtual assets. LiDARsim [27] uses a multi-stage and data-driven approach to reconstruct the surfel-based [36] scene from real-world data and model the ray-drop property via a neural network for improving realism. PCGen [20] utilizes the first peak averaging (FPA) ray-casting and surrogate model ray-drop to further close the domain gap. Nevertheless, these explicit methods [20, 27, 56] are sensitive to the geometry quality and only applicable to static scenes. By leveraging generative models, some works [6, 65, 66] provide an alternative but lack the physical control to model the real-world LiDAR sensors.
+
+Several recent methods [16, 44, 53, 57, 59] are proposed for high quality novel view LiDAR synthesis based on neural radiance fields (NeRF) [29], which combines the differentiable rendering capability of NeRF and the physical model of LiDAR sensors. Notably, NFL [16] demonstrates the detailed physical modeling of LiDAR sensors firstly, and provide a comprehensive reference for following works. NeRF-LiDAR [59] and UniSim [57] take multimodal inputs to enhance the performance of LiDAR re-simulation. Furthermore, with the introduction of 4D hybrid features and additional tracking labels, some methods [43, 45, 49, 61] extend to dynamic driving scenes. However, all these NeRF-based approaches are constrained primarily by the high computational demands during training and rendering, and struggle to accurately model or re-simulate scenes with complex motions.
+
+Dynamic Scene Reconstruction. Expanding on the accomplishments of NeRF, some methods [2, 7, 25, 33, 37] build 4D neural representation to reconstruct object-level scenes via various extensions, such as continuous deformation fields [32] or spatial-temporal encoding [12]. Some recent methods extend to dynamic urban scenes with extra supervision like optical flow [46, 51] and transformer features [55]. Apart from these works, another group of methods [31, 45, 50, 57] model the dynamic scene as the composition of dynamic objects and static background.
+
+![](images/5787bad3f92356f4b62adb7d5071e772e41dc94955da26ca585f588d87fa7bb7.jpg)
+
+![](images/7b0f462aa05825e9e6cc037b5397b6b01eb3fb3623a5e0257c9e2d3dec62d32b.jpg)
+
+![](images/108e78e4dd24e46186891bb8945295d892bd549259784b601ac4bfc29c40b878.jpg)  
+Figure 2. Overview of LiDAR-RT. (a) We decompose the dynamic scene into a background model and multiple object models, with each represented by a set of Gaussian primitives. In addition to geometric attributes, we introduce learnable parameters (SHs) on Gaussians to emulate the intrinsic properties  $(\zeta, \beta)$  of LiDAR sensors. (b) Based on this representation, we design a differentiable ray tracing framework. We first construct the proxy geometry for Gaussian primitives and then cast rays from the sensor to perform intersection tests. (c) By evaluating the response from these intersections, we accumulate point-wise properties along each ray, and finally render the novel LiDAR view as range images. (d) The range images are fused and re-projected into LiDAR point clouds for downstream tasks.
+
+![](images/71993d5d9a67acef36ce36590730ff54fc1a5272dea57483925b4434d2b5232e.jpg)
+
+UniSim [57] and NeuRAD [45] also simulate LiDAR observations at new views, which is similar to our work. Nevertheless, these methods suffer from high computational costs on large scale scenes and cannot perform real-time rendering. Aiming for rapid reconstruction and rendering, some methods prefer to represent the dynamic scene with 3D Gaussians [8, 48, 54, 62, 63], which perform impressive results for novel view synthesis of camera sensors. OmniRe [9] further constructs multiple local canonical spaces to model diverse dynamic objects in a driving log, including non-rigid pedestrians and cyclists. Despite these advancements, there is a significant gap when they simulate other types of sensors like LiDAR, which is crucial for many perception and planning tasks.
+
+Gaussian Splatting. 3D Gaussian Splatting [17, 24] made a breakthrough by using a differentiable splatting algorithm to render a scene represented by Gaussian primitives, many works [38, 52, 58] conduct extensions to 3DGS, such as anti-aliasing [58] and view-consistent rendering [38]. Based on the 3DGS, 2D Gaussian Splatting [15] collapses the 3D volume into a set of 2D oriented planar Gaussian disks and design a perspective-accurate 2D splatting process to model and reconstruct geometrically accurate radiance fields from multi-view images. However, these
+
+rasterization-based rendering is difficult to model general ray effects (shadows, reflections etc.) and image formation processes that exhibit non-linear optical models, which limits its application for many tasks. To address this issue, some approaches [5, 13, 26, 30] propose to combine the ray tracing technologies with Gaussian particles. 3DGRT [30] utilizes the high-performance GPU ray tracing hardware to render the particle scenes in real-time. They also show applications on autonomous vehicle scene reconstruction for camera sensors.
+
+# 3. Method
+
+In this section, we begin by delineating the problem formulation for the novel LiDAR view synthesis and the preliminary of Gaussian Splatting [17]. Following that, we provide a detailed exposition of our proposed LiDAR-RT.
+
+Problem Formulation. In this problem, our input is a collection of LiDAR scans  $\mathcal{L}$  captured by a moving sensor within a driving scenario, along with the corresponding calibrated sensor poses  $P$  and timestamps  $T$ . Additionally, a group of bounding boxes  $\mathcal{B}$  are provided to track the moving vehicles in the scene.
+
+Our goal is to reconstruct this dynamic scene as an explicit representation and render realistic LiDAR views
+
+from any given moment  $t_{new}$  and novel viewpoint  $P_{new}$ . Furthermore, rendering must maintain high fidelity for various scene manipulations and sensor configurations.
+
+Gaussian Splatting. Kerbl et al. [17] propose to represent 3D scenes with 3D Gaussian primitives and render images using differentiable volume splatting. The  $i$ -th Gaussian is characterized by a full 3D covariance matrix  $\Sigma_{i}$  defined in world space [64] centered at point (mean)  $\mu_{i}$ :
+
+$$
+\mathcal {G} _ {i} (\mathbf {x}) = \exp \left(- \frac {1}{2} \left(\mathbf {x} - \mu_ {i}\right) ^ {\top} \boldsymbol {\Sigma} _ {i} ^ {- 1} \left(\mathbf {x} - \mu_ {i}\right)\right), \tag {1}
+$$
+
+where the covariance matrix  $\mathbf{\Sigma}_i = \mathbf{R}_i\mathbf{S}_i\mathbf{S}_i^\top \mathbf{R}_i^\top$  is factorized into a scaling matrix  $\mathbf{S}_i$  and a rotation matrix  $\mathbf{R}_i$ . Each Gaussian is paired with an opacity value  $\sigma_i$  and the spherical harmonics coefficients (SHs) [39] to model the view-dependent appearance  $\mathbf{c}_i$ .
+
+When rendering novel views, 3D Gaussians are rasterized to image planes and form 2D Gaussians  $\mathcal{G}'$  with the 2D covariance  $\boldsymbol{\Sigma}_i' = \mathbf{J}\mathbf{W}\boldsymbol{\Sigma}_i\mathbf{W}^\top \mathbf{J}^\top$ , where  $\mathbf{W}$  is the viewing transformation and  $\mathbf{J}$  is the Jacobian of the local affine transformation [64]. The color of a pixel is calculated via alpha blending with depth ordered 2D Gaussians:
+
+$$
+\mathcal {C} (\mathbf {x}) = \sum_ {i = 1} ^ {K} T _ {i} \alpha_ {i} \mathbf {c} _ {i}, \tag {2}
+$$
+
+$$
+\text {w h e r e} \alpha_ {i} = \sigma_ {i} \mathcal {G} _ {i} ^ {\prime} (\mathbf {x}) \quad \text {a n d} \quad T _ {i} = \prod_ {j = 1} ^ {i - 1} (1 - \alpha_ {j}). \tag {3}
+$$
+
+# 3.1. Overview of LiDAR-RT
+
+Towards the target of rendering realistic novel LiDAR views in real-time, we propose a novel framework named LiDAR-RT. As illustrated in Fig. 2, we represent the dynamic driving scene as a set of point clouds consisting of a static background and multiple foreground vehicles, each associated with Gaussian primitives (Section 3.2). To ensure physical realism and high fidelity in rendering, we design a efficient and effective ray tracer based on Gaussian primitives to model the LiDAR imaging process (Section 3.3). Moreover, we implement the backward pass of ray tracing to support differentiable LiDAR rendering (Section 3.4) and scene optimization (Section 3.5).
+
+# 3.2. Dynamic Scene Representation
+
+We decompose the dynamic scene into a static background and several moving vehicles, with each component represented by a distinct set of Gaussian primitives to softly learn the continuous scene geometry and radiance. Similar to 3DGS [17], both the Gaussian primitives of background model and dynamic actor models share a set of common base parameters, including the mean position  $\mu$ , covariance matrix  $\Sigma$ , opacity  $\sigma$ , and SH coefficients, the covariance
+
+matrix  $\boldsymbol{\Sigma}$  can further be factorized into a scaling matrix  $\mathbf{S}$  and a rotation matrix  $\mathbf{R}$  as in Eq. 1.
+
+Additionally, we introduce learnable parameters on Gaussian primitives to emulate the intrinsic properties of LiDAR sensors, denoted by  $\mathcal{P} = (\zeta, \beta)$ , where  $\zeta \in \mathbb{R}^1$  represents the reflection intensity and  $\beta \in [0,1]$  indicates the ray-drop probability. Ray-drop is a common phenomenon of real-world LiDAR sensors that occurs when the return signal is too weak [28], and the emitted ray is considered as dropped. Unlike previous methods that directly model the ray-drop with a single variable [16, 44, 49, 61], we learn the ray-drop probability  $\beta$  with two logits  $(\beta_{\mathrm{drop}}, \beta_{\mathrm{hit}})$ , activated by the softmax function [4]: Since the intensity and ray-drop are strongly affected by view directions, our method models  $(\zeta, \beta_{\mathrm{drop}}, \beta_{\mathrm{hit}})$  with a set of SH coefficients as shown in Fig. 2 (a).
+
+To handle the foreground moving vehicles, we utilize tracked bounding boxes to trace their motion trajectories. Different from the background model, the mean position  $\pmb{\mu}_{o}$  and rotation matrix  $\mathbf{R}_o$  of the Gaussian primitives for dynamic objects are defined within the object local coordinate system. To transform them into the world coordinate system, same as [45, 54], we define the tracked poses for each rigid object as a series of rotation matrices  $\{\mathbf{R}_t\}_{t = 1}^{N_t}(\mathbf{R}_t\in \mathbb{R}^{3\times 3})$  and translation vectors  $\{\mathbf{T}_t\}_{t = 1}^{N_t}(\mathbf{T}_t\in \mathbb{R}^{3\times 1})$ , where  $N_{t}$  represents the number of frames. The transformation is formulated as:
+
+$$
+\boldsymbol {\mu} _ {w} = \mathbf {R} _ {t} \boldsymbol {\mu} _ {o} + \mathbf {T} _ {t}, \tag {4}
+$$
+
+$$
+\mathbf {R} _ {w} = \mathbf {R} _ {t} \mathbf {R} _ {o},
+$$
+
+where  $\pmb{\mu}_{w}$  and  $\mathbf{R}_w$  denote the mean position and rotation matrix of the Gaussian primitives in the world coordinate system, respectively. With this representation, we can reconstruct and render the dynamic scene with easy composition of separate models, which further enables flexibly scene editing applications.
+
+For the initialization of point clouds for background model, we estimate the normals of all Gaussian primitives with KNN algorithms and initialize the Gaussian orientations towards the normals. Then we fuse the multi-frame LiDAR point clouds and downsample them via voxel downsampling with a voxel size of 0.15. For object model less than  $8K$  points, we randomly sample points inside the 3D bounding box and concatenate with the original points to reach  $8K$  points.
+
+# 3.3. Gaussian-based Ray Tracing
+
+To render novel LiDAR views, a straightforward approach is to rasterize the Gaussian primitives onto the LiDAR imaging plane and accumulated LiDAR properties through Eq. 2, similar to the process of general camera sensors. However, the vanilla rasterization approach of 3DGS [17] does not support the rendering of cylindrical range image
+
+produced by LiDAR sensors. Furthermore, the rasterization imaging process is not aligned with the active nature of LiDAR sensors, which rely on the emission and reception of laser beams. Therefore, a ray-based rendering approach is essential for accurately simulating the LiDAR sensors. Building upon these insights and inspired by the latest point-based ray tracing methodologies [5, 13, 26, 30], we extend a Gaussian-based ray tracer [30] based on the NVIDIA OptiX framework [34] for hardware acceleration.
+
+![](images/582351b1860489160de613850da8d4441a8e4cd7d93da6c3ede0744b63cec6bc.jpg)  
+Figure 3. Ray intersection with proxy geometries. We construct the proxy geometry for each 2D Gaussian primitive as a pair of co-planar triangles, then the ray tracer performs intersection tests with the vertices  $\vec{v}$  and surface normal  $\vec{n}$ .
+
+Proxy Geometries. In the realm of traditional graphics rendering [1, 23], proxy geometries serve as the simplified representations to approximate the complex original geometries, which can accelerate the ray tracing process. Considering the efficiency in constructing the BVH and the performance of intersection tests [30], we opt for a two-dimensional Gaussian primitive in the form of a planar disk, as elaborated in [15]. Thereby, the most efficient and simplest proxy geometry for encapsulating such Gaussian primitive is a pair of co-planar triangles (Fig. 3). Compared to axis-aligned bounding boxes (AABBs) or other polyhedron meshes, this approach reduces the number of meshes and tightly wraps the Gaussian primitive. Additionally, the sample locations are same as the ray intersections, without the approximation with maximum response, which is different with [19, 30]. More details on proxy geometries for Gaussian variants are in our supplementary material.
+
+Forward Ray Tracing. After constructing the acceleration structures, our method proceeds to generate batch rays from the LiDAR sensor, formulated as  $\mathcal{R} = \{\mathbf{r}_o,\mathbf{r}_d\}$ , where  $\mathbf{r}_o\in \mathbb{R}^{N_r\times 3}$  and  $\mathbf{r}_d\in \mathbb{R}^{N_r\times 3}$  denote the ray origins and normalized ray directions, with  $N_{r}$  being the total number of batch rays. Our ray tracing pipeline is initialized by the optixLaunch [34] program. Specifically, given a ray  $r$  within a batch of rays  $\mathcal{R}$ , the ray-gen program is invoked to cast the ray against the BVH. The tracer then utilizes triangle vertices and surface normal to compute intersections (Fig. 3), using the any-hit program to maintain the intersections in an sorted buffer. However, sorting all
+
+intersections along each ray directly is inefficient, particularly in large-scale scenes with many Gaussian primitives. To deal with this problem, we divide the ray into several chunks during the round of tracing [30], each containing a fixed number of intersections, thereby reducing the sorting overhead to a single chunk. When the count of intersections reaches the chunk size, we take out the indices  $\mathcal{I}$  of the intersected primitives and depth values  $\mathcal{D}$  at the intersections from the sorted buffer. Subsequently, we evaluate the Gaussian response and calculate the point-wise LiDAR properties  $(\zeta_i,\beta_i)$  at each sample point. The pixel value is rendered through Eq. 2 by replacing  $\mathbf{c}_i$  with  $\zeta_{i}$  and  $\beta_{i}$ . Following this, ray tracing advances to the next chunk, starting from the last evaluated point [30]. This iterative process continues until all Gaussian primitives intersecting the ray have been traversed, or the accumulated transmittance along the ray falls below a predefined minimum threshold  $T_{\mathrm{min}}$ .
+
+# 3.4. Differentiable LiDAR Rendering
+
+LiDAR Modeling. With the purpose of rendering LiDAR views, we present the LiDAR view as the form of range image. Given a LiDAR scan  $\mathcal{L}_i$  contains  $\mathcal{M}_i$  points each parameterized by  $(x,y,z,\zeta)$ , we first calculate the distance  $d$  to the sensor center with  $d = \sqrt{x^2 + y^2 + z^2}$ . Then the azimuth angle  $\theta$  and elevation angle  $\phi$  is computed as follows:
+
+$$
+\begin{array}{l} \theta = \arctan (y, x), \tag {5} \\ \phi = \arcsin (z, d). \\ \end{array}
+$$
+
+Considering a LiDAR sensor with H laser beams in the vertical plane and W horizontal emissions, we can project the points onto the LiDAR imaging plane from the world coordinate system:
+
+$$
+\binom {h} {w} = \binom {1 - (\phi + | f _ {\text {d o w n}} | / f _ {v})} {(1 - \theta / \pi) / 2} \cdot \binom {\mathrm {H}} {\mathrm {W}}, \tag {6}
+$$
+
+where  $(h,w)$  is the 2D coordinates on range image, and  $f_{v} = |f_{up}| + |f_{down}|$  is the vertical FOV of LiDAR sensor.
+
+Differentiable Rendering. Apart from the forward Li-DAR rendering, our ray tracer also supports differentiable rendering to optimize the scene representation. In previous works [15, 17], the back-propagation is conducted in a back-to-front blending order:
+
+$$
+\frac {\partial L}{\partial \alpha_ {i}} = T _ {i} \boldsymbol {c} _ {i} - \sum_ {j = i + 1} ^ {N} T _ {j} \alpha_ {j} \boldsymbol {c} _ {j}, \tag {7}
+$$
+
+To compute gradients for the  $i$ -th Gaussian, we need the contributions from all subsequent blended Gaussians. 3DGS [17] meets this need by using per-tile sorted buffers. However, this approach is not available for us due to the distinction between the panoramic LiDAR models and
+
+![](images/2a4cec49387db7057feeb08f6b589f3e8f3ca1152a13e290adb8908f4b5b6ff6.jpg)  
+Figure 4. Qualitative comparison on the KITTI-360 [21] dataset. Dynamic vehicles are zoomed in for better visualization.
+
+camera models. A naive method to record the blending order in a global buffer during the forward pass is impractical, as it leads to unaffordable memory overhead and reduced ray tracing efficiency. To address this issue, we take the strategy proposed by [38] to perform the back-propagation in a front-to-back blending order, same as forward rendering:
+
+$$
+\frac {\partial L}{\partial \alpha_ {i}} = T _ {i} \boldsymbol {c} _ {i} - \left(\boldsymbol {C} - \mathcal {C} _ {i}\right) / \left(1 - \alpha_ {i}\right), \tag {8}
+$$
+
+where  $\mathcal{C}$  is the rendered pixel value and  $\mathcal{C}_i$  is the accumulated attribute including the  $i$ -th Gaussian in front-to-back order. Specifically, our backward pass starts by launching a new optixLaunch program defined in the backwards kernel, we then re-cast the same rays against the BVH to get the sorted intersections along the ray, computing the gradients via Eq. 8 and accumulating them in shared global buffers with atomic operations.
+
+# 3.5. Optimization
+
+Loss Function. Our method optimize the scene representation with the following loss functions:
+
+$$
+\mathcal {L} = \lambda_ {d} \mathcal {L} _ {d} + \lambda_ {i} \mathcal {L} _ {i} + \lambda_ {r} \mathcal {L} _ {r} + \lambda_ {C D} \mathcal {L} _ {C D}, \tag {9}
+$$
+
+where the  $\lambda_{*}$  denote the weights of the individual loss terms  $\mathcal{L}_{*}$ . The depth loss  $\mathcal{L}_d$  and intensity loss  $\mathcal{L}_i$  follow  $\mathcal{L}_1$  loss, and ray-drop loss  $\mathcal{L}_r$  follows  $\mathcal{L}_{bce}$  loss. We employ the Chamfer Distance (CD) loss  $\mathcal{L}_{CD}$  [11, 61] to jointly supervise scene geometry. The CD loss is calculated with the point-wise distance between the rendered and ground-truth point clouds:
+
+$$
+\mathcal {L} _ {\mathrm {C D}} = \frac {1}{K} \left(\sum_ {\hat {p} _ {i} \in \hat {\mathcal {S}}} \min  _ {p _ {i} \in S} \| \hat {p} _ {i} - p _ {i} \| _ {2} ^ {2} + \sum_ {p _ {i} \in S} \min  _ {\hat {p} _ {i} \in \hat {\mathcal {S}}} \| p _ {i} - \hat {p} _ {i} \| _ {2} ^ {2}\right), \tag {10}
+$$
+
+where  $K$  is  $\min (|\hat{S}|, |S|)$ ,  $\hat{S}$  and  $S$  are the rendered and ground-truth point clouds, respectively.
+
+Ray-drop Refinement. In driving scenarios, we categorize the ray-drop effects into two types: scene-level and sensor-level. Scene-level ray-drop occurs due to environmental factors like reflective materials and long detection ranges. While sensor-level ray-drop is caused by the inherent sensor biases that are independent of the scene representation, such as the hardware noises and limited visibility. Through our practice, we discovered that modeling ray-drops solely with SHs and optimizing them jointly with Gaussian primitives leads to inaccurate estimations in several areas. Inspired by LiDAR4D [61], we utilize a UNet [40]  $\mathcal{F}_{\mathrm{refine}}$  to refine the sensor-level ray-drop effects after the Gaussian optimization. Contrary to LiDAR4D, we feed the ray origins and ray directions as additional inputs so that the UNet can better percept the spatial movement of the sensor:
+
+$$
+P = \mathcal {F} _ {\text {r e f i n e}} (d, \zeta , \beta , \mathbf {r} _ {o}, \mathbf {r} _ {d}). \tag {11}
+$$
+
+We refine the rendered ray-drop mask via binary cross-entropy loss as follows:
+
+$$
+\mathcal {L} _ {r} = \frac {1}{| \mathcal {R} |} \sum_ {\mathbf {r} \in \mathcal {R}} \mathcal {L} _ {b c e} (\hat {P} (\mathbf {r}), P (\mathbf {r})). \tag {12}
+$$
+
+# 4. Implementation details
+
+The implementation of LiDAR-RT is based on PyTorch [35] and our custom CUDA kernels [14] with NVIDIA OptiX framework [34]. We train LiDAR-RT for 30000 iterations with Adam optimizers [18] following the configurations of 3DGS [17]. After that, we refine the UNet [40] model for 1000 iterations with a learning rate of  $1e^{-3}$ . In practice, the loss weights  $\lambda_{d},\lambda_{i},\lambda_{r}$ , and  $\lambda_{CD}$  are set to 0.1, 0.1, 0.01,
+
+Table 1. Quantitative comparison on the Waymo Open Dataset [42]. The resolution of range image is  $64\times 2650$  and metrics are averaged over all sequences. The cell colors present the best and the second best results, respectively.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">Efficiency</td><td colspan="5">Depth</td><td colspan="5">Intensity</td><td colspan="2">Point Cloud</td></tr><tr><td>FPS</td><td>Storage</td><td>RMSE↓</td><td>MedAE↓</td><td>LPIPS↓</td><td>SSIM↑</td><td>PSNR↑</td><td>RMSE↓</td><td>MedAE↓</td><td>LPIPS↓</td><td>SSIM↑</td><td>PSNR↑</td><td>CD↓</td><td>F-score↑</td></tr><tr><td>LiDAR-NeRF [44]</td><td>0.98</td><td>1.6 GB</td><td>7.7258</td><td>0.0518</td><td>0.3414</td><td>0.6817</td><td>20.5204</td><td>0.0659</td><td>0.0108</td><td>0.1893</td><td>0.7492</td><td>23.1612</td><td>0.1815</td><td>0.9184</td></tr><tr><td>DyNFL [49]</td><td>0.21</td><td>14.9 GB</td><td>6.9787</td><td>0.0388</td><td>0.3010</td><td>0.7080</td><td>21.3094</td><td>0.0662</td><td>0.0093</td><td>0.1382</td><td>0.7555</td><td>24.0473</td><td>0.1182</td><td>0.7786</td></tr><tr><td>LiDAR4D [61]</td><td>0.17</td><td>7.7 GB</td><td>6.6234</td><td>0.0379</td><td>0.3406</td><td>0.7008</td><td>21.8413</td><td>0.0634</td><td>0.0086</td><td>0.1854</td><td>0.7756</td><td>24.0838</td><td>0.1060</td><td>0.9437</td></tr><tr><td>Ours</td><td>20.1</td><td>1.37 GB</td><td>6.4577</td><td>0.0340</td><td>0.2918</td><td>0.7330</td><td>22.1581</td><td>0.0627</td><td>0.0101</td><td>0.1652</td><td>0.7828</td><td>23.9079</td><td>0.1002</td><td>0.9458</td></tr></table>
+
+Table 2. Quantitative comparison on the KITTI-360 benchmarks [21]. The resolution of range image is  $66\times 1030$  and metrics are averaged over all sequences. The color annotations are consistent with the Table 1 above.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">Efficiency</td><td colspan="5">Depth</td><td colspan="5">Intensity</td><td colspan="2">Point Cloud</td></tr><tr><td>FPS</td><td>Storage</td><td>RMSE↓</td><td>MedAE↓</td><td>LPIPS↓</td><td>SSIM↑</td><td>PSNR↑</td><td>RMSE↓</td><td>MedAE↓</td><td>LPIPS↓</td><td>SSIM↑</td><td>PSNR↑</td><td>CD↓</td><td>F-score↑</td></tr><tr><td>PCGen [20]</td><td>0.05</td><td>5.23 GB</td><td>5.6853</td><td>0.2040</td><td>0.5391</td><td>0.4903</td><td>23.1675</td><td>0.1970</td><td>0.0763</td><td>0.5926</td><td>0.1351</td><td>14.1181</td><td>0.4636</td><td>0.8023</td></tr><tr><td>LiDARsim [27]</td><td>0.9</td><td>0.76 GB</td><td>6.9153</td><td>0.1279</td><td>0.2926</td><td>0.6342</td><td>21.4608</td><td>0.1666</td><td>0.0569</td><td>0.3276</td><td>0.3502</td><td>15.5853</td><td>3.2228</td><td>0.7157</td></tr><tr><td>LiDAR-NeRF [44]</td><td>1.8</td><td>1.61 GB</td><td>4.0886</td><td>0.0556</td><td>0.2712</td><td>0.6309</td><td>26.0590</td><td>0.1464</td><td>0.0438</td><td>0.3590</td><td>0.3567</td><td>16.7621</td><td>0.1502</td><td>0.9073</td></tr><tr><td>LiDAR4D [61]</td><td>0.4</td><td>7.38 GB</td><td>3.5256</td><td>0.0404</td><td>0.1051</td><td>0.7647</td><td>27.4767</td><td>0.1195</td><td>0.0327</td><td>0.1845</td><td>0.5304</td><td>18.5561</td><td>0.1089</td><td>0.9272</td></tr><tr><td>Ours</td><td>42.7</td><td>0.41 GB</td><td>3.4671</td><td>0.0512</td><td>0.1016</td><td>0.8406</td><td>27.6755</td><td>0.1115</td><td>0.0271</td><td>0.1812</td><td>0.6077</td><td>19.0862</td><td>0.1077</td><td>0.9255</td></tr></table>
+
+0.01 respectively. During ray tracing, we set the chunk size to 16 for the trade-off between memory consumption and efficiency. The near plane is set to 0.2. All the experiments are conducted on one single RTX 4090 GPU.
+
+# 5. Experiments
+
+# 5.1. Experimental Setup
+
+Datasets. We conducted experiments on the public Waymo Open Dataset [42] and KITTI-360 benchmarks [21]. Both datasets is equipped with a 64-beam LiDAR sensor and an acquisition frequency of  $10\mathrm{Hz}$ . On Waymo dataset, we selecting 4 dynamic sequences and 4 static sequences for experiments. Each selected sequence has 50 continuous frames, we sample every  $10^{th}$  frame in the sequence as the test frames and use the remaining for training. On KITTI-360 dataset, we select 6 dynamic sequences and 4 static sequences for experiments and evaluate our method with the settings of LiDAR4D [61]. The sample strategy is the same as the Waymo dataset. However, the KITTI-360 dataset only provides per-frame point clouds instead of the raw range images, so we fuse the multi-frame point clouds and project the fused point clouds to range images.
+
+Baseline Methods. We perform a comprehensive comparison of our method with various types of baselines: (1) LiDARsim [27] and PCGen [20] are mesh-based reconstruction methods, we reproduce the results under the same settings in their papers. (2) LiDAR-NeRF [44] is the first NeRF-based method for LiDAR re-simulation, we use the official implementation for comparison. (3) LiDAR4D [61] and DyNFL [49] extend neural fields to dynamic scenes through 4D hybrid features and tracked bounding boxes, which are the primary methods we compare with. Please refer to the supplementary materials for more implementation details of baseline methods.
+
+Table 3. Ablation studies on dynamic sequence of the KITTI-360 dataset [21].  $\mathcal{L}_{\mathrm{CD}}$ : Chamfer Distance loss,  $\mathcal{I}$ : Point cloud initialization with normals,  $\mathcal{M}_s$ : Spatial perception ray-drop modeling. Sec. 5.3 provides the detailed description for ablation terms.  
+
+<table><tr><td rowspan="2"></td><td colspan="3">Depth</td><td colspan="3">Intensity</td><td colspan="2">Point Cloud</td></tr><tr><td>RMSE↓</td><td>SSIM↑</td><td>PSNR↑</td><td>RMSE↓</td><td>SSIM↑</td><td>PSNR↑</td><td>CD↓</td><td>F-score↑</td></tr><tr><td>w/o LCD</td><td>3.5053</td><td>0.8393</td><td>27.5526</td><td>0.1120</td><td>0.6068</td><td>19.0553</td><td>0.1192</td><td>0.9464</td></tr><tr><td>w/o I</td><td>4.0597</td><td>0.8343</td><td>26.2554</td><td>0.1141</td><td>0.6024</td><td>18.8896</td><td>0.1363</td><td>0.9389</td></tr><tr><td>w/o M</td><td>3.7445</td><td>0.7989</td><td>26.9473</td><td>0.1179</td><td>0.5687</td><td>18.6051</td><td>0.1234</td><td>0.9286</td></tr><tr><td>Ours</td><td>3.4671</td><td>0.8406</td><td>27.6755</td><td>0.1115</td><td>0.6077</td><td>19.0862</td><td>0.1077</td><td>0.9255</td></tr></table>
+
+Evaluation Metrics. Following the previous works [16, 44, 49, 61], we evaluate the performance of our method with following metrics: We use Chamfer Distance (CD) [11] and F-score (error threshold is  $5\mathrm{cm}$ ) to quantify the 3D geometric error between the generated and ground-truth point clouds. For evaluating range accuracy, we report the Root Mean Square Error (RMSE) and Median Absolute Error (MedAE), along with the PSNR, SSIM [47], and LPIPS [60] to measure the overall variance. The intensity results are evaluated in the same manner with the range. In addition, we present the efficiency of our method in terms of the inference FPS and training GPU storage.
+
+# 5.2. Comparisons with the State-of-the-art
+
+Tabs. 1, 2 and Fig. 4 show the quantitative and qualitative comparisons with the SOTA NeRF-based methods [44, 49, 61] on the Waymo [42] and KITTI-360 [21] datasets. As evident in Tab. 1 and Tab. 2, our method achieves notably better rendering quality compared to the SOTA methods [49, 61], while rendering at two orders of magnitude faster and requiring significantly less training storage. As shown in Fig. 4, LiDAR-NeRF [44] fails to model the dynamic objects, while LiDAR4D [61] suffers from blurry results and ray-drop estimation errors due to the lack of capacity of their model to capture the complex scenes. In contrast, our LiDAR-RT is capable of generating high-fidelity and physically plausible LiDAR views.
+
+![](images/8692ff57f854549418f182a80ece9a527a0b52e6abe04b52ef08551d29e24e6a.jpg)
+
+# 5.3. Ablations Studies
+
+We perform ablation studies on the dynamic sequence of the KITTI-360 dataset [21]. More qualitative and quantitative results of the ablation studies are provided in our supplementary materials.
+
+Ablation study on loss functions. As shown in Tab. 3 row 1, remove the  $\mathcal{L}_{\mathrm{CD}}$  terms not only reduces the scene geometric accuracy (CD and F-score), but also leads to the degradation of other performance metrics.
+
+Ablation study on point cloud initialization with normals. The 'w/o  $\mathcal{I}$  variant removes the normal-guided initialization for LiDAR point clouds (Sec. 3.2), which significantly impedes the quality of the scene geometry.
+
+Ablation study on ray-drop modeling. The  $w/o \mathcal{M}_s$  variant removes the proposed spatial perception ray-drop modeling module (Sec. 3.5), instead employing a naive ray-drop estimation method. This variant results in compromised ray-drop prediction accuracy and substantially degrades the final rendering quality.
+
+# 5.4. Applications
+
+Scene editing. Our instance-aware scene representation (Sec. 3.2) models each component separately and enables a wide range of scene editing operations. Fig. 5 demonstrates the high-fidelity scene editing results on the Waymo dataset [42], including trajectory manipulation (b), object insertion (c), and object removal (d).
+
+Sensor re-simulation. Thanks to our effective Gaussian-based ray tracer (Sec. 3.3), we can easily re-simulate LiDAR sensors with varying configurations. As shown in Fig. 6, our method can generate realistic LiDAR point clouds with different sensor poses, beam numbers and FOV settings. This flexibility is particularly beneficial for downstream tasks in autonomous driving.
+
+# 6. Conclusion and Discussion
+
+This paper introduces LiDAR-RT, a novel framework designed for real-time, high-fidelity LiDAR re-simulation of driving scenarios. We decompose dynamic scenes into
+
+![](images/123e9539751884f8333583773dce9e33f190314a581cd553373087520c696991.jpg)  
+Figure 5. Scene editing results on the Waymo dataset [42]. Our method supports various scene editing operations, including trajectory manipulation, object insertion, and object removal. The boxes  $(\square/\square)$  highlight the edited objects.  
+Figure 6. LiDAR re-simulation results with different sensor configurations on the Waymo dataset [42].
+
+a static background and multiple moving objects, each represented by a set of Gaussian primitives, and incorporate scene graphs to handle scene dynamics. Furthermore, we have developed a differentiable rendering pipeline that utilizes the hardware-accelerated ray tracing algorithms to generate realistic novel LiDAR views, also maintaining great performance under various scene editing operations and sensor configurations. Extensive experiments across various public autonomous driving benchmarks have demonstrated that our method achieves SOTA performance in terms of rendering quality and efficiency.
+
+However, our method has certain limitations. Firstly, LiDAR-RT cannot accurately model non-rigid objects such as pedestrians and cyclists due to their substantial deformations across frames, which are important for some downstream tasks. Moreover, the performance and rendering speed of LiDAR-RT are impacted when dealing with long driving sequences, as the number of Gaussian primitives increases dramatically. How to model non-rigid objects and improve the efficiency for long sequences are remaining challenges for future works. Additionally, more physically accurate LiDAR modeling is worth exploring, such as the material estimation and reflections.
+
+# Acknowledgement
+
+This paper was partially supported by National Natural Science Foundation of China (NO. 62402427, U23A20313, 62372471), The Science Foundation for Distinguished Young Scholars of Hunan Province (NO. 2023JJ10080), and Zhejiang University Education Foundation Qizhen Scholar Foundation.
+
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CVPR/2025/LiMoE_ Mixture of LiDAR Representation Learners from Automotive Scenes/full.md

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+# LiMoE: Mixture of LiDAR Representation Learners from Automotive Scenes
+
+Xiang  $\mathrm{Xu}^{*,1}$
+
+Lingdong Kong\*,2,3
+
+Hui Shuai4
+
+Liang Pan<sup>3</sup>
+
+Ziwei Liu<sup>5</sup>
+
+Qingshan Liu4,
+
+$^{1}$ Nanjing University of Aeronautics and Astronautics
+
+$^{2}$ National University of Singapore
+
+$^{3}$ Shanghai AI Laboratory
+
+$^{4}$ Nanjing University of Posts and Telecommunications
+
+$^{5}$ S-Lab, Nanyang Technological University
+
+Code & Checkpoints: https://github.com/Xiangxu-0103/LiMoE
+
+# Abstract
+
+LiDAR data pretraining offers a promising approach to leveraging large-scale, readily available datasets for enhanced data utilization. However, existing methods predominantly focus on sparse voxel representation, overlooking the complementary attributes provided by other LiDAR representations. In this work, we propose LiMoE, a framework that integrates the Mixture of Experts (MoE) paradigm into LiDAR data representation learning to synergistically combine multiple representations, such as range images, sparse voxels, and raw points. Our approach consists of three stages: i) Image-to-LiDAR Pretraining, which transfers prior knowledge from images to point clouds across different representations; ii) Contrastive Mixture Learning (CML), which uses MoE to adaptively activate relevant attributes from each representation and distills these mixed features into a unified 3D network; iii) Semantic Mixture Supervision (SMS), which combines semantic logits from multiple representations to boost downstream segmentation performance. Extensive experiments across eleven large-scale LiDAR datasets demonstrate our effectiveness and superiority. The code has been made publicly accessible.
+
+# 1. Introduction
+
+LiDAR perception is a cornerstone of modern autonomous driving systems, offering precise 3D spatial understanding crucial for navigation and safety [24, 38, 51, 57]. However, developing accurate and scalable 3D perception models typically relies on large-scale, human-annotated datasets - a process that is both costly and labor-intensive [9, 23, 75]. This reliance presents a significant bottleneck in scaling autonomous systems, especially given the vast amount of sensor data generated in real-world driving environments [47].
+
+Recently, data representation learning has emerged as a promising solution to this challenge. By leveraging largescale, easily accessible datasets, representation learning enables the extraction of meaningful data attributes without heavy reliance on manual annotations [3, 83]. One line of
+
+![](images/125b7581ca0f1a244eab021c7e688dba02467fcf3e4986d5847218e4092dbe6e.jpg)  
+Figure 1. Illustration of the proposed mixture of LiDAR representation learning (LiMoE) design. We observe unique patterns of each LiDAR representation (range, voxel, and point) in image-to-LiDAR data pretraining. Our framework aims to integrate distinct attributes from different LiDAR representations into a unified feature space, enabling enhanced 3D scene understanding.
+
+this research [77, 87] augments point clouds into different views and employs contrastive learning across these views for feature consistency. The other line [43, 45, 63, 80] transfers knowledge from the image [18, 25] to LiDAR space [14], facilitating cross-modal learning for large-scale LiDAR scene understanding. However, these methods rely solely on sparse voxels [14], failing to fully explore the complementary information existing in the LiDAR scene.
+
+LiDAR data can be converted into various representations, i.e., range view, sparse voxels, and raw points, each offering unique advantages. Range images provide a compact 2D representation that excels at capturing dynamic elements and medium-range objects [36, 50, 81]. Raw points preserve fine geometric details, enabling precise modeling of intricate structures [30, 82]. Sparse voxels efficiently represent static objects and sparse regions, making them ideal for large-scale environments [14, 28, 91]. Harnessing the complementary strengths of these representations holds the key to robust and comprehensive LiDAR-based perception.
+
+In this work, we present LiMoE, a novel framework that synergistically integrates three LiDAR representations into
+
+a unified representation for feature learning. The framework operates in three stages: ① Image-to-LiDAR pretraining, where knowledge from pretrained image backbone is transferred to LiDAR points for each representation [63, 80], initializing diverse representation-specific features; ② Contrastive mixture learning (CML), which fuses pretrained features across representations into a unified representation, leveraging their complementary strengths; and ③ Semantic mixture supervision (SMS), which enhances downstream performance by combining multiple semantic logits.
+
+We observe that pretrained models with different LiDAR representations capture distinct data attributes (see Fig. 1). Range images primarily focus on middle laser beams and distances, sparse voxels emphasize upper beams and longer distances, while points capture lower beams and near distances. To effectively integrate these complementary attributes into a unified representation, CML employs a Mixture of Experts (MoE) layer that dynamically activates the relevant data attributes during pretraining. By distilling the combined features into a single representation feature, CML encourages the pretrained network to comprise comprehensive attributes derived from various representations.
+
+In the downstream stage, we observe that different representation models capture distinct object attributes. Range images primarily focus on dynamic objects, sparse voxels emphasize static background structures, while points preserve fine-grained details. To further improve downstream performance, we extend the MoE layer into SMS, which dynamically activates relevant semantic features from various representations. With the supervision of semantic labels, SMS establishes a robust and scalable framework that enhances 3D scene understanding by leveraging complementary semantic features from each LiDAR representation.
+
+To summarize, this work makes contributions as follows:
+
+- We propose LiMoE, a novel framework that integrates multiple LiDAR representations dynamically through the MoE paradigm. To our knowledge, this is the first work to explore MoE for LiDAR representation learning.  
+- We introduce a three-stage pipeline for enhanced LiDAR scene understanding, comprising knowledge transfer from images to LiDAR, the mixture of data attributes for single-representation pretraining, and integration of semantic attributes for downstream tasks, which offers a robust solution for LiDAR representation learning.  
+- Extensive experiments verify the effectiveness of our approach, achieving large gains over the state-of-the-art method on 11 datasets, paving the way for developing scalable, robust, and generalizable automotive systems.
+
+# 2. Related Work
+
+LiDAR Data Representations. LiDAR point clouds, being irregular and unstructured, pose significant challenges for scene understanding [23, 29, 47]. Recent approaches
+
+have sought to address this by transforming point clouds into structured representations. Point-based methods [30, 66, 82] process point clouds directly, preserving their full structure and enabling the capture of fine-grained details. Range view-based methods [17, 36, 50, 78, 81] and bird's eye view-based methods [10, 86, 89] convert point clouds into 2D representations, leveraging image-processing techniques for efficient identification of dynamic or significant objects. Voxel-based methods [14, 28, 91] discretize point clouds into regular voxel grids and use sparse convolutions [16, 70, 71] to efficiently process sparse regions within the data, making them suitable for large-scale environments.
+
+Multi-Representation LiDAR Segmentation. To capture comprehensive information from various LiDAR representations, recent works have combined multiple representations to explore their complementary strengths [44, 58]. AMVNet [41] and RPVNet [79] employ late-fusion strategies, where features from each representation are processed independently and fused at the final stage. GFNet [59] introduces a more advanced fusion method by combining features from multiple views at different stages. UniSeg [42] uses hierarchical fusion to integrate low-level features with high-level semantic information. In contrast, our approach leverages the Mixture of Experts (MoE) framework, which dynamically activates the most relevant features from multiple representations based on task context.
+
+Image-to-LiDAR Data Pretraining. Inspired by the success of self-supervised learning in the image domain [11, 26, 27], recent work has explored 3D data representation learning [5, 64, 77, 87], which are limited to single-modality learning for small-scale scenes. The SLidR framework [63] introduced multi-modal self-supervised learning by transferring 2D image knowledge to 3D LiDAR models using contrastive learning. Subsequent works expanded this framework with class balancing [48], hybrid-view distillation [85], VFM-assisted superpixels [43], spatiotemporal cues [80], etc. Our work builds upon this by extending image-to-LiDAR pretraining to multiple LiDAR representations, capturing comprehensive LiDAR attributes.
+
+Mixture of Experts. The Mixture of Experts (MoE) framework consists of multiple sub-models that collectively enhance the model's capacity [7, 20, 49]. MoE dynamically selects a subset of experts to activate based on input, which increases scalability and flexibility for handling diverse tasks. This approach has been widely successful in Large Language Models (LLMs) [19, 21, 40, 88, 90]. Recently, MoE has been applied to vision tasks, including image classification [13, 61, 65], object detection [12, 31, 73], and segmentation [33, 56]. However, MoE remains under-explored in 3D perception. In this work, we extend MoE to 3D data representation, enabling dynamic fusion of multiple LiDAR representations for improved scene understanding.
+
+# 3. Methodology
+
+This work addresses LiDAR-based perception by leveraging multiple data representations to capture complementary information and enhance 3D scene understanding. We first describe the three common LiDAR representations and analyze their strengths (Sec. 3.1). Then, we detail the components of the LiMoE framework, as illustrated in Fig. 2. This comprises three stages: ① cross-sensor knowledge transfer from images to LiDAR data (Sec. 3.2); ② mixture of LiDAR data attributes for pretraining (Sec. 3.3); ③ mixture of semantic attributes, supervised by human-annotated labels, for downstream segmentation tasks (Sec. 3.4).
+
+# 3.1. LiDAR Representation
+
+Let  $\mathcal{P} = \{\mathbf{p}_i\mid i = 1,\dots ,N\}$  denote a LiDAR point cloud consisting of  $N$  points, where each point  $\mathbf{p}_i\in \mathbb{R}^{3 + L}$  includes 3D coordinates  $(x_{i},y_{i},z_{i})$  and  $L$  -dimensional features (e.g., intensity, elongation). To harness the unstructured and irregular points, various methods convert point clouds into intermediate representations, including range images  $\mathcal{P}_{\mathbf{r}}$ , sparse voxels  $\mathcal{P}_{\mathbf{v}}$ , and raw points  $\mathcal{P}_{\mathbf{p}}$ .
+
+Range View. The range image methods project the point cloud  $\mathcal{P}$  onto 2D grids in spherical coordinates. Each point  $\mathbf{p}_i$  is mapped to a 2D grid  $(u_i^r, v_i^r)$  in the range image as:
+
+$$
+\binom {u _ {i} ^ {r}} {v _ {i} ^ {r}} = \binom {\frac {1}{2} \left[ 1 - \arctan \left(y _ {i}, x _ {i}\right) \pi^ {- 1} \right] W _ {r}} {\left[ 1 - \left(\arcsin \left(z _ {i} d _ {i} ^ {- 1}\right) + \phi_ {\text {d o w n}}\right) \phi^ {- 1} \right] H _ {r}}, \tag {1}
+$$
+
+where  $d_{i}$  represents the depth of the point;  $\phi$  denotes the vertical field-of-view of the sensor;  $\phi_{\mathrm{down}}$  is the inclination angles in the downward directions;  $H_{r}$  and  $W_{r}$  are the height and width of the range image. This projection results in a range image  $\mathcal{P}_{\mathrm{r}} \in \mathbb{R}^{H_r \times W_r \times (3 + L)}$ , allowing for efficient processing with image-based techniques. Range images offer a compact 2D representation of the 3D scene, capturing both geometric and intensity-based features [36, 50]. They are particularly effective in tackling dynamic or significant objects in the scene [39, 81].
+
+Sparse Voxels. The voxel-based methods discretize the point cloud  $\mathcal{P}$  into regular voxel grids  $\mathcal{P}_{\mathbf{v}}$ , where each voxel represents a small region of 3D space. For each point  $\mathbf{p}_i$ , its position is mapped to the corresponding voxel grid index as  $[v_i^x, v_i^y, v_i^z] = [\lfloor x_i / s_x \rfloor, \lfloor y_i / s_y \rfloor, \lfloor z_i / s_z \rfloor]$ , where  $(s_x, s_y, s_z)$  are the voxel sizes along the  $x, y$  and  $z$  dimensions. This discretization results in sparse voxel grids  $\mathcal{P}_{\mathbf{v}} \in \mathbb{R}^{M \times C}$ , where  $M < N$  is the number of non-empty voxels. To effectively process sparse voxels, sparse convolutions [14, 16, 70, 71] are employed, significantly reducing the computational complexity compared to regular voxel grids. Sparse voxels are particularly well-suited for representing large, sparsely populated areas, but can lose detail in dense regions due to quantization effects [14, 91].
+
+Raw Points. The point-based methods process the point
+
+cloud (i.e.,  $\mathcal{P}_{\mathrm{p}} = \mathcal{P}$ ) without converting to other representations. These methods typically involve three key steps: 1) Sampling a set of central points (centroids) from the point cloud; 2) Neighbor search, where points in the vicinity of each centroid are identified based on spatial proximity; 3) Feature aggregation, where MLPs are used to combine the features of neighboring points and propagate them to the centroids. While raw points preserve the fine-grained structure of the scene, they are computationally expensive due to the need for point-wise operations [30, 82].
+
+# 3.2. Image-to-LiDAR Pretraining
+
+Image-to-LiDAR pretraining aims to transfer knowledge from images to LiDAR data, facilitating the learning of effective 3D representations even in the absence of extensive LiDAR labels. Previous works [43, 48, 63, 80] have largely focused on sparse voxel representations for this task, as they offer efficient processing for large-scale LiDAR data.
+
+Given a set of  $V$  synchronized images  $\mathcal{I} = \{\mathbf{I}_i\mid i = 1,\dots ,V\}$  and their corresponding LiDAR point clouds  $\mathcal{P}$  where each image  $\mathbf{I}\in \mathbb{R}^{H\times W\times 3}$  has a spatial resolution with height  $H$  and width  $W$ . Each LiDAR point  $\mathbf{p}_i$  can be projected onto the corresponding image plane  $(u_{i},v_{i})$  as:
+
+$$
+\left[ u _ {i}, v _ {i} \right] ^ {\mathrm {T}} = \left(1 / z _ {i}\right) \times \Gamma_ {K} \times \Gamma_ {l \rightarrow c} \times \left[ x _ {i}, y _ {i}, z _ {i} \right] ^ {\mathrm {T}}, \qquad (2)
+$$
+
+where  $\Gamma_{l\rightarrow c}$  is the transformation matrix from the LiDAR to the camera coordinate system, and  $\Gamma_K$  is the camera intrinsic matrix. This pretraining process involves two key steps, as shown on the left side (Phase #1) of Fig. 2.
+
+Superpixel & Superpoint Generation. To establish correlations between images and the point cloud, prior works use the unsupervised SLIC algorithm [1] or vision foundation models (VFMs) [34, 84, 92, 93] to generate a set of  $S$  superpixels for each image, denoted as  $\Psi = \{\psi_i \mid i = 1, \dots, S\}$ . The corresponding superpoint set  $\Omega = \{\omega_i \mid i = 1, \dots, S\}$  is then derived by projecting these superpixels onto the point cloud using the transformation in Eq. (2).
+
+Contrastive Objective. To transfer the knowledge from images to LiDAR, both image and sparse voxel data are passed through their respective backbones: the 2D pretrained backbone  $\mathcal{F}_c$  for images and the 3D voxel backbone  $\mathcal{F}_{\mathbf{v}}$  for sparse voxels. This generates the respective image and voxel features. These features are then processed by linear projection heads  $\mathcal{H}_c$  and  $\mathcal{H}_{\mathbf{v}}$ , which align the feature spaces and produce  $D$ -dimensional feature embeddings. The image and voxel features are then grouped based on superpixels  $\Psi$  and superpoints  $\Omega$ , resulting in superpixel embeddings  $\mathbf{Q} \in \mathbb{R}^{S \times D}$  and superpoint embeddings  $\mathbf{K} \in \mathbb{R}^{S \times D}$ . Finally, a contrastive loss is applied to ensure that each superpoint embedding is closely correlated with its corresponding superpixel embedding:
+
+$$
+\mathcal {L} _ {\mathrm {c o n}} = \frac {1}{S} \sum_ {i = 1} ^ {S} \log \frac {e ^ {\langle \mathbf {k} _ {i} , \mathbf {q} _ {i} \rangle / \tau}}{\sum_ {j \neq i} e ^ {\langle \mathbf {k} _ {i} , \mathbf {q} _ {j} \rangle / \tau}}, \tag {3}
+$$
+
+![](images/1715540640e15cbeb924a4fda7397bd5fc451f9d3ceaf4ba223a3b6e55b871a6.jpg)  
+Figure 2. Overview of the LiMoE framework. Our design consists of three stages: (#1) The image-to-LiDAR pretraining transfers knowledge from images to various LiDAR representations (cf. Sec. 3.2); (#2) The contrastive mixture learning (CML) integrates the MoE framework to mix data attributes into a unified representation for pretraining (cf. Sec. 3.3); and (#3) The semantic mixture supervision (SMS) fuses semantic logits from multiple representations to further enhance performance across different downstream tasks (cf. Sec. 3.4).
+
+![](images/3ad33b400f6fd05e8f5b8fe6b106bc7ec9de26fcdc0584b2a5756b356318b144.jpg)
+
+![](images/3f528d686319e101879d04884983d7befef695b283d90f3455b4cd02587d48ae.jpg)
+
+where  $\langle \cdot ,\cdot \rangle$  denotes the dot product between the superpixel and superpoint embeddings, and  $\tau >0$  is a temperature.
+
+However, sparse voxel-based pretraining is limited in its ability to fully exploit the detailed geometry and appearance characteristics of 3D scenes. In fact, LiDAR point clouds can be represented in various forms, each emphasizing different attributes, such as laser beams, distance, and static/dynamic objects, within the scene [79]. To this end, we propose a novel pretraining paradigm that integrates multiple representations of LiDAR point clouds. This approach enables a more comprehensive understanding of the scenes by capturing both geometric and detailed information across diverse representations, ultimately constructing a richer, more detailed representation of 3D environments.
+
+# 3.3. CML: Contrastive Mixture Learning
+
+We extend the image-to-LiDAR pretraining method by independently training three separate 3D networks for each representation: range images, sparse voxels, and raw points. These networks serve as the foundation for our CML approach. As shown in the middle of Fig. 2, each network processes the point cloud in its respective representation form:
+
+$$
+\mathbf {E} _ {\mathrm {r}} = \mathcal {H} _ {\mathrm {r}} \left(\mathcal {F} _ {\mathrm {r}} \left(\mathcal {P} _ {\mathrm {r}}\right)\right) \in \mathbb {R} ^ {H _ {r} \times W _ {r} \times D},
+$$
+
+$$
+\mathbf {E} _ {\mathbf {v}} = \mathcal {H} _ {\mathbf {v}} \left(\mathcal {F} _ {\mathbf {v}} \left(\mathcal {P} _ {\mathbf {v}}\right)\right) \in \mathbb {R} ^ {M \times D}, \tag {4}
+$$
+
+$$
+\mathbf {E} _ {\mathrm {p}} = \mathcal {H} _ {\mathrm {p}} (\mathcal {F} _ {\mathrm {p}} (\mathcal {P} _ {\mathrm {p}})) \in \mathbb {R} ^ {N \times D}.
+$$
+
+Following the success of the Mixture of Experts (MoE) approach [40, 88], we introduce an MoE layer that dynamically selects and combines relevant features from different representations for each point.
+
+Feature Alignment. The features generated from each representation, as in Eq. (4), vary significantly due to the different representation attributes. To align these features, we project the range image and sparse voxel features into the point cloud space. This results in aligned feature sets  $\widehat{\mathbf{E}}_{\mathrm{r}}$ ,  $\widehat{\mathbf{E}}_{\mathrm{v}}$ , and  $\widehat{\mathbf{E}}_{\mathrm{p}}$ , all with the form  $\mathbb{R}^{N\times D}$ , ensuring consistent feature space across these three representations.
+
+MoE Layer. This layer takes  $\widehat{\mathbf{E}}_{\mathrm{r}}$ ,  $\widehat{\mathbf{E}}_{\mathrm{v}}$ , and  $\widehat{\mathbf{E}}_{\mathrm{p}}$  as the input. To combine the features from these three representations, we first concatenate them and then apply an MLP layer to reduce the channel dimension. The MoE layer consists of two key components: a gate module, which dynamically selects the activated representation for each point, and a noise module, which introduces perturbations to prevent overfitting. This process can be formulated as follows:
+
+$$
+\mathbf {G} = \mathbf {E} \cdot \mathbf {Z} _ {g} + \chi \cdot \sigma (\mathbf {E} \cdot \mathbf {Z} _ {n}), \tag {5}
+$$
+
+$$
+\mathbf {E} = \operatorname {M L P} \left(\left[ \widehat {\mathbf {E}} _ {\mathrm {r}}, \widehat {\mathbf {E}} _ {\mathrm {v}}, \widehat {\mathbf {E}} _ {\mathrm {p}} \right]\right). \tag {6}
+$$
+
+Here,  $\mathbf{Z}_g\in \mathbb{R}^{D\times 3}$  and  $\mathbf{Z}_n\in \mathbb{R}^{D\times 3}$  are trainable weights for the gate and noise modules, respectively. The variable  $\chi$  represents a random noise distribution, which is applied in the noise module to introduce variability into the feature
+
+![](images/a5b861cde11baaf6c1b1598a39af25ae6086d08e6dea42a714fdf8ad109e16d8.jpg)  
+Figure 3. Visual interpretations of the expert activation paths in CML. The experts are #1 range view, #2 voxel, and #3 point, respectively.
+
+![](images/56e2b9efa131184255dd4d0da6d3f4e0c6a7bc6241ffe95d1715cbbe61c35e3a.jpg)
+
+selection process. The function  $\sigma$  denotes the Softplus activation [52], ensuring that the perturbations remain positive and smooth. The operation  $[\cdot, \cdot]$  denotes feature concatenation. A softmax function is then applied to the gate values  $\mathbf{G}$ , yielding selection scores  $\widehat{\mathbf{G}} \in \mathbb{R}^{N \times 3}$ . These scores are then split into  $\alpha$ ,  $\beta$ , and  $\gamma$  for each representation, respectively, indicating the importance of each representation for each point. The final output features are obtained by weighting and summing the features from each representation:  $\mathbf{E}_{\mathrm{moe}} = \alpha \widehat{\mathbf{E}}_{\mathrm{r}} + \beta \widehat{\mathbf{E}}_{\mathrm{v}} + \gamma \widehat{\mathbf{E}}_{\mathrm{p}}$ . These features capture the dynamic contributions of each representation, enabling the model to adaptively prioritize the most relevant features for each point in the LiDAR point cloud. This selective feature fusion enables the network to leverage the strengths of each representation dependent on the context, thereby improving its ability to capture detailed scene attributes.
+
+Training Objective. In this stage, the goal is to distill the MoE features from multiple representations into a single Li-DAR representation (range, voxel, or point). To accomplish this, we use a 3D student network to extract corresponding student features  $\mathbf{E}_l^s = \mathcal{H}_l^s (\mathcal{F}_l^s (\mathcal{P}_l))$ $(l\in \{\mathbf{r},\mathbf{v},\mathbf{p}\})$ . Then, the MoE features and student features are grouped based on superpoints to generate the superpoint embeddings  $\mathbf{K}^{\mathrm{moe}}$  and  $\mathbf{K}^l$ . A contrastive loss is then applied between them as:
+
+$$
+\mathcal {L} _ {\mathrm {C M L}} = \frac {1}{S} \sum_ {i = 1} ^ {S} \log \frac {e ^ {\langle \mathbf {k} _ {i} ^ {l} , \mathbf {k} _ {i} ^ {\mathrm {m o e}} \rangle / \tau}}{\sum_ {j \neq i} e ^ {\langle \mathbf {k} _ {i} ^ {l} , \mathbf {k} _ {j} ^ {\mathrm {m o e}} \rangle / \tau}}. \tag {7}
+$$
+
+The contrastive loss encourages the student features to align with the MoE features, allowing the single 3D student network to effectively capture informative structures from all the different representations. As depicted in Fig. 3, CML encourages the MoE framework to focus on data attributes from laser beams and distances.
+
+# 3.4. SMS: Semantic Mixture Supervision
+
+To further improve downstream semantic segmentation performance, we extend the MoE layer into the downstream tasks, as shown in the right side of Fig. 2. This integration enables the model to dynamically select and prioritize the most relevant object attributes from each representation, tailoring feature fusion to the specific context of the task. Building upon the pretrained representations in Sec. 3.3, each backbone independently processes the point cloud to
+
+generate semantic logits for each representation:
+
+$$
+\mathbf {Y} _ {\mathrm {r}} = \widetilde {\mathcal {H}} _ {\mathrm {r}} ^ {s} \left(\mathcal {F} _ {\mathrm {r}} ^ {s} \left(\mathcal {P} _ {\mathrm {r}}\right)\right) \in \mathbb {R} ^ {H _ {r} \times W _ {r} \times C},
+$$
+
+$$
+\mathbf {Y} _ {\mathbf {v}} = \widetilde {\mathcal {H}} _ {\mathbf {v}} ^ {s} \left(\mathcal {F} _ {\mathbf {v}} ^ {s} \left(\mathcal {P} _ {\mathbf {v}}\right)\right) \in \mathbb {R} ^ {M \times C}, \tag {8}
+$$
+
+$$
+\mathbf {Y} _ {\mathrm {p}} = \widetilde {\mathcal {H}} _ {\mathrm {p}} ^ {s} (\mathcal {F} _ {\mathrm {p}} ^ {s} (\mathcal {P} _ {\mathrm {p}})) \in \mathbb {R} ^ {N \times C},
+$$
+
+where  $C$  is the number of semantic classes.  $\widetilde{\mathcal{H}}_{\mathrm{r}}^{s}$ ,  $\widetilde{\mathcal{H}}_{\mathrm{v}}^{s}$ , and  $\widetilde{\mathcal{H}}_{\mathrm{p}}^{s}$  are linear heads that project backbone features into semantic logits for each representation. To align logits across representations, we project them into the point cloud space, yielding  $\widehat{\mathbf{Y}}_{\mathrm{r}}$ ,  $\widehat{\mathbf{Y}}_{\mathrm{v}}$ , and  $\widehat{\mathbf{Y}}_{\mathrm{p}}$ , each with a form of  $\mathbb{R}^{N\times C}$ .
+
+The MoE layer consists of a gating module that dynamically selects the activated representations for each point, and a noise module that introduces perturbations to the features during training to mitigate overfitting. Different from Eq. (5), the noise gate is only active during training. The whole process can be formulated as:
+
+$$
+\mathbf {G} _ {d} = \mathbf {Y} \cdot \mathbf {Z} _ {g} + \zeta \cdot \chi \cdot \sigma (\mathbf {Y} \cdot \mathbf {Z} _ {n}), \tag {9}
+$$
+
+where  $\zeta = 1$  for training and  $\zeta = 0$  for inference, and  $\mathbf{Y} = \mathrm{MLP}([\widehat{\mathbf{Y}}_{\mathrm{r}},\widehat{\mathbf{Y}}_{\mathrm{v}},\widehat{\mathbf{Y}}_{\mathrm{p}}])$ . After applying the softmax function to the gate value  $\mathbf{G}_d$ , we obtain the coefficients  $\alpha_d$ ,  $\beta_d$ , and  $\gamma_d$ , which indicate the relative importance of each representation for every point. The final semantic logits are obtained by a weighted sum of the logits from each representation:  $\mathbf{Y}_{\mathrm{moe}} = \alpha_d\widehat{\mathbf{Y}}_{\mathrm{r}} + \beta_d\widehat{\mathbf{Y}}_{\mathrm{v}} + \gamma_d\widehat{\mathbf{Y}}_{\mathrm{p}}$ .
+
+Training Objective. Let  $\mathcal{X} \in \mathbb{R}^N$  denote the semantic labels for the point cloud  $\mathcal{P}$ . For each representation, these labels can be projected as follows:  $\mathcal{X}_{\mathrm{r}} \in \mathbb{R}^{H_r \times W_r}$  for the range image,  $\mathcal{X}_{\mathrm{v}} \in \mathbb{R}^M$  for the sparse voxels, and  $\mathcal{X}_{\mathrm{p}} \in \mathbb{R}^N$  for raw points. Each representation is fine-tuned independently with a supervised loss that aligns the predicted logits with the corresponding projected semantic labels. In addition, we apply an MoE-based supervised loss at the output to further refine the model by selecting the most relevant features from each representation. The overall loss is:
+
+$$
+\mathcal {L} _ {\mathrm {S M S}} = \mathcal {L} _ {\mathrm {d}} (\mathcal {X}, \mathbf {Y} _ {\mathrm {m o e}}) + \sum_ {l \in \{\mathbf {r}, \mathbf {v}, \mathbf {p} \}} \mathcal {L} _ {l} (\mathcal {X} _ {l}, \mathbf {Y} _ {l}), \tag {10}
+$$
+
+where each  $\mathcal{L}_l$  (for  $l\in \{d,\mathbf{r},\mathbf{v},\mathbf{p}\}$ ) is a weighted combination of Cross-Entropy, Lovasz-Softmax [4], and Boundary loss [60], contributing to a comprehensive optimization of the segmentation performance across all representations.
+
+Table 1. Comparisons of state-of-the-art LiDAR pretraining methods pretrained on nuScenes [6] and fine-tuned on nuScenes [22], SemanticKITTI [2], and Waymo Open [68] datasets, respectively, with specified data portions. LP denotes linear probing with frozen backbones. All scores are given in percentage (\%). The best and 2nd best scores under each group are highlighted in bold and underline.  
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">Venue</td><td rowspan="2">Backbone (2D)</td><td rowspan="2">Backbone (3D)</td><td rowspan="2">Expert</td><td colspan="6">nuScenes</td><td rowspan="2">KITTI 1%</td><td rowspan="2">Waymo 1%</td></tr><tr><td>LP</td><td>1%</td><td>5%</td><td>10%</td><td>25%</td><td>Full</td></tr><tr><td>Random</td><td>-</td><td>-</td><td>-</td><td>-</td><td>8.10</td><td>30.30</td><td>47.84</td><td>56.15</td><td>65.48</td><td>74.66</td><td>39.50</td><td>39.41</td></tr><tr><td>SLidR [63]</td><td>CVPR&#x27;22</td><td>ResNet-50</td><td>MinkUNet-34</td><td>Single○</td><td>38.80</td><td>38.30</td><td>52.49</td><td>59.84</td><td>66.91</td><td>74.79</td><td>44.60</td><td>47.12</td></tr><tr><td>TriCC [55]</td><td>CVPR&#x27;23</td><td>NeurIPS&#x27;23</td><td>[25]</td><td>Single○</td><td>38.00</td><td>41.20</td><td>54.10</td><td>60.40</td><td>67.60</td><td>75.60</td><td>45.90</td><td>-</td></tr><tr><td>Seal [43]</td><td>CSC [8]</td><td>CVPR&#x27;24</td><td>[14]</td><td>Single○</td><td>44.95</td><td>45.84</td><td>55.64</td><td>62.97</td><td>68.41</td><td>75.60</td><td>46.63</td><td>49.34</td></tr><tr><td>HVDistill [85]</td><td>[85]</td><td>IJCV&#x27;24</td><td></td><td>Single○</td><td>46.00</td><td>47.00</td><td>57.00</td><td>63.30</td><td>68.60</td><td>75.70</td><td>47.20</td><td>-</td></tr><tr><td></td><td></td><td></td><td></td><td>Single○</td><td>39.50</td><td>42.70</td><td>56.60</td><td>62.90</td><td>69.30</td><td>76.60</td><td>49.70</td><td>-</td></tr><tr><td>SLidR [63]</td><td>CVPR&#x27;22</td><td>Vit-S</td><td>MinkUNet-34</td><td>Single○</td><td>44.70</td><td>41.16</td><td>53.65</td><td>61.47</td><td>66.71</td><td>74.20</td><td>44.67</td><td>47.57</td></tr><tr><td>+ LiMoE</td><td>Ours</td><td></td><td></td><td>Multi○</td><td>45.80</td><td>46.82</td><td>57.54</td><td>63.85</td><td>68.61</td><td>75.64</td><td>46.81</td><td>48.81</td></tr><tr><td>Seal [43]</td><td>NeurIPS&#x27;23</td><td>ECCV&#x27;24</td><td>[14]</td><td>Single○</td><td>45.16</td><td>44.27</td><td>55.13</td><td>62.46</td><td>67.64</td><td>75.58</td><td>46.51</td><td>48.67</td></tr><tr><td>SuperFlow [80]</td><td>+ LiMoE</td><td>Ours</td><td></td><td>Single○</td><td>46.44</td><td>47.81</td><td>59.44</td><td>64.47</td><td>69.20</td><td>76.54</td><td>47.97</td><td>49.94</td></tr><tr><td></td><td></td><td></td><td></td><td>Multi○</td><td>48.20</td><td>49.60</td><td>60.54</td><td>65.65</td><td>71.39</td><td>77.27</td><td>49.53</td><td>51.42</td></tr><tr><td>SLidR [63]</td><td>CVPR&#x27;22</td><td>Vit-B</td><td>MinkUNet-34</td><td>Single○</td><td>45.35</td><td>41.64</td><td>55.83</td><td>62.68</td><td>67.61</td><td>74.98</td><td>45.50</td><td>48.32</td></tr><tr><td>+ LiMoE</td><td>Ours</td><td></td><td></td><td>Multi○</td><td>46.56</td><td>46.89</td><td>58.09</td><td>63.87</td><td>69.02</td><td>75.87</td><td>47.96</td><td>49.50</td></tr><tr><td>Seal [43]</td><td>NeurIPS&#x27;23</td><td>ECCV&#x27;24</td><td>[14]</td><td>Single○</td><td>46.59</td><td>45.98</td><td>57.15</td><td>62.79</td><td>68.18</td><td>75.41</td><td>47.24</td><td>48.91</td></tr><tr><td>SuperFlow [80]</td><td>+ LiMoE</td><td>Ours</td><td></td><td>Single○</td><td>47.66</td><td>48.09</td><td>59.66</td><td>64.52</td><td>69.79</td><td>76.57</td><td>48.40</td><td>50.20</td></tr><tr><td></td><td></td><td></td><td></td><td>Multi○</td><td>49.07</td><td>50.23</td><td>61.51</td><td>66.17</td><td>71.56</td><td>77.81</td><td>50.30</td><td>51.77</td></tr><tr><td>SLidR [63]</td><td>CVPR&#x27;22</td><td>Vit-L</td><td>MinkUNet-34</td><td>Single○</td><td>45.70</td><td>42.77</td><td>57.45</td><td>63.20</td><td>68.13</td><td>75.51</td><td>47.01</td><td>48.60</td></tr><tr><td>+ LiMoE</td><td>Ours</td><td></td><td></td><td>Multi○</td><td>47.43</td><td>46.92</td><td>58.41</td><td>64.54</td><td>69.69</td><td>76.32</td><td>48.25</td><td>50.23</td></tr><tr><td>Seal [43]</td><td>NeurIPS&#x27;23</td><td>ECCV&#x27;24</td><td>[14]</td><td>Single○</td><td>46.81</td><td>46.27</td><td>58.14</td><td>63.27</td><td>68.67</td><td>75.66</td><td>47.55</td><td>50.02</td></tr><tr><td>SuperFlow [80]</td><td>+ LiMoE</td><td>Ours</td><td></td><td>Single○</td><td>48.01</td><td>49.95</td><td>60.72</td><td>65.09</td><td>70.01</td><td>77.19</td><td>49.07</td><td>50.67</td></tr><tr><td></td><td></td><td></td><td></td><td>Multi○</td><td>49.35</td><td>51.41</td><td>62.07</td><td>66.64</td><td>71.59</td><td>77.85</td><td>50.69</td><td>51.93</td></tr></table>
+
+Table 2. Domain generalization study of different LiDAR pretraining methods pretrained on the nuScenes [6] dataset and fine-tuned on a collection of seven different LiDAR semantic segmentation datasets [32, 35, 54, 62, 72, 74, 76], respectively, with specific data portions. All scores are given in percentage (\%). The best and 2nd best scores from each metric are highlighted in bold and underline.  
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">Venue</td><td colspan="2">SciKITTI</td><td colspan="2">Rellis-3D</td><td colspan="2">SemPOSS</td><td colspan="2">SemSTF</td><td colspan="2">SynLiDAR</td><td colspan="2">DAPS-3D</td><td colspan="2">Synth4D</td></tr><tr><td>1%</td><td>10%</td><td>1%</td><td>10%</td><td>Half</td><td>Full</td><td>Half</td><td>Full</td><td>1%</td><td>10%</td><td>Half</td><td>Full</td><td>1%</td><td>10%</td></tr><tr><td>Random</td><td>-</td><td>23.81</td><td>47.60</td><td>38.46</td><td>53.60</td><td>46.26</td><td>54.12</td><td>48.03</td><td>48.15</td><td>19.89</td><td>44.74</td><td>74.32</td><td>79.38</td><td>20.22</td><td>66.87</td></tr><tr><td>PPKT [45]</td><td>arXiv&#x27;21</td><td>36.50</td><td>51.67</td><td>49.71</td><td>54.33</td><td>50.18</td><td>56.00</td><td>50.92</td><td>54.69</td><td>37.57</td><td>46.48</td><td>78.90</td><td>84.00</td><td>61.10</td><td>62.41</td></tr><tr><td>SLidR [63]</td><td>CVPR&#x27;22</td><td>39.60</td><td>50.45</td><td>49.75</td><td>54.57</td><td>51.56</td><td>55.36</td><td>52.01</td><td>54.35</td><td>42.05</td><td>47.84</td><td>81.00</td><td>85.40</td><td>63.10</td><td>62.67</td></tr><tr><td>+ LiMoE</td><td>Ours</td><td>41.48</td><td>53.41</td><td>51.28</td><td>55.21</td><td>53.14</td><td>56.42</td><td>53.16</td><td>55.51</td><td>43.72</td><td>49.57</td><td>81.70</td><td>85.76</td><td>64.69</td><td>66.79</td></tr><tr><td>Seal [43]</td><td>NeurIPS&#x27;23</td><td>40.64</td><td>52.77</td><td>51.09</td><td>55.03</td><td>53.26</td><td>56.89</td><td>53.46</td><td>55.36</td><td>43.58</td><td>49.26</td><td>81.88</td><td>85.90</td><td>64.50</td><td>66.96</td></tr><tr><td>SuperFlow [80]</td><td>ECCV&#x27;24</td><td>42.70</td><td>54.00</td><td>52.83</td><td>55.71</td><td>54.41</td><td>57.33</td><td>54.72</td><td>56.57</td><td>44.85</td><td>51.38</td><td>82.43</td><td>86.21</td><td>65.31</td><td>69.43</td></tr><tr><td>+ LiMoE</td><td>Ours</td><td>43.95</td><td>55.96</td><td>53.74</td><td>56.67</td><td>55.42</td><td>57.83</td><td>55.60</td><td>57.31</td><td>45.79</td><td>52.27</td><td>83.24</td><td>86.68</td><td>66.54</td><td>71.07</td></tr></table>
+
+# 4. Experiments
+
+# 4.1. Configurations
+
+Datasets. Following the practical settings [43, 80], we use the nuScenes [6] for pretraining and evaluate it across 11 Li-DAR semantic segmentation datasets, including nuScenes [22], SemanticKITTI [2], Waymo Open [68], ScribbleKITTI [72], RELLIS-3D [32], SemanticPOSS [54], SemanticSTF [76], SynLiDAR [74], DAPS-3D [35], Synth4D [62], and Robo3D [37]. More details are in the Appendix.
+
+Implementation Details. All experiments are conducted using the MMDetection3D [15] codebase. For each LiDAR representation, we select FRNet [81] (range), MinkUNet [14] (voxel), and SPVCNN [69] (point) as the backbones. For image-to-LiDAR pretraining, we adopt the SLidR [63] and SuperFlow [80] paradigms. The learning rate for pretraining is set to 0.01, while the learning rate for the second CML stage is 0.001. In the third stage, we use a sepa
+
+rate learning rate scheme: 0.001 for the backbone and 0.01 for other parts. We use the AdamW optimizer [46] and a OneCycle scheduler [67] for all stages. In line with standard protocol, we report the mean Intersection-over-Union (mIoU) for segmentation, as well as mean Corruption Error (mCE) and mean Resilience Rate (mRR) for robustness.
+
+# 4.2. Comparative Study
+
+Comparisons to State of the Arts. In Tab. 1, we compare LiMoE with state-of-the-art pretraining methods using both Linear Probing (LP) and fine-tuning on various portions of the nuScenes [22] dataset. In the LP setting, where the backbone is frozen and only the task-specific head is trained, our approach outperforms single-representation methods [63, 80], achieving mIoU gains from  $1.10\%$  to  $1.76\%$ . In the fine-tuning setting, where both the backbone and task head are updated, we observe even greater improvements, with mIoU gains ranging from  $0.66\%$  to  $5.66\%$ . These re
+
+![](images/c4c5d9402ae05f12f0f7fab6c6c236929bf61ea80b7a11b8f6f6af688cf321e2.jpg)
+
+![](images/4d6aca42e798bea91b42c931be11e31183880e5006fc1fe06c659a1a0fb562f8.jpg)  
+Figure 4. Cosine similarity between learned features of a query point (denoted as the red dot) and: (1) the features of the image of the same scene (the first row); and (2) the features of the LiDAR points projected onto the image (the second row). Best viewed in colors.
+
+![](images/15a827ea5beec98b46ecce2ce8a3f0e79eae0aa78dc870b4bdb32694d2708ab0.jpg)
+
+![](images/38e77caba0012f80f375de8893a64703b22be67f4d747925936395a323132e28.jpg)
+
+![](images/1822056bfed834301c3281b8a8d7556f03431ca68149b23a4bb987439c24317c.jpg)
+
+![](images/209e5d3ae7de5d10c1e64da0c09c59c6a55baf9f813d5efc7f7dae28013ac1f0.jpg)
+
+![](images/e46024baeddc6e05e2c64e689fe31c240ee1e469e5e7098fe9cb25c6db946ddf.jpg)
+
+![](images/f41962462e025e250d2039ad14c95a95ccc0b81a37aa7969b7dea64f7ee5e396.jpg)
+
+![](images/fddf450e533a9771c36a06fd4d500e8c8de41635c60f12caaa04a3e676029ab5.jpg)
+
+Table 3. Out-of-distribution robustness assessment of LiDAR pretraining methods under corruptions and sensor failures in the nuScenes-C dataset from the Robo3D benchmark [37]. Full denotes fine-tuning with full labels. LP denotes linear probing with frozen backbones. All mCE, mRR, and mIoU scores are given in percentage (\%). The best and 2nd best scores are highlighted in bold and underline.  
+
+<table><tr><td>#</td><td>Method</td><td>Venue</td><td>mCE↓</td><td>mRR↑</td><td>Fog↑</td><td>Rain↑</td><td>Snow↑</td><td>Blur↑</td><td>Beam↑</td><td>Cross↑</td><td>Echo↑</td><td>Sensor↑</td><td>Average↑</td></tr><tr><td>Full</td><td>Random</td><td>-</td><td>112.20</td><td>72.57</td><td>62.96</td><td>70.65</td><td>55.48</td><td>51.71</td><td>62.01</td><td>31.56</td><td>59.64</td><td>39.41</td><td>54.18</td></tr><tr><td rowspan="6">Full</td><td>PPKT [45]</td><td>arXiv&#x27;21</td><td>105.64</td><td>75.87</td><td>64.01</td><td>72.18</td><td>59.08</td><td>57.17</td><td>63.88</td><td>36.34</td><td>60.59</td><td>39.57</td><td>56.60</td></tr><tr><td>SLidR [63]</td><td>CVPR&#x27;22</td><td>106.08</td><td>75.99</td><td>65.41</td><td>72.31</td><td>56.01</td><td>56.07</td><td>62.87</td><td>41.94</td><td>61.16</td><td>38.90</td><td>56.83</td></tr><tr><td>+ LiMoE</td><td>Ours</td><td>101.74</td><td>77.77</td><td>67.92</td><td>73.25</td><td>57.02</td><td>56.30</td><td>64.72</td><td>44.81</td><td>61.23</td><td>45.37</td><td>58.83</td></tr><tr><td>Seal [43]</td><td>NeurIPS&#x27;23</td><td>92.63</td><td>83.08</td><td>72.66</td><td>74.31</td><td>66.22</td><td>66.14</td><td>65.96</td><td>57.44</td><td>59.87</td><td>39.85</td><td>62.81</td></tr><tr><td>SuperFlow [80]</td><td>ECCV&#x27;24</td><td>91.67</td><td>83.17</td><td>70.32</td><td>75.77</td><td>65.41</td><td>61.05</td><td>68.09</td><td>60.02</td><td>58.36</td><td>50.41</td><td>63.68</td></tr><tr><td>+ LiMoE</td><td>Ours</td><td>88.43</td><td>83.28</td><td>71.10</td><td>75.92</td><td>65.66</td><td>63.86</td><td>68.52</td><td>60.78</td><td>61.91</td><td>50.66</td><td>64.80</td></tr><tr><td rowspan="6">LP</td><td>PPKT [45]</td><td>arXiv&#x27;21</td><td>183.44</td><td>78.15</td><td>30.65</td><td>35.42</td><td>28.12</td><td>29.21</td><td>32.82</td><td>19.52</td><td>28.01</td><td>20.71</td><td>28.06</td></tr><tr><td>SLidR [63]</td><td>CVPR&#x27;22</td><td>179.38</td><td>77.18</td><td>34.88</td><td>38.09</td><td>32.64</td><td>26.44</td><td>33.73</td><td>20.81</td><td>31.54</td><td>21.44</td><td>29.95</td></tr><tr><td>+ LiMoE</td><td>Ours</td><td>163.75</td><td>75.49</td><td>37.29</td><td>43.41</td><td>36.04</td><td>38.33</td><td>40.66</td><td>22.46</td><td>37.61</td><td>25.38</td><td>35.15</td></tr><tr><td>Seal [43]</td><td>NeurIPS&#x27;23</td><td>166.18</td><td>75.38</td><td>37.33</td><td>42.77</td><td>29.93</td><td>37.73</td><td>40.32</td><td>20.31</td><td>37.73</td><td>24.94</td><td>33.88</td></tr><tr><td>SuperFlow [80]</td><td>ECCV&#x27;24</td><td>161.78</td><td>75.52</td><td>37.59</td><td>43.42</td><td>37.60</td><td>39.57</td><td>41.40</td><td>23.64</td><td>38.03</td><td>26.69</td><td>35.99</td></tr><tr><td>+ LiMoE</td><td>Ours</td><td>155.77</td><td>78.23</td><td>40.35</td><td>45.28</td><td>39.14</td><td>42.10</td><td>44.21</td><td>27.33</td><td>39.20</td><td>29.49</td><td>38.39</td></tr></table>
+
+sults highlight the advantages of combining multiple representations, leading to enhanced performance.
+
+Cross-Dataset Knowledge Transfer. To evaluate the scalability of LiMoE, we conduct a comprehensive study across nine diverse 3D semantic segmentation datasets. Notably, except for the SemanticKITTI [2] and ScribbleKITTI [72] datasets, the remaining seven datasets cannot be effectively converted into range images due to the unknown FoV parameters of their LiDAR sensors. As a result, for these datasets, we combine only voxel and point representations in the SMS stage, since range image representations are not feasible. As shown in Tab. 1 and Tab. 2, our method consistently outperforms single-representation methods across all datasets, demonstrating superior adaptability and robustness for a wide range of 3D segmentation tasks.
+
+Robustness Assessments. The robustness of a 3D perception model against unprecedented conditions is crucial for its development in real-world applications. In Tab. 3, we compare LiMoE with previous pretraining methods using the nuScenes-C dataset from the Robo3D benchmark [37]. The results show that our method excels in handling various types of corruption, demonstrating its robustness and resilience under challenging real-world conditions.
+
+Qualitative Results. Fig. 4 illustrates the similarity be
+
+Table 4. Ablation study on experts in CML. Only sparse voxel representation is employed for the downstream task. All scores are given in percentage (\%). The best scores are highlighted in bold.  
+
+<table><tr><td rowspan="2">Pretrain</td><td rowspan="2">Voxel</td><td colspan="2">Experts</td><td colspan="2">nuScenes</td><td>KITTI</td></tr><tr><td>Point</td><td>Range</td><td>LP</td><td>1%</td><td>1%</td></tr><tr><td>Random</td><td>✓</td><td>X</td><td>X</td><td>8.10</td><td>30.30</td><td>39.50</td></tr><tr><td>SLidR [63]</td><td>✓</td><td>X</td><td>X</td><td>45.35</td><td>41.64</td><td>45.50</td></tr><tr><td rowspan="4">LiMoE</td><td>✓</td><td>✓</td><td>X</td><td>45.73</td><td>43.28</td><td>46.54</td></tr><tr><td>✓</td><td>X</td><td>✓</td><td>45.89</td><td>43.81</td><td>46.60</td></tr><tr><td>X</td><td>✓</td><td>✓</td><td>45.56</td><td>42.56</td><td>46.21</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>46.02</td><td>44.85</td><td>46.92</td></tr></table>
+
+tween a query point and the pretrained 2D image backbone, as well as other LiDAR points during the CML stage. The visual results confirm that combining multiple representations enhances the semantic features during pretraining, resulting in more effective feature learning.
+
+# 4.3. Ablation Study
+
+Route Activations. In Fig. 5, we present the distributions of beam numbers and distances loaded by each representation during the CML stage. Range images predominantly capture middle beams and distances, sparse voxels focus on upper beams and longer distances, while points concentrate
+
+![](images/916f1cffa866d4419afb861193a93a8859048d87433189c28b3f2450a25274f6.jpg)
+
+![](images/46bb8ad609d513d60e6c94fe4f9721d8073fea3e1e9316c49851c59c02c01dd2.jpg)  
+Figure 5. Ablation study on distributions of expert loadings in CML. The distributions are based on (a) LiDAR beam numbers and (b) distances. The three experts are #1 range view, #2 voxel, and #3 point, respectively.
+
+Table 5. Ablation study on experts in SMS. All scores are given in percentage (\%). The best scores are highlighted in bold.  
+
+<table><tr><td rowspan="2">Pretrain</td><td colspan="3">Experts</td><td colspan="2">nuScenes</td><td>KITTI</td></tr><tr><td>Voxel</td><td>Point</td><td>Range</td><td>LP</td><td>1%</td><td>1%</td></tr><tr><td rowspan="3">Random</td><td>✓</td><td>X</td><td>X</td><td>8.10</td><td>30.30</td><td>39.50</td></tr><tr><td>X</td><td>✓</td><td>X</td><td>8.80</td><td>34.79</td><td>38.74</td></tr><tr><td>X</td><td>X</td><td>✓</td><td>11.85</td><td>29.56</td><td>39.20</td></tr><tr><td rowspan="7">LiMoE</td><td>✓</td><td>X</td><td>X</td><td>46.02</td><td>44.85</td><td>46.92</td></tr><tr><td>X</td><td>✓</td><td>X</td><td>45.97</td><td>44.79</td><td>47.06</td></tr><tr><td>X</td><td>X</td><td>✓</td><td>45.09</td><td>40.88</td><td>44.34</td></tr><tr><td>✓</td><td>✓</td><td>X</td><td>46.37</td><td>45.74</td><td>47.51</td></tr><tr><td>✓</td><td>X</td><td>✓</td><td>46.28</td><td>45.70</td><td>47.35</td></tr><tr><td>X</td><td>✓</td><td>✓</td><td>46.09</td><td>45.32</td><td>47.49</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>46.56</td><td>46.89</td><td>47.96</td></tr></table>
+
+on lower beams and near distances. This distribution highlights the complementary nature of these representations, which provide a more comprehensive representation of the LiDAR data when combined in the MoE layer. In Fig. 6, we show the distributions of semantic classes loaded by each representation during the SMS stage. Range images are more sensitive to dynamic objects, sparse voxels highlight background objects, and raw points capture more detailed objects with complex structures. These results demonstrate how each representation contributes to the feature fusion.
+
+Scaling LiDAR Representations. In this ablation study, we explore the effect of combining multiple representations in both the CML and SMS stages. First, we test different combinations of representations for pretraining in the CML stage, using a sparse voxel-based network for the downstream task. The results shown in Tab. 4 demonstrate that combining multiple representations consistently outperforms single-representation pretraining. Next, we explore various combinations in the SMS stage, where each representation is pretrained using the CML stage. As presented in Tab. 5, incorporating multiple representations in the SMS stage further boosts performance, validating the advantages of multi-representation fusion in both pretraining and downstream tasks.
+
+Effect of Representation Diversity. To evaluate the impact of representation diversity, we conduct an ablation study by replacing the three heterogeneous experts in our framework with three identical sparse voxel-based models. Compared to single-representation learning, which achieves 41.64 and
+
+![](images/231483c76e21caf8dad3db9bc8e23f0a08448bab8d324e83fdb7dd5be4ab52b0.jpg)  
+Figure 6. Class-wise expert loadings in SMS. The three experts are #1 range view, #2 voxel, and #3 point, respectively.
+
+45.50 mIoU on nuScenes [22] and SemanticKITTI [2] with only  $1\%$  annotations, using three identical experts provides a minor improvement, reaching 42.72 and 46.35 mIoU, respectively. However, this configuration remains suboptimal compared to LiMoE, which achieves 46.89 and 47.96 mIoU. These results highlight the advantage of incorporating diverse representations, as the MoE layer can better exploit the unique characteristics and complementary features of each representation, leading to superior performance.
+
+Downstream Efficiency. Finally, we analyze the impact of LiMoE on downstream efficiency. CML integrates multiple LiDAR representations into a unified network for pretraining, with no impact on downstream efficiency. In contrast, SMS combines multiple representations for downstream tasks, which introduces additional computational costs. Specifically, our framework (SMS) has 85.8M parameters and achieves 8.3 FPS, remaining high efficiency.
+
+# 5. Conclusion
+
+In this work, we introduced LiMoE, a novel framework designed to leverage multiple LiDAR representations for enhanced feature learning in LiDAR scenes. By combining range images, sparse voxels, and raw points through a Mixture of Experts framework, our approach captures complementary information from different representations, enabling more robust scene understanding. We proposed a three-stage feature learning process, consisting of Image-to-LiDAR Pretraining, Contrastive Mixture Learning (CML), and Semantic Mixture Supervision (SMS). Extensive experiments demonstrate that our design outperforms existing approaches across multiple benchmarks. We hope this work paves the way for more scalable and robust LiDAR-based perception systems for real-world applications.
+
+# Acknowledgments
+
+This work is supported in part by the Natural Science Foundation of China under Grants U24B20155 and U21B2044, and in part by the Jiangsu Province Science and Technology Project under Grants BA2022026 and BK20243051. This work is also supported by the Ministry of Education, Singapore, under its MOE AcRF Tier 2 (MOET2EP20221-0012, MOE-T2EP20223-0002), and under the RIE2020 Industry Alignment Fund - Industry Collaboration Projects (IAF-ICP) Funding Initiative, as well as cash and in-kind contribution from the industry partner(s). Lingdong Kong is supported by the Apple Scholars in AI/ML Ph.D. Fellowship program.
+
+The authors would like to sincerely thank the Program Chairs, Area Chairs, and Reviewers for the time and efforts devoted during the review process.
+
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+# LiSu: A Dataset and Method for LiDAR Surface Normal Estimation
+
+Dušan Malić<sup>1,2</sup> Christian Fruhwirth-Reisinger<sup>1,2</sup> Samuel Schulter<sup>3,†</sup> Horst Possegger<sup>1,2</sup>
+
+$^{1}$ Christian Doppler Laboratory for Embedded Machine Learning
+
+$^{2}$ Institute of Visual Computing, Graz University of Technology  $^{3}$ Amazon
+
+{dusan.malic, reisinger, possegger}@tugraz.at
+
+![](images/0d856485a82c2cf27db9123fb766a932c877daae60f315f98ce1475418c07906.jpg)  
+(a) LiSu dataset sample
+
+![](images/038df2cc38a764df7940f8998db4f8e5f6190c6317fde7fd125c4b43029c0a97.jpg)  
+(b) Our method applied on a Waymo frame
+
+![](images/d8769b3a4761554ef32e72d553aa17af1344927648d95d08b568c864c043615c.jpg)  
+(c) SHS-Net [28] applied on a Waymo frame  
+Figure 1. Our synthetic LiSu dataset (a) enables focusing research on the challenging task of LiDAR surface normal estimation. When combined with our proposed method, we achieve state-of-the-art results (b) on challenging real-world datasets like Waymo Open Dataset [45], outperforming the current state-of-the-art SHS-Net [28] (c). Best viewed in color on screen.
+
+# Abstract
+
+While surface normals are widely used to analyse 3D scene geometry, surface normal estimation from LiDAR point clouds remains severely underexplored. This is caused by the lack of large-scale annotated datasets on the one hand, and lack of methods that can robustly handle the sparse and often noisy LiDAR data in a reasonable time on the other hand. We address these limitations using a traffic simulation engine and present LiSu, the first large-scale, synthetic LiDAR point cloud dataset with ground truth surface normal annotations, eliminating the need for tedious manual labeling. Additionally, we propose a novel method that exploits the spatiotemporal characteristics of autonomous driving data to enhance surface normal estimation accuracy. By incorporating two regularization terms, we enforce spatial consistency among neighboring points and temporal smoothness across consecutive LiDAR frames. These regularizers are particularly effective in self-training settings, where they mitigate the impact of noisy pseudo-labels, enabling robust real-world deployment. We demonstrate the effectiveness of our method on LiSu, achieving state-of-the-art performance in LiDAR surface normal estimation. Moreover, we showcase its full potential in addressing the challenging task of synthetic-to-real domain adaptation, leading to improved neural surface reconstruction on real-world data.
+
+# 1. Introduction
+
+Representing 3D surfaces by their surface normals is beneficial for a wide range of computer vision tasks, such as neural rendering [48, 52, 59], robotics [3, 37, 43, 61], autonomous driving [13, 35, 47], etc. While significant strides have been made in monocular surface normal estimation, particularly with large models trained on extensive datasets [2, 21, 23], research on surface normal estimation from LiDAR point clouds in the autonomous driving domain remains limited.
+
+Existing methods for point cloud surface normal estimation [12, 29, 30, 67] are tailored for small-scale CAD datasets, such as PCPNet [18] dataset, and often based on non- scalable architectures like PointNet [39]. Consequently, these methods struggle with large-scale point clouds and require either down-sampling or partitioning, which results in increased runtime. They often assume dense and uniform point distributions, making them ill-suited for LiDAR data, which is characterized by sparsity, non-uniformity, and noise. Moreover, the evaluation of these methods on LiDAR data is hindered by the lack of publicly available datasets with surface normal annotations.
+
+To overcome these limitations, we present LiSu, a novel synthetic LiDAR dataset targeted for research on surface normal estimation. We leverage CARLA [11], a versatile simulation environment offering diverse urban and rural landscapes, including downtown areas, small towns, and multi-lane highways. By extending CARLA's LiDAR sensor to capture not only point locations but also surface normal vectors, we curate an extensive dataset of roughly 50k frames.
+
+Leveraging the strong feature extraction capabilities of Point Transformer V3 (PTv3) [54], we propose a single-step
+
+approach for surface normal estimation. Our novel method explicitly accounts for the inherent noise in LiDAR data by incorporating two regularization terms: spatial consistency and temporal consistency. These terms enforce smoothness and temporal coherence, respectively, leading to more robust and accurate normal estimates across consecutive frames. Importantly, our method can be straightforwardly applied to domain adaptation scenarios, where our regularization terms effectively alleviate the adverse effects of noisy pseudo-labels in self-supervised learning [57, 60, 62, 64, 65]. This enables us to successfully bridge the synthetic-to-real domain gap, making our model suitable for real-world deployment.
+
+We evaluate our method on our LiSu dataset, benchmarking it against two classical and four state-of-the-art methods for point cloud surface normal estimation. In the absence of real-world datasets with surface normal annotations, we assess the effectiveness of our adaptation method by applying it to the real-world downstream task of neural surface reconstruction [19, 49, 51, 59]. For this, we integrate our surface normal estimator model as an oracle into a LiDAR-only surface reconstruction method [62], demonstrating a substantial performance improvement.
+
+In summary, our main contributions are:
+
+- Extending CARLA's LiDAR sensor to capture surface normals, enabling the generation of synthetic datasets for LiDAR-based surface normal estimation methods.  
+- LiSu: A novel, synthetic LiDAR dataset for autonomous driving, uniquely featuring labeled surface normals.  
+- Method employing data term regularizers to explicitly model spatiotemporal dependencies within autonomous driving datasets  
+- Extensive evaluation on both LiSu and real-world data.  
+Publicly accessible code, dataset, and trained models at https://github.com/malicd/LiSu
+
+# 2. Related Work
+
+Surface normal estimation from 3D point clouds involves the computation of the normal vector at each point on a 3D surface. Traditional methods achieve this by fitting a geometric primitive, such as a tangent plane [20], jets [7] or sphere [17], to a local neighborhood of the query point. The normal vector of this fitted primitive is then used as an estimate of the surface normal at the query point. More recently, approaches leverage deep learning models to enhance surface fitting [4, 12, 24, 25, 68]. Building upon the PointNet architecture [39], several methods [5, 18, 26] directly regress the surface normal vector from input point clouds.
+
+These methods commonly utilize the PCPNet dataset [18], which contains 30 synthetic objects. Each object consists of  $100\mathrm{k}$  points representing geometric shapes and figurines. To mitigate the limited data, Guerrero et al. [18] introduced a local patch sampling strategy, where  $N$  -point patches are extracted from the objects and used for training and inference.
+
+However, this approach suffers from two limitations: patches from the same object share an underlying distribution, and complete shape estimation necessitates multiple inference steps. The lack of data diversity and iterative inference routine render such approaches unsuitable for large-scale Li-DAR point clouds.
+
+Surface normal estimation from LiDAR point clouds remains a challenging problem due to the data's inherent sparsity, non-uniformity, and noise. Traditional surface fitting methods often struggle with these characteristics. Badino et al. [1] addressed this by extending plane fitting to LiDAR range images and incorporating a normalization module for noise reduction. More recent approaches, such as Bogoslavskyi et al. [6], leverage LiDAR scan lines to define local neighborhoods and infer surface normals.
+
+With the rise of autonomous driving datasets (e.g. [14, 45]), data from calibrated LiDAR and camera have become widely accessible. This has spurred the development of multimodal methods like Lin et al. [31] and DeepLiDAR [40], which leverage both modalities. Scheuble et al. [42] introduced PolLidar, a novel LiDAR sensor capable of capturing time-resolved polarimetric wavefronts. They demonstrate that surface normals can be derived from LiDAR characteristics beyond traditional geometric cues. However, these methods rely on calibrated multi-sensor setups or specialized hardware, limiting their adoption in real-world applications.
+
+The field of LiDAR surface normal estimation is hindered by the lack of a standardized benchmark dataset. While the aforementioned works have made notable strides in addressing this, their datasets still exhibit limitations. For example, DeepLiDAR primarily focuses on image-based tasks and employs LiDAR merely as sparse depth information, not providing LiDAR normals. Additionally, the datasets of Pol-Lidar [42] and Lin et al. [31] are relatively small (1969 and 151 frames, respectively) and may not fully capture the diversity of real-world scenarios. Crucially, these datasets were not publicly available at the time of this submission.
+
+To address these challenges, we introduce LiSu, a synthetic LiDAR dataset of 50k frames with surface normal annotations, freely available to our research community. Additionally, we propose a novel method to effectively leverage synthetic and unlabeled real-world data, enabling the development of robust models that generalize well to real-world scenarios.
+
+Synthetic-to-Real Unsupervised Domain Adaptation (UDA) for LiDAR point clouds transfers knowledge from models trained on synthetic source data to real-world target datasets [56, 60, 62, 63, 66]. Self-training is a widely employed UDA technique for various LiDAR-based tasks [8, 36, 41, 57, 62, 64, 65]. Our method closely aligns with existing UDA techniques. However, we introduce a novel spatial and temporal regularization strategy to explicitly address the inherent noise in pseudo-labels.
+
+<table><tr><td>Dataset</td><td># Beams</td><td>PPF</td><td># Fr.</td><td>SN</td><td>Pub.</td></tr><tr><td>Waymo [46]</td><td>64</td><td>160k</td><td>230k</td><td>×</td><td>✓</td></tr><tr><td>PolLidar [42]</td><td>150</td><td>-</td><td>1.9k</td><td>✓</td><td>×</td></tr><tr><td>Lin et al. [31]</td><td>-</td><td>-</td><td>151</td><td>✓</td><td>×</td></tr><tr><td>LiSu</td><td>64</td><td>100k</td><td>50k</td><td>✓</td><td>✓</td></tr></table>
+
+Table 1. Overview of autonomous driving datasets, including LiDAR sensor configurations (number of beams, points per frame (PPF)), total frames (Fr.), surface normal (SN) annotation availability, and public (Pub.) accessibility.
+
+Neural implicit surface reconstruction parametrizes 3D surfaces as Signed Distance Functions (SDFs) predicted by a multi-layer perceptron (MLP) [38, 44, 51]. A common optimization strategy involves guiding the learning objective with surface normal cues estimated with monocular off-the-shelf networks [16, 19, 49, 59]. These approaches leverage the fact that SDF gradients at surface points correspond to inward surface normals [22]. Naturally, the quality of normal estimates plays a crucial role [16]. While LiDAR-only methods (e.g. [62]) may neglect surface normal regularization, our work underscores the substantial benefits of precise surface normal estimations for superior surface reconstruction.
+
+# 3. Surface Normals from LiDAR Point Clouds
+
+To enable LiDAR-based surface normal estimation research, we introduce LiSu (Sec. 3.1), a large-scale synthetic LiDAR dataset with surface normal annotations. Moreover, we propose a novel method (Sec. 3.2) which leverages the spatiotemporal nature of autonomous driving data through two data term regularizers, achieving state-of-the-art performance on LiDAR surface normal estimation task. This method also serves as a robust signal for mitigating pseudolabel noise in self-supervised learning.
+
+# 3.1. LiSu: LiDAR Surface Normal Dataset
+
+We generate our dataset using CARLA [11], a simulation framework based on the Unreal Engine. Specifically, we leverage nine of CARLA's twelve pre-built maps, excluding two reserved for the CARLA Autonomous Driving challenges and one undecorated map with low geometric detail (i.e. without buildings, sidewalks, etc.). These selected maps represent diverse urban and rural environments, including downtown areas, small towns, and multi-lane highways. For each simulation, we populated the scenes with a large number of dynamic actors, such as vehicles (cars, trucks, buses, vans, motorcycles, bicycles) and pedestrians (adults, children, police) as well as static props (barrels, garbage cans, road barriers, etc.). The dynamic actors exhibited realistic movement patterns, governed by the underlying physics engine and adhered to real-world traffic rules, such as driving on designated roads and obeying traffic signals.
+
+![](images/858bc3610445a5518def39925bcc81b35e4a06c63d8ca16236cd2a2730283538.jpg)  
+Figure 2. Spherical KDE plot using a von Mises-Fisher kernel to visualize surface normal distribution. Yellow regions indicate higher density of surface normals. White regions in the south correspond to physically impossible orientations, while those in the north represent extremely rare occurrences.
+
+To capture realistic driving scenarios, we employ a virtual LiDAR sensor mounted atop a car operating in autopilot mode. The LiDAR sensor is configured to emit 64 laser beams, a  $10^{\circ}$  upper and a  $-30^{\circ}$  lower field of view. Such a common sensor configuration (e.g. [14, 45]) strikes a balance between sparsity and density, providing a challenging yet fair evaluation environment. To further mimic real-world conditions, we set the maximum range to 100 meters and introduce Gaussian noise with a standard deviation of 0.02 meters to the LiDAR point cloud. The sensor captures data at a rate of  $10\mathrm{Hz}$ . We provide additional information about our simulation setup in the supplemental material.
+
+CARLA's default LiDAR sensor implementation is limited to position and intensity channels. To enable surface normal collection, we extend CARLA's ray tracer to query surface normals at each intersection point between a ray and a mesh object. These surface normals are then transformed into the sensor's coordinate frame and appended to the LiDAR data. This requires modifications to both CARLA's  $\mathrm{C}++$  backend and Python frontend, adding three extra channels to store the  $x, y$ , and  $z$  components of the normal vector for each LiDAR point.
+
+For each map, we conduct eleven randomly initialized and independent simulation runs. A simulation is terminated early if prolonged traffic halts, such as red lights, occur. On average, each simulation lasts approximately 50 seconds, resulting in total of 50 045 labeled frames. To ensure rigorous evaluation, we partition our dataset into training, validation, and testing sets. We assign each map to exactly one split, preventing data leakage (i.e. using the same "city" in multiple splits). One map is designated for validation, while the remaining eight maps are divided equally between the training and testing sets. This results in 25 053 training, 22 167 testing, and 2825 validation frames. The full dataset will be released publicly via a Research Data Management platform upon publication.
+
+Surface normals, being unit vectors, can be intuitively visualized as points on a unit sphere. Fig. 2 illustrates a
+
+![](images/69f41a8f278a365ffda4e379b765dc750c3393eaea4d79429959db6fdffaacd3.jpg)  
+Figure 3. Exemplary LiDAR frames from our LiSu dataset (left: tunnel portal, right: urban scene). Surface normals are linearly mapped to the RGB color space. The color legend spheres in the bottom right corners provide a visual reference to interpret the normal directions.
+
+spherical Kernel Density Estimate (KDE) plot using a von Mises-Fisher kernel to represent the distribution of surface normals. Our CARLA simulation, mirroring real-world environments, inherently produces imbalanced datasets. For instance, the southern hemisphere, excluding a minor region around the south pole corresponding to ceiling surfaces (e.g. in tunnels in Fig. 3), is largely unoccupied, since it is not physically possible for a surface to be oriented away from the LiDAR sensor. Additionally, real-world scenes are dominated by road surfaces (concentrated near the north pole) and wall surfaces (near the equator), leading to a highly skewed dataset. We address the challenges posed by this data imbalance in Sec. 4.1.
+
+# 3.2. LiDAR Surface Normal Estimation
+
+Given a LiDAR point cloud  $\mathbf{P} \in \mathbb{R}^{N \times 3}$ , we aim to learn a mapping  $\Phi: \mathbb{R}^{N \times 3} \mapsto \mathbb{R}^{N \times 3}$  that, for each point  $\mathbf{p}_i \in \mathbf{P}$ , predicts a corresponding surface normal  $\hat{\mathbf{n}}_i \in \mathbb{R}^3$ . While our method is architecture agnostic, we employ state-of-the-art Point Transformer V3 (PTv3) [54] as  $\Phi$ . Given the ground truth label  $\mathbf{n}$ , our loss function is defined as
+
+$$
+\mathcal {L} _ {L 1} = \frac {1}{N} \sum_ {i \in N} \left| \left| \mathbf {n} _ {i} - \hat {\mathbf {n}} _ {i} \right| \right| _ {1}. \tag {1}
+$$
+
+While this type of supervision can guide the overall training procedure towards a local minima, it often fails to guarantee spatial and temporal coherence or accurate unit sphere estimates: As a result, the model may produce inconsistent predictions, such as assigning opposing normal directions to points on the same surface or generating significantly different surface normal estimates for the same surface across consecutive frames.
+
+To overcome these limitations, we propose three additional data terms that exploit the following key observations: (1) normal vectors should be piecewise smooth, (2) normal vectors should exhibit temporal consistency, and (3) normal vectors, being unit vectors, should be constrained to the unit
+
+sphere. To enforce both spatial and temporal coherence, we adopt Graph Total Variation (GTV) regularization. While our formulation shares similarities with prior works in point cloud super-resolution [9, 10], we deviate by incorporating GTV as a data term regularizer instead of the primary objective function. In the following, we delve deeper into our regularization terms and present the overall loss objective.
+
+Spatial GTV (SGTV) Regularization. The spatial regularization term operates under the assumption that geometrically close LiDAR points belong to the same surface and thus share the same surface normal vector. We first convert our point cloud  $\mathbf{P}$  into a  $k$ -neighborhood graph  $\mathcal{G} = (\mathcal{V}, \mathcal{E}, \mathbf{W})$  with set of nodes  $\mathcal{V}$  and edges  $\mathcal{E}$ . We associate each node  $i \in \mathcal{V}$  with a location  $\mathbf{p}_i$  and the respective surface normal prediction  $\Phi(\mathbf{p}_i) = \hat{\mathbf{n}}_i$ . The edge weights are defined with an adjacency matrix  $\mathbf{W}_{ij} = [w_{ij}]$ , where
+
+$$
+w _ {i j} = \exp \left(- \frac {\left\| \mathbf {p} _ {i} - \mathbf {p} _ {j} \right\| _ {2} ^ {2}}{\sigma^ {2}}\right) \tag {2}
+$$
+
+considers the spatial proximity between points  $p_i$  and  $p_j$ . It assumes values close to 1 for nearby points and tends towards 0 as the distance between them grows. The parameter  $\sigma$  determines the scale at which proximity is measured, influencing the rate of decay of the edge weights with increasing distance. During optimization, we penalize spatially inconsistent surface normal predictions by
+
+$$
+\mathcal {L} _ {\mathrm {S G T V}} = \frac {1}{| \mathcal {E} |} \sum_ {(i, j) \in \mathcal {E}} w _ {i j} \| \hat {\mathbf {n}} _ {i} - \hat {\mathbf {n}} _ {j} \| _ {1}. \tag {3}
+$$
+
+Temporal GTV (TGTV) Regularization. LiDAR point clouds are commonly captured sequentially at high frequency (e.g.  $10\mathrm{Hz}$  as in ONCE [34], WOD [45], or Argoverse [53]), resulting in substantial overlap between consecutive LiDAR scans. Global registration modules, such as GPS coupled with IMU, allow for alignment of these frames to a common key frame. This is particularly effective for static objects,
+
+while dynamic objects, such as moving vehicles, may exhibit slight misalignments. However, in typical autonomous driving settings, the number of LiDAR points corresponding to static scene contents vastly outnumber the number of points corresponding to dynamic objects. We exploit the sequential nature of these datasets to enforce temporally coherent surface normal predictions.
+
+During training, we employ mini-batches comprising pairs of consecutive point clouds,  $(\mathbf{P}^t,\mathbf{P}^{t + 1})$ , along with their corresponding global poses (with respect to the key frame),  $(\mathbf{T}^t,\mathbf{T}^{t + 1})\in \mathbb{R}^{4\times 4}$ . Both point clouds undergo random affine transformations,  $(\mathbf{A}^t,\mathbf{A}^{t + 1})\in \mathbb{R}^{4\times 4}$ , encompassing rotations, translations, flips, and other standard augmentations. For improved readability, we adopt the convention  $\mathbf{P}\triangleq \mathbf{ATP}$  throughout the paper.
+
+After the forward pass  $\Phi (\mathbf{P}^t)$  and  $\Phi (\mathbf{P}^{t + 1})$  , we construct a bipartite graph  $\mathcal{G} = \left(\{\mathcal{V}^t,\mathcal{V}^{t + 1}\} ,\mathcal{E},\mathbf{W}\right)$  , where each node  $i\in \mathcal{V}^t$  is associated with the transformed key frame point  $(\mathbf{T}^t\mathbf{A}^t)^{-1}\mathbf{p}_i^t$  and key frame surface normal prediction  $(\mathbf{T}^t\mathbf{A}^t)^{-1}\hat{\mathbf{n}}_i^t$  . Similarly, each node  $j\in \mathcal{V}^{t + 1}$  is associated with the point  $(\mathbf{T}^{t + 1}\mathbf{A}^{t + 1})^{-1}\mathbf{p}_j^{t + 1}$  and surface normal prediction  $(\mathbf{T}^{t + 1}\mathbf{A}^{t + 1})^{-1}\hat{\mathbf{n}}_j^{t + 1}$  . Analogous to Eq. (2), the weight adjacency matrix is defined as
+
+$$
+w _ {i j} = \exp \left(- \frac {\left\| \left(\mathbf {T} ^ {t} \mathbf {A} ^ {t}\right) ^ {- 1} \mathbf {p} _ {i} ^ {t} - \left(\mathbf {T} ^ {t + 1} \mathbf {A} ^ {t + 1}\right) ^ {- 1} \mathbf {p} _ {j} ^ {t + 1} \right\| _ {2} ^ {2}}{\sigma^ {2}}\right). \tag {4}
+$$
+
+Finally, we penalize incoherence between two consecutive frames with
+
+$$
+\begin{array}{l} \mathcal {L} _ {\mathrm {T G T V}} = \frac {1}{| \mathcal {E} |} \sum_ {(i, j) \in \mathcal {E}} w _ {i j} \| (\mathbf {T} ^ {t} \mathbf {A} ^ {t}) ^ {- 1} \hat {\mathbf {n}} _ {j} ^ {t} - \\ \left(\mathbf {T} ^ {t + 1} \mathbf {A} ^ {t + 1}\right) ^ {- 1} \hat {\mathbf {n}} _ {j} ^ {t + 1} \| _ {1}, \tag {5} \\ \end{array}
+$$
+
+which enforces temporal smoothness.
+
+Eikonal Regularization. Recent studies [15, 19, 50] have shown that enforcing unit-norm constraints on SDF gradients at object boundaries significantly improves model robustness. Notably, these gradients directly correspond to surface normals, a relationship that existing surface normal methods fail to exploit. It is a low-cost term that not only improves in-domain performance (Tab. 3) but also effectively suppresses gradient noise arising from imperfect pseudo-labels (Tab. 4). In line with this, we integrate the Eikonal loss as an additional regularization term:
+
+$$
+\mathcal {L} _ {\text {E i k o n a l}} = \frac {1}{N} \sum_ {i \in N} \left(\left\| \hat {\mathbf {n}} _ {i} \right\| _ {2} - 1\right) ^ {2}. \tag {6}
+$$
+
+Training Objective. Our training objective is a weighted combination of the loss and data regularization terms:
+
+$$
+\mathcal {L} = \mathcal {L} _ {L 1} + \gamma \left(\mathcal {L} _ {\mathrm {S G T V}} + \mathcal {L} _ {\mathrm {T G T V}} + \mathcal {L} _ {\text {E i k o n a l}}\right). \tag {7}
+$$
+
+We empirically determined the optimal trade-off parameter  $\gamma$  to be 0.1.
+
+# 4. Experiments
+
+In the following, we present a comprehensive experimental evaluation demonstrating the superior performance of our method on LiSu for LiDAR surface normal estimation (Sec. 4.1). We further highlight the positive impact of our LiSu on direct transfer to real-world datasets (Sec. 4.2) and self-supervised domain adaptation. Finally, we show how our regularization terms mitigate the negative effects of noisy pseudo-labels (Sec. 4.2) in real-world neural surface reconstruction.
+
+# 4.1. Surface Normal Evaluation
+
+Dataset. Due to the lack of LiDAR datasets with surface normal annotations, in the following we conduct our experiments on our LiSu dataset. We train our models on the designated training split, comprising 25 053 labeled samples. Previous methods, including PCPNet [18] and SHS-Net [28], partition point clouds into  $N$ -point patches, necessitating multiple inference steps for each frame. These methods require on average over 10 seconds per frame, making comprehensive evaluation time-consuming. To enable a fair comparison within a reasonable timeframe, we downsampled our test set to every fifth frame, reducing the number of test frames to 4433. In contrast, our proposed method processes the entire point cloud in a single inference step. This allows us to process each frame in approximately 50 milliseconds. Metric. Previous works on LiDAR surface normal estimation, such as [31], have adopted evaluation protocols inspired by PCPNet [18]. However, these protocols, which involve progressively adding artificial noise, are not ideal for inherently noisy LiDAR data. Other methods, like [42], impose overly strict error thresholds (e.g.  $3^{\circ}$ ), making them equally unsuitable. Instead, we propose a more realistic evaluation protocol that accounts for the natural noise and sparsity of LiDAR data. More specifically, we report the mean (mean), median (median) and root mean square (RMSE) angular error in degrees. Additionally, we provide accuracy metrics for various angular error thresholds:  $5.0^{\circ}$ ,  $7.5^{\circ}$ ,  $11.25^{\circ}$ ,  $22.5^{\circ}$ , and  $30.0^{\circ}$ . These metrics indicate the percentage of predictions with angular error below the respective threshold. Baseline. First, we benchmark our method against two unsupervised surface normal estimation methods: PCA [20] and Jet [7]. For both, we utilize a neighborhood size of  $k = 32$  points and orient normals towards a common viewpoint. Subsequently, we train seven state-of-the-art supervised methods on the training split of our LiSu dataset: PCPNet [18], CMGNet [55], GraphFit [25], Du et al. [12], NGL [27], NeuralGF [30], and SHS-Net [28]. To adapt to the characteristics of LiDAR data, we modify the original implementations by reducing the number of points per patch from 500 (within
+
+<table><tr><td>Method</td><td>mean ↓</td><td>median ↓</td><td>RMSE ↓</td><td>5.0° ↑</td><td>7.5° ↑</td><td>11.25° ↑</td><td>22.5° ↑</td><td>30.0° ↑</td><td>Avg. Runtime</td></tr><tr><td>PCA [20]</td><td>76.18</td><td>29.10</td><td>110.95</td><td>44.95</td><td>46.86</td><td>48.45</td><td>51.02</td><td>52.09</td><td>0.06</td></tr><tr><td>Jet [7]</td><td>39.02</td><td>25.11</td><td>53.96</td><td>11.08</td><td>20.75</td><td>33.31</td><td>50.47</td><td>56.97</td><td>14.55</td></tr><tr><td>PCPNet [18]</td><td>9.88</td><td>1.42</td><td>20.56</td><td>67.42</td><td>72.41</td><td>76.87</td><td>84.75</td><td>88.10</td><td>14.31</td></tr><tr><td>CMG-Net [55]</td><td>10.05</td><td>2.44</td><td>20.24</td><td>65.15</td><td>71.09</td><td>75.94</td><td>78.40</td><td>80.03</td><td>40.01</td></tr><tr><td>GraphFit [25]</td><td>8.98</td><td>0.93</td><td>19.57</td><td>73.49</td><td>75.68</td><td>77.42</td><td>79.88</td><td>80.80</td><td>19.42</td></tr><tr><td>Du et al. [12]</td><td>8.81</td><td>0.93</td><td>19.54</td><td>73.53</td><td>75.92</td><td>77.75</td><td>80.05</td><td>80.88</td><td>16.26</td></tr><tr><td>NGL [27]</td><td>9.88</td><td>1.21</td><td>18.43</td><td>77.39</td><td>79.48</td><td>81.44</td><td>84.70</td><td>86.24</td><td>26.27</td></tr><tr><td>NeuralGF [30]</td><td>8.57</td><td>1.19</td><td>19.57</td><td>67.08</td><td>71.42</td><td>74.84</td><td>79.48</td><td>81.37</td><td>17.58</td></tr><tr><td>SHS-Net [28]</td><td>6.46</td><td>0.67</td><td>18.40</td><td>79.66</td><td>83.57</td><td>86.77</td><td>90.79</td><td>92.06</td><td>24.27</td></tr><tr><td>Ours</td><td>6.30</td><td>0.43</td><td>17.58</td><td>81.10</td><td>84.44</td><td>87.32</td><td>91.66</td><td>93.09</td><td>0.09</td></tr></table>
+
+a 0.1 meter radius) to 32. To accommodate the two orders of magnitude increase in scale of the training data, we have opted to reduce the number of training epochs. This allows us to maintain the same total number of iterations, ensuring that the model is exposed to an equivalent amount of training data. We provide more detailed information in the supplemental material.
+
+Implementation Details. We adopt the default PTv3 [54] configuration, which consists of a four-stage encoder-decoder architecture. We optimize our model using AdamW [33] with a maximum learning rate of 0.003 and a weight decay of 0.005. The learning rate schedule comprises a short (1 epoch) warm-up phase followed by cosine annealing [32]. We train our model on 8 A100 GPUs using mixed precision with a batch size of 32. Standard point cloud augmentation techniques, such as rotation, flipping, and scaling, are utilized. Training is terminated after 50 epochs.
+
+To address the class imbalance in our dataset (illustrated in Fig. 2), we employ a weighted loss function: Each data sample is weighted inversely proportional to the frequency of its ground truth surface normal occurrence. This effectively upweights underrepresented classes, such as less common surface orientations, while downweighting overrepresented classes. Consequently, the model is encouraged to focus more on the challenging, less frequent samples.
+
+Results. Table 2 presents the comparison of the surface normal estimation methods. Traditional methods, such as PCA [20] and Jet [7], are known to be sensitive to noise and prone to ambiguities in the orientation of their surface normal estimates. When applied to sparse and non-uniform Li-DAR data, as demonstrated in Tab. 2, these methods exhibit significant limitations, often producing unreliable results.
+
+Our proposed training method allows us to build a PTv3-based surface normal estimator that comfortably surpasses state-of-the-art supervised methods in both accuracy and speed. Compared to PCPNet [18], GraphFit [25], and Du et
+
+Table 2. Evaluation of surface normal estimation methods on the LiSu test split. Mean, median, and root mean square (RMSE) angular error in degrees, as well as accuracy for various angular error thresholds, and average runtime per LiDAR point cloud (in seconds) are reported. Best and second-best values are highlighted in bold and underlined, respectively.  
+
+<table><tr><td>\( \mathcal{L}_{L1} \)</td><td>\( \mathcal{L}_{\text{SGTV}} \)</td><td>\( \mathcal{L}_{\text{TGTV}} \)</td><td>\( \mathcal{L}_{\text{Eikonal}} \)</td><td>RMSE \( \downarrow \)</td><td>\( 5.0^{\circ}\uparrow \)</td></tr><tr><td>✓</td><td></td><td></td><td></td><td>19.82</td><td>78.70</td></tr><tr><td>✓</td><td>✓</td><td></td><td></td><td>17.78</td><td>81.06</td></tr><tr><td>✓</td><td></td><td>✓</td><td></td><td>17.72</td><td>81.08</td></tr><tr><td>✓</td><td></td><td></td><td>✓</td><td>17.74</td><td>80.65</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>17.58</td><td>81.10</td></tr></table>
+
+Table 3. Influence of proposed components on the in-domain model performance. Models are trained on the full LiSu training split and evaluated on a  $20\%$  test split.
+
+al. [12], we achieve a significant reduction of over  $2.5^{\circ}$  in mean average angular error and an  $8\%$  increase in accuracy at the  $5.0^{\circ}$  threshold. Additionally, we outperform SHS-Net [28] by reducing the median angular error by  $0.24^{\circ}$  and improve the  $5.0^{\circ}$  accuracy by  $1.44^{\circ}$ . Furthermore, our model processes a single LiSu frame in just 90 milliseconds on average, significantly outperforming state-of-the-art methods like SHS-Net, PCPNet, and GraphFit (which require over 14 seconds). This substantial speedup is attributed to our approach of processing the entire LiDAR point cloud at once, eliminating the need for partitioning and multiple inference steps, as required by state-of-the-art methods.
+
+Regularization Ablation Study. To assess the individual contribution of each component proposed in Sec. 3.2, we conduct an ablation study shown in Tab. 3. Each component, when trained from scratch on our full training split, outperforms our baseline model (trained with  $\mathcal{L}_{L1}$  loss only). The model incorporating all proposed losses demonstrates the best overall performance.
+
+# 4.2. Synthetic-to-Real Domain Adaptation
+
+In the following, we qualitatively assess the state-of-the-art in surface normal estimation on real-world LiDAR point clouds from the Waymo Open Dataset [45]. We highlight the limitations of traditional methods and show that direct trans
+
+fer from our LiSu dataset significantly reduces the synthetic-to-real domain gap compared to the existing PCPNet [18] dataset. Furthermore, we demonstrate how our method can effectively bridge this gap.
+
+Classical approaches based on PCA [20] (see Figure 4, first row) do not require labeled data but suffer from surface normal orientation ambiguities, particularly with noisy LiDAR point clouds. For instance, points on a road with upward (blue) or downward (brown) normals can be interpreted as correct, depending on the perspective. Yet, physical constraints dictate a single correct orientation, which is upward in this case. More recent approaches, such as SHS-Net [28] (second row in Figure 4), trained on the PCPNet dataset, exhibit similar limitations while providing smoother predictions. Our direct domain transfer experiments (third and forth row in Fig. 4), i.e. models trained on our LiSu dataset and employed without any adaptation to Waymo, reveal already tremendous improvement. This demonstrates that for the downstream task of LiDAR surface normal estimation, our LiSu dataset, as anticipated, is much better suited than existing CAD-based datasets like PCPNet.
+
+To further enhance model robustness and generalization, we leverage our surface estimation method (Sec. 3.2) within a self-training paradigm, successfully reducing the domain gap. We first pretrain our model on the LiSu training split, followed by a second phase on the Waymo train split, leveraging pseudo-labels and our proposed data term regularization to mitigate noise. In the second (self-training) phase, we optimize our model using AdamW [33] with a maximum learning rate of 0.001 and weight decay of 0.005. To preserve the learned feature representation from the clean data, we employ differential learning rates [58], assigning lower learning rates to shallow layers and exponentially decaying them with network depth by a factor of 0.85. We employ standard point cloud augmentation techniques, such as rotation, flipping, and scaling. The learning rate schedule employs a short warm-up phase followed by linear annealing [32]. Our model is trained on 4 A100 GPUs using mixed precision with a batch size of 32 for 10 epochs. In contrast to other approaches, our method consistently produces accurate, smooth, and correctly oriented surface normal predictions.
+
+# 4.3. Neural Surface Reconstruction
+
+Our work demonstrates that the combination of our method with LiSu effectively reduces the domain gap between datasets. However, the specific influence of our regularization technique on the overall self-training process remains unclear. Due to the scarcity of real-world LiDAR datasets with surface normal annotations, we opted to evaluate its effectiveness indirectly through a downstream task: neural surface reconstruction.
+
+Previous methods in this domain often leverage geometric priors, such as surface normals derived from monocu
+
+![](images/449da24fb14b647f9c67689a777b07a72c141dce67634be73ed1595a963321fe.jpg)
+
+![](images/12fa5c4f058243ba4745a559afc08b7e83b86b2a49fded47c3f28d29c1168731.jpg)
+
+![](images/0e040552ffe6b0ea33f3d7de2cd714b20adf8f28be7ba6da344ead01e703c412.jpg)
+
+![](images/ce7df8549291898aa01326da302029cf2e4019b728287db98cd49d319fe96034.jpg)
+
+![](images/6ffaa2d9c3a0dc4a74ac0fd54cdd3bbf5aac4f86fde91bd38515643ad1247bff.jpg)  
+Figure 4. Qualitative evaluation of traditional and learning-based methods on a challenging Waymo frame. Notably, the current state-of-the-art (SHS-Net [28] trained on PCPNet [18]) struggles to generalize to noisy and sparse LiDAR data. When trained on our proposed dataset (LiSu), both SHS-Net and our method yield reasonable results on the Waymo frame. In the last row, we demonstrate how leveraging our method within a self-supervised learning paradigm significantly enhances overall estimation, resulting in accurate, smooth, and consistently oriented predictions.
+
+lar images [16, 19, 49], to improve reconstruction quality. These methods typically penalize discrepancies between the SDF boundary gradients and the predicted surface normals [59]. However, LiDAR-only neural surface reconstruction approaches, such as ReSimAD [62], are limited by the absence of reliable surface normal estimation methods for real-world LiDAR data. Therefore, we leverage our unsupervised training approach from Sec. 4.2, to learn a robust LiDAR surface normal estimator from the real-world Waymo dataset. This prior is then integrated into ReSimAD to enhance its surface reconstruction capabilities.
+
+We inherit the evaluation protocol established in [19, 62]: For each sequence, we train a SDF model using point cloud data from all five Waymo LiDAR sensors, as described in [62]. A single mesh is then reconstructed for the entire sequence using this trained model. To simulate a real-world
+
+<table><tr><td>Seq.</td><td>ReSimAD [62]</td><td>DT</td><td>\( \mathcal{L}_{\text{L1}} \)</td><td>\( \mathcal{L} \)</td></tr><tr><td>1006130</td><td>2.53 / 0.25</td><td>2.51 / 0.26</td><td>2.51 / 0.24</td><td>2.51 / 0.23</td></tr><tr><td>1172406</td><td>1.95 / 0.52</td><td>1.95 / 0.50</td><td>1.96 / 0.51</td><td>1.90 / 0.47</td></tr><tr><td>1323841</td><td>2.16 / 0.70</td><td>2.15 / 0.75</td><td>2.16 / 0.74</td><td>2.12 / 0.68</td></tr><tr><td>1347637</td><td>2.07 / 0.33</td><td>2.05 / 0.25</td><td>2.05 / 0.29</td><td>2.02 / 0.28</td></tr><tr><td>1486973</td><td>1.80 / 0.19</td><td>1.83 / 0.21</td><td>1.79 / 0.20</td><td>1.79 / 0.20</td></tr><tr><td>1506235</td><td>1.54 / 0.38</td><td>1.50 / 0.38</td><td>1.52 / 0.37</td><td>1.46 / 0.34</td></tr><tr><td>1664636</td><td>2.15 / 0.53</td><td>2.19 / 0.51</td><td>2.10 / 0.48</td><td>2.08 / 0.47</td></tr><tr><td>4058410</td><td>1.91 / 0.36</td><td>1.91 / 0.34</td><td>1.91 / 0.40</td><td>1.90 / 0.31</td></tr><tr><td>average</td><td>2.01 / 0.41</td><td>2.01 / 0.40</td><td>2.00 / 0.40</td><td>1.97 / 0.37</td></tr></table>
+
+Table 4. We evaluate neural surface reconstruction on diverse Waymo sequences using Root Mean Square Error (RMSE) / Chamfer Distance (CD). Lower values indicate better performance. ReSi-mAD [62] omits surface normal loss during reconstruction. Direct Transfer (DT) applies a model trained on LiSu without adaptation.  $\mathcal{L}$  (Eq. (7)) and  $\mathcal{L}_{\mathrm{L1}}$  (Eq. (1)) denote Waymo self-trained models with and without regularization, respectively.
+
+top-mounted LiDAR, virtual sensors are positioned at the locations of the real physical sensors and synthetic point clouds are generated by ray-casting the reconstructed mesh. We evaluate the accuracy of these synthetic point clouds by comparing them to the corresponding real-world point clouds using Root Mean Square Error (RMSE) and Chamfer Distance (CD) metrics in Table 4.
+
+Surface reconstruction in ReSimAD is solely guided by the LiDAR point cloud information. While this already produces reasonably good meshes, the SDF of regions that are not hit by a LiDAR beam remain undefined. This leads to coarse meshes and jittering artifacts clearly visible in the exemplary ReSimAD results in Fig. 5. Incorporating estimated surface normals into ReSimAD improves the mesh reconstruction notably, as illustrated in the three bottom rows of Fig. 5: Directly transferring (DT) a surface normal estimator trained (solely) on LiSu to the Waymo data results in better surface normal estimates and, consequently, a smoother surface reconstruction near the ego vehicle. Subsequently applying our proposed self-supervised domain adaption further improves the results: the bottom row of Fig. 5 illustrates the benefits of our proposed regularization, which leads to smooth surface meshes, even at far distances from the ego vehicle. Naively performing self-supervised adaptation without our regularization (i.e. solely using the  $\mathcal{L}_{L1}$  loss from Eq. (1)), on the other hand, does not improve the results.
+
+# 5. Conclusion
+
+We introduced LiSu, a synthetic dataset designed to advance research on LiDAR-based surface normal estimation. With more than 50 000 LiDAR frames, obtained from a state-of-the-art traffic simulation engine, LiSu presents an ideal testbed to develop and benchmark LiDAR surface normal estimation approaches. To properly leverage this large-scale synthetic data we propose a method that exploits the spa
+
+![](images/c44689071b2b5b34e627b132937e017e8d580df2c346afe5e7460f5b0e39e80d.jpg)  
+Figure 5. Reconstructed meshes from Waymo sequence 1172406, color-coded with surface normals. ReSimAD [62] omits surface normal loss during reconstruction. Direct Transfer (DT) applies a model trained on LiSu without adaptation.  $\mathcal{L}$  (Eq. (7)) and  $\mathcal{L}_{\mathbf{L1}}$  (Eq. (1)) denote Waymo self-trained models with and without regularization, respectively.
+
+tiotemporal nature of LiDAR scans in autonomous driving settings via meticulously designed regularization constraints. Moreover, we show that our method can be seamlessly extended to domain adaptation scenarios, where it helps to alleviate the negative effects of noisy pseudo-labels. Across several experiments, we demonstrate the utility of LiSu and our method to obtain outstanding results in surface normal estimation and their positive impact on the downstream task of surface reconstruction from real-world LiDAR point clouds. We believe the LiSu dataset will help our research community to improve LiDAR-based surface normal estimation approaches and, consequently, leverage these to advance autonomous driving: For example, scenario generation for domain adaptation research (i.e., re-rendering scenes with different simulated LiDAR configurations) will benefit from improved surface reconstructions.
+
+Acknowledgments. We gratefully acknowledge the financial support by the Austrian Federal Ministry for Digital and Economic Affairs, the National Foundation for Research, Technology and Development and the Christian Doppler Research Association. The presented experiments have been achieved using the Vienna Scientific Cluster.
+
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CVPR/2025/LiVOS_ Light Video Object Segmentation with Gated Linear Matching/full.md

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+# LiVOS: Light Video Object Segmentation with Gated Linear Matching
+
+Qin Liu $^{1}$  Jianfeng Wang $^{2}$  Zhengyuan Yang $^{2}$  Linjie Li $^{2}$   
+Kevin Lin $^{2}$  Marc Niethammer $^{1}$  Lijuan Wang $^{2}$ $^{1}$ UNC Chapel Hill  ${}^{2}$ Microsoft
+
+https://github.com/uncbiag/LiVOS
+
+# Abstract
+
+Semi-supervised video object segmentation (VOS) has been largely driven by space-time memory (STM) networks, which store past frame features in a spatiotemporal memory to segment the current frame via softmax attention. However, STM networks face memory limitations due to the quadratic complexity of softmax matching, restricting their applicability as video length and resolution increase. To address this, we propose LiVOS, a lightweight memory network that employs linear matching via linear attention, reformulating memory matching into a recurrent process that reduces the quadratic attention matrix to a constant-size, spatiotemporal-agnostic 2D state. To enhance selectivity, we introduce gated linear matching, where a data-dependent gate matrix is multiplied with the state matrix to control what information to retain or discard. Experiments on diverse benchmarks demonstrated the effectiveness of our method. It achieved 64.8 J&F on MOSE and 85.1 J&F on DAVIS, surpassing all non-STM methods and narrowing the gap with STM-based approaches. For longer and higher-resolution videos, it matched STM-based methods with  $53\%$  less GPU memory and supports 4096p inference on a 32G consumer-grade GPU-a previously cost-prohibitive capability-opening the door for long and high-resolution video foundation models.
+
+# 1. Introduction
+
+Video object segmentation (VOS) involves separating specific objects from the background in a sequence of video frames. It plays a critical role in various real-world applications, including robotics [41], video editing [28], and medical imaging [45]. Based on the level of user input, VOS tasks are generally categorized into three settings: unsupervised, semi-supervised (or one-shot), and interactive [20]. In this work, we focus on the semi-supervised setting, where the segmentation of the first frame is provided, and the model is required to propagate this segmentation across subsequent frames.
+
+![](images/34e2051e28d7581da44c7bd0dec29820b0aa16e710ba98270883517a2adf5aee.jpg)  
+Figure 1. Top: Conceptual comparison of softmax vs. linear matching in video object segmentation. Bottom: Softmax matching suffers from memory constraints due to its quadratic attention complexity, while linear matching achieves linear growth with a constant-size state. Curves are based on results in Tab. 3.
+
+Semi-supervised VOS is primarily driven by space-time memory (STM) networks [10, 12, 14, 36, 43], which store past frames and their segmentations as keys and values in the memory bank to help segment the query frame. Segmentation occurs by matching each pixel in the query frame to all spatiotemporal pixels in the memory frames via softmax attention [49]. This softmax matching process is highly inefficient due to the large attention matrix with space and time complexities of  $\mathcal{O}(HW \times THW)$ , where  $H$  and  $W$  indicate the spatial dimensions of an image and  $T$  is the num
+
+![](images/6fab704b82a441d252aa513d5cc46ef5a84939d3e1877312fdc39eb39c46d39f.jpg)  
+Figure 2. CPU latency comparison between softmax matching and linear matching. Softmax attention scales linearly over time (i.e., the number of memory frames  $T$ ) and quadratically with input resolution  $HW$ . Latency is measured on an Intel Core-i7 (2.80GHz) CPU with PyTorch 2.0, batch size 1, and fp32.
+
+![](images/684b9ca9e7837b1f8ecd981bd377af3da181564e6e370d5498a89bd162448e41.jpg)
+
+ber of memory frames. Here the number of objects is not considered for simplicity. As shown in Fig. 2, the CPU latency of softmax matching increases linearly over time and quadratically with spatial dimensions. This is problematic as video length or resolution increase, making computations too slow or causing out-of-memory issues (Fig. 1).
+
+To alleviate these issues, one could limit the number of memory frames or downsample the video's spatial resolution. However, a fixed-size memory bank may lead to failures in challenging scenarios such as for occlusions or fast-moving objects [10]. Further, downsampling a video's spatial resolution may lose fine details in object masks, as shown in Fig. 3, leading to inaccurate segmentations. Therefore, memory networks relying on softmax matching face significant challenges as video lengths and resolutions increase, limiting their applicability on resource-constrained devices.
+
+To address these challenges, strategies such as knowledge distillation [34], recurrent feature embedding [29], and spatiotemporal redundancy compressing [53] have been explored. However, these methods still rely on softmax matching, which we identify as the core memory bottleneck. We address this limitation by introducing linear matching, reformulating the memory matching process into a recurrent framework that reduces the large attention matrix to a constant-size 2D state, yielding space and time complexities of  $\mathcal{O}(THW)$ . To enhance selectivity, we further introduce gated linear matching, where the state is multiplied by a data-dependent transition matrix [58] that determines what information to retain or discard. Additionally, we leverage lightweight sensory memory [10] and object memory [14] to improve performance (we claim no contribution for these components). We thus present LiVOS, the first light memory network that maintains constant memory usage for arbitrarily long videos and achieves linear memory growth as video resolution increases.
+
+We evaluated LiVOS on a diverse range of video benchmarks, including both short- and long-term video datasets, as well as high-resolution videos. It achieved 64.8 J&F
+
+![](images/98112c666149691a4c7e57c504945c00259b21dad2bd0ca389fd60b6bcc8ff52.jpg)
+
+![](images/51178fb82f94dd50f18ae0b4a73975b887a54510619a918bd7171e61dc3b5a76.jpg)
+
+![](images/cf13689831832324ef298a79b8ba9bf5c21bec04707cd9f2161de3264f8c1eb9.jpg)  
+Figure 3. Masks of thin structures at different resolutions. Thin structures may lose fine details at  $480\mathrm{p}$ , the standard resolution for VOS. However, existing memory networks relying on softmax matching are not efficient for processing high resolution videos.
+
+![](images/9eab36ed537cf24b7b4f3df90025ee0e3302c404b76b368e2c9eddb2d5bf6198.jpg)
+
+on MOSE and 85.1  $\mathcal{I}\&\mathcal{F}$  on DAVIS, surpassing all non-STM methods and narrowing the gap with STM-based approaches. For longer and higher-resolution videos, it matched STM-based methods with  $53\%$  less GPU memory and supports 4096p inference on a 32G consumer-grade GPU, which is not easily possible with softmax attention. While our method is not optimized for high-resolution videos, it paves the way for developing foundation models tailored to the high-resolution regime.
+
+In summary, we introduce a lightweight memory network that: 1) employs linear instead of softmax attention for memory matching, enabling efficient video object segmentation, 2) maintains constant memory usage regardless of video length, and 3) supports 4096p high-resolution inference on 32G consumer-grade hardware. Our method demonstrates competitive performance across various video benchmarks, offering computational efficiency compared to state-of-the-art methods.
+
+# 2. Related Work
+
+Semi-supervised VOS. Semi-supervised VOS methods propagate sparse manual annotations, typically provided as one or more labeled frames, across the entire video sequence. Note that the term "semi-supervised" refers to the level of supervision required during inference, not training [39]. Early VOS methods [1, 2, 25, 33, 38] solve an optimization problem with an energy defined over a graph structure with hand-crafted energy terms. With the success of deep learning, various deep networks [3-5, 7, 24, 30, 47, 48, 50, 52-55] have been proposed, including propagation-based [40], detection-based [7], and hybrid methods [35, 57]. Among these deep networks, online learning [7, 32, 51] is a common practice in which networks are trained or fine-tuned during test time. However,
+
+online learning results in slow inference, which limits its practical use. To eliminate the need for online adaptation, offline methods [10-14, 36, 59] design deep networks that can perform object-agnostic segmentation at test time. Our method belongs to offline learning approaches; specifically, it uses a memory network with linear matching.
+
+Memory-based VOS. Space-time memory (STM) networks [10, 12, 14, 36, 61] are popular memory-based methods. The seminal work of Oh et al. [36] stores past frames and their object masks as key-value pairs to help segment the current frame, treated as a query. Segmentation is performed by matching each spatial position in the query to all spatiotemporal positions in the memory frames via softmax attention [49]. This softmax matching mechanism has been widely adopted in subsequent works [10, 12, 14, 43], with improved computational efficiency [12, 61] and hierarchical memory storage [10]. Recently, Cutie [14] achieved state-of-the-art performance by enhancing memory readout with an object transformer using cross attention. However, such methods encounter high computational costs and out-of-memory issues as video length and resolution increase [10, 12-14, 29]. In contrast, our method applies linear attention for memory matching, reducing the large softmax attention matrix to a constant-size 2D state. This enables constant computational costs for arbitrarily long videos and greatly improves memory efficiency as resolution scales.
+
+Efficient attention. Traditional softmax attention [49] suffers from significant memory bottlenecks with high-resolution videos segmentation, as it requires storing an attention matrix that is quadratic to the number of pixels in each frame. Linear attention [27] reduces the computational complexity of attention from quadratic to linear by linearizing the attention, which can be computed recurrently as a linear recurrent neural network. While linear attention is computationally more efficient, it often comes with a trade-off in model performance. Shen et al. [44] improve linear attention by proposing a separate normalization of queries and keys using a softmax function before computing the inner product. Cai et al. [8] propose multiscale linear attention for high-resolution dense prediction tasks, achieving state-of-the-art performance. Flash Attention [16] accelerates GPU training by optimizing the use of memory hierarchy, while sparse-local attention [15] and sliding window attention [26] reduce global attention costs through selective focusing on parts of the spatio-temporal volume. Recently, Yang et al. [58] introduced gated linear attention, an improved version of linear attention with data-dependent gates, delivering competitive performance in language modeling compared to standard softmax attention and other linear-time-inference models such as Ret-
+
+Net [46] and Mamba [21]. Building on these advances, we investigate linear attention for semi-supervised VOS to overcome the scalability challenges of softmax-based memory networks in long, high-resolution settings.
+
+Efficient VOS. With the rise of long and high-resolution videos, efficiency in VOS has become crucial to handle larger data volumes and computational demands while ensuring high-quality performance. Early propagation-based methods [9, 57] are fast and memory-efficient but less accurate. Recent memory networks [12, 36] improve efficiency by updating the memory bank every five frames for long videos. XMem [10] enhances memory efficiency further by bounding memory bank size and introducing a training-free memory consolidation mechanism for long-term VOS, along with a sensory memory for temporal smoothness. This hierarchical memory design is adopted by Cutie [14], which uses cross-attention in an object transformer to boost performance. However, Cutie's fixed-size memory bank still faces computational limits with increasing resolution and struggles with occlusions and fast motion. Our approach overcomes these limitations by replacing softmax matching, the primary memory bottleneck, with linear matching, ensuring constant costs for long videos and linear memory growth as resolution scales.
+
+# 3. Method
+
+We propose LiVOS, a light memory network for video object segmentation. The key innovation lies in replacing softmax matching with linear matching in standard spacetime memory networks, effectively eliminating the large attention matrix that grows linearly over time and quadratically with spatial dimensions. With linear matching, LiVOS maintains a constant-size state matrix that is updated recurrently, making it highly efficient and well-suited for long and high-resolution videos. In the following sections, we first outline the architecture of the light memory networks (Sec. 3.1), then present gated linear matching (Sec. 3.2), an enhanced form of linear matching at the core of our method, and conclude with implementation details (Sec. 3.4).
+
+# 3.1. Light Memory Networks
+
+As discussed in Sec. 1, classical space-time memory (STM) networks are highly inefficient due to the quadratic complexity of softmax attention, leading to memory issues as video length and resolution grow. To address this, we reduce computational complexity by using linear attention for memory matching, replacing the large attention matrix with a lightweight, constant-size state matrix. This design forms the basis of our light memory network, as illustrated in Fig. 4. We first encode video frames into keys with an image encoder and masks into values with a mask encoder.
+
+![](images/54d9d77ee65ea5a751f15279f7a99815c5db3e217bd8ca6589084e252cba2800.jpg)  
+Figure 4. LiVOS Overview. Given a query frame, we first extract its key using an image encoder and retrieve its value via gated linear matching. This value is then enhanced by two external memories before being processed by a lightweight mask decoder for segmentation. Notably, during memory matching, our method requires only a constant-size state and gate matrix. The gate matrix is generated by a gate projector that converts the pixel-level features from the last memory frame into a sparse vector, which is then transformed to a gate matrix for element-wise multiplication with the state.
+
+We then employ gated linear matching, an enhanced form of linear matching, to generate the query frame's memory readout. Following Cutie [14], we enrich the memory readout by two lightweight memories: a sensory memory [10] for low-level object information and an object memory [14] for high-level object semantics. The sensory memory is fused with the readout via element-wise addition, while the object memory is fused via an object transformer consisting with cross-attention layers. The enriched readout is then processed by a mask decoder to generate the final segmentation mask. Additionally, we reuse features from the key encoder to enhance the features for both the value encoder and the mask decoder. In the next section, we detail gated linear matching, the core of our light memory network.
+
+# 3.2. Gated Linear Matching
+
+Notations. Given  $t$  memory frames  $\mathbf{I}_{1:t}$  and their segmentations  $\mathbf{M}_{1:t}$ , we extract from them memory keys  $\mathbf{K}_{1:t} \in \mathbb{R}^{tHW \times C_k}$  and values  $\mathbf{V}_{1:t} \in \mathbb{R}^{tHW \times C_v}$ . Here,  $H$  and  $W$  denotes the spatial dimensions, and  $C_k$  and  $C_v$  are the feature dimensions for the keys and values, respectively. Given a query frame  $\mathbf{I}_{t+1}$ , we aim to obtain its segmentation  $\mathbf{M}_{t+1}$ . We first extract its key  $\mathbf{K}_{t+1} \in \mathbb{R}^{HW \times C_k}$  and then retrieve its value  $\mathbf{V}_{t+1} \in \mathbb{R}^{HW \times C_v}$  through gated linear matching. To illustrate this, we begin by introducing the traditional softmax matching.
+
+Softmax Matching. Softmax matching is widely used in space-time memory (STM) networks [10, 12, 14, 36]. Suppose we have a spatiotemporal memory consisting of memory keys  $\mathbf{K}_{1:t} \in \mathbb{R}^{tHW \times C_k}$  and values  $\mathbf{V}_{1:t} \in \mathbb{R}^{tHW \times C_v}$ . Given a query frame  $\mathbf{I}_{t+1}$ , we first extract its key  $\mathbf{K}_{t+1} \in \mathbb{R}^{HW \times C_k}$  and then retrieve its value  $\mathbf{V}_{t+1} \in \mathbb{R}^{HW \times C_v}$  via softmax attention:
+
+$$
+\mathbf {V} _ {t + 1} = \operatorname {S o f t m a x} \left(\mathbf {K} _ {t + 1} \mathbf {K} _ {1: t} ^ {T}\right) \mathbf {V} _ {1: t}. \tag {1}
+$$
+
+We reformulate the above softmax attention in a parallel form for  $t$  memory frames:
+
+$$
+\mathbf {V} _ {t + 1} = \frac {\sum_ {i = 1} ^ {t} e x p \left(\mathbf {K} _ {t + 1} \mathbf {K} _ {i} ^ {T}\right) \mathbf {V} _ {i}}{\sum_ {i = 1} ^ {t} e x p \left(\mathbf {K} _ {t + 1} \mathbf {K} _ {i} ^ {T}\right) \mathbf {1}}, \tag {2}
+$$
+
+where  $\exp(\cdot)$  is an element-wise exponential for the matrix entries and  $\mathbf{1} \in \mathbb{R}^{HW \times 1}$  is an all-one vector. The division in the above equation is applied element-wise over the spatial dimensions  $HW$ . Unless specified otherwise, we will continue using this element-wise division throughout the manuscript to keep the notation concise.
+
+Based on Eq. 2, we can write a generalized memory matching for any similarity function as follows,
+
+$$
+\mathbf {V} _ {t + 1} = \frac {\sum_ {i = 1} ^ {t} \operatorname {s i m} \left(\mathbf {K} _ {t + 1} , \mathbf {K} _ {i}\right) \mathbf {V} _ {i}}{\sum_ {i = 1} ^ {t} \operatorname {s i m} \left(\mathbf {K} _ {t + 1} , \mathbf {K} _ {i}\right) \mathbf {1}}. \tag {3}
+$$
+
+Eq. 3 is equivalent to Eq. 2 if we use the similarity function  $\text{sim}(\mathbf{K}_{\mathbf{t} + 1}, \mathbf{K}_{\mathbf{i}}) = \exp(\mathbf{K}_{\mathbf{t} + 1} \mathbf{K}_{\mathbf{i}}^T)$ .
+
+Linear Matching (Parallel Form). The similarity function  $sim(\cdot)$  in Eq. 3 needs to be non-negative. Given a kernel  $k(x,y) = \langle \phi(x), \phi(y) \rangle$  with a feature representation  $\phi(\cdot)$ , we can rewrite Eq. 3 as follows,
+
+$$
+\mathbf {V} _ {t + 1} = \frac {\sum_ {i = 1} ^ {t} \phi \left(\mathbf {K} _ {t + 1}\right) \phi \left(\mathbf {K} _ {i}\right) ^ {T} \mathbf {V} _ {i}}{\sum_ {i = 1} ^ {t} \phi \left(\mathbf {K} _ {t + 1}\right) \phi \left(\mathbf {K} _ {i}\right) ^ {T} \mathbf {1}}, \tag {4}
+$$
+
+and then further simplify it by making use of the associative property of matrix multiplication to
+
+$$
+\mathbf {V} _ {t + 1} = \frac {\phi (\mathbf {K} _ {t + 1}) \sum_ {i = 1} ^ {t} \phi (\mathbf {K} _ {i}) ^ {T} \mathbf {V} _ {i}}{\phi (\mathbf {K} _ {t + 1}) \sum_ {i = 1} ^ {t} \phi (\mathbf {K} _ {i}) ^ {T} \mathbf {1}}. \tag {5}
+$$
+
+$\phi (\cdot)$  can be any non-linear function. Inspired by Shen et al. [44], we set  $\phi (\cdot)$  as softmax function that is applied rowwise to the keys  $\mathbf{K}_i\in \mathbb{R}^{HW\times C_k}$ .
+
+Linear Matching (Recurrent Form). Letting  $\mathbf{S}_t = \sum_{i=1}^t \phi(\mathbf{K}_i)^T \mathbf{V}_i$  and  $\mathbf{Z}_t = \sum_{i=1}^t \phi(\mathbf{K}_i)^T \mathbf{1}$  where  $\mathbf{S}_t \in \mathbb{R}^{C_k \times C_v \times N}$  and  $\mathbf{Z}_t \in \mathbb{R}^{C_k \times HW}$ , we can rewrite Eq. 5 in a recurrent form,
+
+$$
+\mathbf {S} _ {t} = \mathbf {S} _ {t - 1} + \phi (\mathbf {K} _ {i}) ^ {T} \mathbf {V} _ {i}, \tag {6}
+$$
+
+$$
+\mathbf {Z} _ {t} = \mathbf {Z} _ {t - 1} + \phi (\mathbf {K} _ {i}) ^ {T} \mathbf {1}, \tag {7}
+$$
+
+$$
+\mathbf {V} _ {t + 1} = \frac {\phi (\mathbf {K} _ {t + 1}) \mathbf {S} _ {t}}{\phi (\mathbf {K} _ {t + 1}) \mathbf {Z} _ {t}}. \tag {8}
+$$
+
+Here,  $\mathbf{S}_t\in \mathbb{R}^{C_k\times C_v}$  can be regarded as a 2D recurrent hidden state that is constant size. From a sequence modeling perspective [27],  $\phi (\mathbf{K}_i)^T\mathbf{V}_i$  expands the state from the key space  $\mathbb{R}^{C_k}$  and value space  $\mathbb{R}^{C_v}$  into the state space  $\mathbb{R}^{C_k\times C_v}$ , while  $\phi (\mathbf{K}_{t + 1})\mathbf{S}_t$  reduces it back.
+
+Complexity Analysis. For softmax matching in Eq. 2, the space and time complexity is  $\mathcal{O}(THW\times HW\times N)$ , where  $T$  is the number of memory frames,  $H$  and  $W$  are spatial dimensions, and  $N$  is the number of objects. It is quadratic in the spatial dimensions  $HW$  because the attention matrix must be stored to compute the weights for values. In contrast, linear matching has space and time complexity of  $\mathcal{O}(HW\times N)$ . It is linear in the spatial dimensions  $HW$  because we reduce the large attention matrix to a constant-size 2D state  $S_{t}$ . Fig. 2 shows the CPU latency comparison between linear and softmax matching.
+
+Gated Linear Matching. The linear matching in Eq. 8 does not have a selection mechanism, which has shown to be crucial in long-context tasks [6]. To enhance selectivity, we propose gated linear matching in Eq. 9, where the state  $\mathbf{S}_t \in \mathbb{R}^{C_k \times C_v}$  is multiplied element-wise by a data-dependent forget gate  $\mathbf{G}_t \in (0,1)^{C_k \times C_v}$ .
+
+$$
+\mathbf {S} _ {t} = \mathbf {G} _ {t} \odot \mathbf {S} _ {t - 1} + \phi (\mathbf {K} _ {i}) ^ {T} \mathbf {V} _ {i}, \tag {9}
+$$
+
+where  $\odot$  denotes element-wise multiplication. The gate  $\mathbf{G}_t$  controls which information is enhanced or suppressed (more details please refer to Sec. 3.4). Although the concept of gated linear matching is inspired by gated linear attention [58] in language modeling, we explore its application in the context of semi-supervised VOS.
+
+# 3.3. Fusion with External Memory
+
+After gated linear matching, we obtain the memory readout  $\mathbf{V}_{t + 1}$  for the query frame  $\mathbf{I}_{t + 1}$ . Following Cutie [14], we enrich it with two lightweight external memories: a sensory memory for low-level object information and an object memory for high-level object semantics. We present ablation studies for these two modules in Sec. 4.4. Since we claim no contributions for these components, we provide additional details in the Appendix.
+
+# 3.4. Implementation Details
+
+Encoder. We use ResNet-50 [22] as the image encoder and ResNet-18 [22] as the mask encoder, each producing multi-scale features:  $\mathbf{f}_4$ ,  $\mathbf{f}_8$ , and the coarsest feature  $\mathbf{f}_{16} \in \mathbb{R}^{HW \times C_f}$ , where the subscript denotes the stride 16. Keys  $\mathbf{K} \in \mathbb{R}^{HW \times C_k}$  are extract from the image encoder's coarsest feature using convolutional layers, and values  $\mathbf{V} \in \mathbb{R}^{HW \times C_v}$  are similarly extracted from the mask encoder's coarsest feature. Following Cutie [14], the image encoder's multi-scale features are reused in the mask encoder for value extraction, with  $C_k = 64$  and  $C_v = 256$ .
+
+Decoder. We adopt the lightweight mask decoder from Cutie [14] for simplicity and efficiency. This decoder takes as input the value readout  $\mathbf{V}$  at stride 16 and skip connections  $\mathbf{f}_4$  and  $\mathbf{f}_8$  from the image encoder at strides 4 and 8, respectively. The value readout is processed with two upsampling blocks, incorporating skip connections to retain high-frequency details. Each block bilinearly upsamples the input feature by a factor of two, then adds the result to the skip-connection features. For multi-object cases, we apply soft-aggregation [36] to merge object logits.
+
+Gate. The state gate can be parameterized in various ways [58], depending on a balance between parameter efficiency, training efficiency, and state size. In our work, we obtain the data-dependent gate via low-rank parameterization  $\mathbf{G}_{\mathbf{t}} \in \mathbb{R}^{C_k \times C_v} = \alpha_{\mathbf{t}} \mathbf{1}^T$ , where  $\mathbf{1} \in \mathbb{R}^{C_v \times 1}$  is an all-one vector and  $\alpha_{\mathbf{t}} \in (0,1)^{C_k \times 1}$  is extracted from the image encoder's coarsest feature map  $\mathbf{f}_t \in \mathbb{R}^{HW \times C_f}$ . To implement this, we first use a depth-wise convolutional layer to convert the feature  $\mathbf{f}_t$  from  $\mathbb{R}^{HW \times C_f}$  to  $\mathbb{R}^{HW \times C_k}$ , and then sum over its spatial dimensions to obtain  $\hat{\alpha}_{\mathbf{t}} \in \mathbb{R}^{C_k \times 1}$ , followed by a Sigmoid function to obtain  $\alpha_{\mathbf{t}} \in (0,1)^{C_k \times 1}$ .
+
+**Pretraining.** Our method relies solely on ImageNet [17] pretraining, without additional pretraining on static images or synthetic videos like BL30K [34]. While static image pretraining is standard in baseline methods (Sec. 4.2), we omit it due to its marginal improvement and increased computational burden.
+
+Training. We use a combined loss function of cross-entropy and soft dice loss with equal weighting following [10, 13, 14]. Following Cutie [14], we adopt point supervision with  $K = 12544$  sampled points instead of the whole mask for efficient training. We use PyTorch [37] and AdamW [31] optimizer with an initial learning rate of  $1e^{-4}$ , a batch size of 16, and a weight decay of 0.001. Each training batch contains 8 frames randomly selected from a video and cropped to a default size  $480 \times 480$ . Our training lasts for  $125\mathrm{K}$  iterations, reducing the learning rate by a factor of 10 after  $100\mathrm{K}$  and  $115\mathrm{K}$  iterations. The state and the gate are updated for each frame in a training batch. To mitigate overfitting, we apply a learning rate multiplier  $r = 0.1$  to the image encoder. We also clip the global gradient norm to  $\tau = 3$  and use stable data augmentation [13]. The training processes were conducted on four NVIDIA A6000 GPUs.
+
+Inference. Unless stated otherwise, we resize the input videos so that the shorter edge is no more than 480 pixels, then rescale the model's prediction to the original resolution. We segment video frames sequentially and update the state as well as the gate for each frame. For datasets such as YouTube-VOS [56] where new objects may appear in intermediate frames, we create a new state for each new object with negligible computational costs. Note that training has no such issue because we fix the number of classes in a training batch. The evaluations were conducted using an NVIDIA A6000 GPU.
+
+# 4. Experiments
+
+# 4.1. Benchmarks
+
+Datasets. We train and evaluate our method on the following datasets: 1) DAVIS 2017 [39, 42], a widely used VOS dataset with three main sets: 1) a training set with 60 videos (4,219 frames, 138 objects), 2) a validation set with 30 videos (2,023 frames, 59 objects), and 3) a test set with 30 videos (2,037 frames, 89 objects). 2) YouTube-VOS 2019 [56], one of the largest VOS dataset, featuring a wide range of challenging real-world scenarios. The dataset consists of a training set with 3,471 videos (197,292 frames) and a validation set with 507 videos (19,981 frames). There are 65 seen object categories in the training set and 26 unseen categories only appear in the validation set, challenging a model's generalization ability. 3) MOSE [18], a large-scale video object segmentation (VOS) benchmark empha
+
+sizing multi-object scenarios in diverse environments. It comprises 2,149 videos, divided into 1,507 training videos, 311 validation videos, and 331 testing videos. The dataset includes 5,200 objects across 36 distinct categories. In this work, we utilize the training set for model training and evaluate performance on the validation set. 4) LVOS [23], a dataset designed specifically for video object segmentation in long, continuous video sequences, focusing on more extended temporal challenges. It's divided into three main sets: 1) a training set with 120 videos, 2) a validation set with 50 videos, and 3) a test set with 50 videos. There are 126,280 frames and 156,432 annotations in total. In this work, we report evaluation results on the validation and test sets without training our model on LVOS [23].
+
+Evaluation Metrics. We report Region Jaccard  $\mathcal{J}$  [39], contour accuracy  $\mathcal{F}$  [19], and their average  $\mathcal{J} \& \mathcal{F}$  to measure the segmentation quality. For YouTube-VOS, we additionally report  $\mathcal{G}$  as the average of  $\mathcal{J} \& \mathcal{F}$  across both seen and unseen classes. We also report frames per second (FPS) and GPU memory consumption (i.e. maximum GPU memory allocated by PyTorch [37]) to measure speed and resource usage, respectively. Both metrics are recorded on the same machine under similar conditions for all methods.
+
+# 4.2. Baselines
+
+We compare LiVOS with various types of approaches, including state-of-the-art space-time memory (STM) networks, represented by Cutie [14] and methods without using STM, represented by RDE [29]. This section only introduces several representative methods. A complete introduction is included in the appendix.
+
+RDE [29] introduces a recurrent dynamic embedding to maintain a constant-size memory, with image and mask encoders based on ResNet-50. We use the version without BL30K [11] pretraining as a baseline.
+
+STCN [12] is a state-of-the-art memory network building on STM [36], enhancing robustness and efficiency. We use the model without BL30K [11] pretraining.
+
+XMem [10] targets long-term videos with a compact long-term memory, a fast-updating sensory memory, and an STCN-based working memory. As with STCN, we use the model without BL30K[11] pretraining.
+
+Cutie [14] enhances XMem[10] with a top-down, object-level memory reading mechanism for improved video segmentation. We use its small and base models as baselines. We also limit Cutie to using a single memory frame during inference for fair comparison with non-STM methods.
+
+# 4.3. Comparisons
+
+We compare our method with baselines on three types of video benchmarks: 1) short videos, 2) long-term videos, and 3) high-resolution videos.
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">with STM</td><td colspan="3">MOSE</td><td colspan="3">DAVIS-17 val</td><td colspan="3">DAVIS-17 test</td><td colspan="6">YouTubeVOS-2019 val</td></tr><tr><td>J&amp;F</td><td>J</td><td>F</td><td>J&amp;F</td><td>J</td><td>F</td><td>J&amp;F</td><td>J</td><td>F</td><td>G</td><td>Js</td><td>Fs</td><td>Ju</td><td>Fu</td><td></td></tr><tr><td>STCN [12] NeurIPS&#x27;21</td><td>✓</td><td>52.5</td><td>48.5</td><td>56.6</td><td>85.4</td><td>82.2</td><td>88.6</td><td>76.1</td><td>72.7</td><td>79.6</td><td>82.7</td><td>81.1</td><td>85.4</td><td>78.2</td><td>85.9</td><td></td></tr><tr><td>AOT [61] NeurIPS&#x27;21</td><td>✓</td><td>58.4</td><td>54.3</td><td>62.6</td><td>84.9</td><td>82.3</td><td>87.5</td><td>79.6</td><td>75.9</td><td>83.3</td><td>85.3</td><td>83.9</td><td>88.8</td><td>79.9</td><td>88.5</td><td></td></tr><tr><td>XMem [10] ECCV&#x27;22</td><td>✓</td><td>56.3</td><td>52.1</td><td>60.6</td><td>86.2</td><td>82.9</td><td>89.5</td><td>81.0</td><td>77.4</td><td>84.5</td><td>85.5</td><td>84.3</td><td>88.6</td><td>80.3</td><td>88.6</td><td></td></tr><tr><td>DeAOT [59] NeurIPS&#x27;22</td><td>✓</td><td>59.0</td><td>54.6</td><td>63.4</td><td>85.2</td><td>82.2</td><td>88.2</td><td>80.7</td><td>76.9</td><td>84.5</td><td>85.6</td><td>84.2</td><td>89.2</td><td>80.2</td><td>88.8</td><td></td></tr><tr><td>DEVA [13] ICCV&#x27;23</td><td>✓</td><td>60.0</td><td>55.8</td><td>64.3</td><td>86.8</td><td>83.6</td><td>90.0</td><td>82.3</td><td>78.7</td><td>85.9</td><td>85.5</td><td>85.0</td><td>89.4</td><td>79.7</td><td>88.0</td><td></td></tr><tr><td>Cutie-small [14] CVPR&#x27;24</td><td>✓</td><td>62.2</td><td>58.2</td><td>66.2</td><td>87.2</td><td>84.3</td><td>90.1</td><td>84.1</td><td>80.5</td><td>87.6</td><td>86.2</td><td>85.3</td><td>89.6</td><td>80.9</td><td>89.0</td><td></td></tr><tr><td>Cutie-small [14] CVPR&#x27;24</td><td>✓</td><td>67.4</td><td>63.1</td><td>71.7</td><td>86.5</td><td>83.5</td><td>89.5</td><td>83.8</td><td>80.2</td><td>87.5</td><td>86.3</td><td>85.2</td><td>89.7</td><td>81.1</td><td>89.2</td><td></td></tr><tr><td>Cutie-base [14] CVPR&#x27;24</td><td>✓</td><td>64.0</td><td>60.0</td><td>67.9</td><td>88.8</td><td>85.4</td><td>92.3</td><td>84.2</td><td>80.6</td><td>87.7</td><td>86.1</td><td>85.5</td><td>90.0</td><td>80.6</td><td>88.3</td><td></td></tr><tr><td>Cutie-base [14] CVPR&#x27;24</td><td>✓</td><td>68.3</td><td>64.2</td><td>72.3</td><td>88.8</td><td>85.6</td><td>91.9</td><td>85.3</td><td>81.4</td><td>89.3</td><td>86.5</td><td>85.4</td><td>90.0</td><td>81.3</td><td>89.3</td><td></td></tr><tr><td>CFBI [60] ECCV&#x27;20</td><td>✗</td><td>-</td><td>-</td><td>-</td><td>81.9</td><td>79.1</td><td>84.6</td><td>74.8</td><td>71.1</td><td>78.5</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td></td></tr><tr><td>CFBI+ [62] TPAMI&#x27;21</td><td>✗</td><td>-</td><td>-</td><td>-</td><td>82.9</td><td>80.1</td><td>85.7</td><td>75.6</td><td>71.6</td><td>79.6</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td></td></tr><tr><td>SwiftNet [53] CVPR&#x27;21</td><td>✗</td><td>-</td><td>-</td><td>-</td><td>81.1</td><td>78.3</td><td>83.9</td><td>-</td><td>-</td><td>-</td><td>77.8</td><td>77.8</td><td>81.8</td><td>72.3</td><td>79.5</td><td></td></tr><tr><td>RDE [29] CVPR&#x27;22</td><td>✗</td><td>46.8</td><td>42.4</td><td>51.3</td><td>84.2</td><td>80.8</td><td>87.5</td><td>77.4</td><td>73.6</td><td>81.2</td><td>81.9</td><td>81.1</td><td>85.5</td><td>76.2</td><td>84.8</td><td></td></tr><tr><td>MobileVOS [34] CVPR&#x27;23</td><td>✗</td><td>-</td><td>-</td><td>-</td><td>83.7</td><td>80.2</td><td>87.1</td><td>-</td><td>-</td><td>-</td><td>82.3</td><td>81.6</td><td>86.0</td><td>76.3</td><td>85.2</td><td></td></tr><tr><td>Cutie-small† [14] CVPR&#x27;24</td><td>✗</td><td>49.3</td><td>45.4</td><td>53.2</td><td>76.4</td><td>73.0</td><td>79.8</td><td>71.6</td><td>67.9</td><td>75.3</td><td>79.0</td><td>78.0</td><td>81.9</td><td>74.5</td><td>81.8</td><td></td></tr><tr><td>Cutie-small† [14] CVPR&#x27;24</td><td>✗</td><td>51.7</td><td>47.7</td><td>55.7</td><td>74.9</td><td>71.7</td><td>78.2</td><td>72.3</td><td>68.8</td><td>75.9</td><td>78.9</td><td>77.6</td><td>81.4</td><td>74.6</td><td>81.9</td><td></td></tr><tr><td>Cutie-base† [14] CVPR&#x27;24</td><td>✗</td><td>50.6</td><td>46.6</td><td>54.6</td><td>79.3</td><td>75.8</td><td>82.7</td><td>73.5</td><td>70.0</td><td>77.0</td><td>80.1</td><td>79.1</td><td>83.3</td><td>75.2</td><td>82.7</td><td></td></tr><tr><td>Cutie-base† [14] CVPR&#x27;24</td><td>✗</td><td>52.6</td><td>48.6</td><td>56.6</td><td>77.5</td><td>74.1</td><td>80.8</td><td>73.2</td><td>69.4</td><td>76.9</td><td>79.5</td><td>78.4</td><td>82.4</td><td>75.1</td><td>82.4</td><td></td></tr><tr><td>LiVOS</td><td>✗</td><td>59.2</td><td>55.6</td><td>62.8</td><td>84.4</td><td>81.2</td><td>87.6</td><td>78.2</td><td>74.8</td><td>81.7</td><td>79.9</td><td>82.6</td><td>86.8</td><td>71.7</td><td>78.4</td><td></td></tr><tr><td>LiVOS*</td><td>✗</td><td>58.4</td><td>54.7</td><td>62.0</td><td>85.1</td><td>81.9</td><td>88.3</td><td>81.0</td><td>77.4</td><td>84.5</td><td>81.3</td><td>83.6</td><td>87.6</td><td>73.3</td><td>80.6</td><td></td></tr><tr><td>LiVOS</td><td>✗</td><td>64.8</td><td>60.9</td><td>68.7</td><td>84.0</td><td>80.6</td><td>87.3</td><td>79.6</td><td>76.2</td><td>82.9</td><td>82.6</td><td>83.5</td><td>87.6</td><td>75.8</td><td>83.3</td><td></td></tr></table>
+
+Table 1. Quantitative comparisons on short videos (480p). All methods are trained on 480p videos and use ResNet as the backbone: Cutie-small uses ResNet-18, CFBI/CFBI+ use ResNet-101, and the rest use ResNet-50.  $\downarrow$  represents models trained on YouTube VOS and DAVIS;  $\downarrow$  denotes additional training with MOSE; * denotes training with 30k additional iterations beyond the standard 125k;  $\dagger$  indicates downgraded Cutie models using only one memory frame during inference (more comparisons with the downgraded Cutie models are shown in the appendix). LiVOS notably improves segmentation quality over non-STM approaches and matches STM-based methods.  
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">with STM</td><td rowspan="2">Key Encoder</td><td rowspan="2">Value Encoder</td><td colspan="5">LVOS val</td><td colspan="5">LVOS test</td></tr><tr><td>J&amp;F</td><td>J</td><td>F</td><td>Mem↓</td><td>FPS↑</td><td>J&amp;F</td><td>J</td><td>F</td><td>Mem↓</td><td>FPS↑</td></tr><tr><td>DEVA [14] ICCV&#x27;23</td><td>✓</td><td>RN-50</td><td>RN-18</td><td>58.3</td><td>52.8</td><td>63.8</td><td>1147M</td><td>48.3</td><td>54.0</td><td>49.0</td><td>59.0</td><td>1347M</td><td>46.6</td></tr><tr><td>DEVA [14] ICCV&#x27;23</td><td>✓</td><td>RN-50</td><td>RN-18</td><td>55.9</td><td>51.1</td><td>60.7</td><td>1147M</td><td>48.3</td><td>56.5</td><td>52.2</td><td>60.8</td><td>1347M</td><td>46.6</td></tr><tr><td>Cutie-small [14] CVPR&#x27;24</td><td>✓</td><td>RN-18</td><td>RN-18</td><td>58.8</td><td>54.6</td><td>62.9</td><td>1013M</td><td>34.0</td><td>57.2</td><td>53.7</td><td>60.7</td><td>1094M</td><td>32.8</td></tr><tr><td>Cutie-small [14] CVPR&#x27;24</td><td>✓</td><td>RN-18</td><td>RN-18</td><td>60.7</td><td>55.6</td><td>65.8</td><td>1013M</td><td>34.0</td><td>56.9</td><td>53.5</td><td>60.2</td><td>1094M</td><td>32.8</td></tr><tr><td>Cutie-base [14] CVPR&#x27;24</td><td>✓</td><td>RN-50</td><td>RN-18</td><td>60.1</td><td>55.9</td><td>64.2</td><td>1092M</td><td>30.1</td><td>56.2</td><td>51.8</td><td>60.5</td><td>1175M</td><td>29.7</td></tr><tr><td>Cutie-base [14] CVPR&#x27;24</td><td>✓</td><td>RN-50</td><td>RN-18</td><td>63.5</td><td>59.1</td><td>67.9</td><td>1092M</td><td>30.1</td><td>63.6</td><td>59.1</td><td>68.0</td><td>1175M</td><td>29.7</td></tr><tr><td>RDE [29] CVPR&#x27;22</td><td>✗</td><td>RN-50</td><td>RN-18</td><td>47.2</td><td>41.7</td><td>52.7</td><td>9.0G‡</td><td>40.6</td><td>44.7</td><td>39.2</td><td>50.2</td><td>12.7G‡</td><td>39.8</td></tr><tr><td>Cutie-small† [14] CVPR&#x27;24</td><td>✗</td><td>RN-18</td><td>RN-18</td><td>48.2</td><td>43.9</td><td>52.5</td><td>585M</td><td>56.1</td><td>45.2</td><td>41.3</td><td>49.0</td><td>686M</td><td>55.2</td></tr><tr><td>Cutie-small† [14] CVPR&#x27;24</td><td>✗</td><td>RN-18</td><td>RN-18</td><td>46.1</td><td>42.1</td><td>50.1</td><td>585M</td><td>56.1</td><td>44.0</td><td>40.1</td><td>48.0</td><td>686M</td><td>55.2</td></tr><tr><td>Cutie-base† [14] CVPR&#x27;24</td><td>✗</td><td>RN-50</td><td>RN-18</td><td>49.1</td><td>44.7</td><td>53.4</td><td>668M</td><td>45.5</td><td>48.7</td><td>44.6</td><td>52.7</td><td>748M</td><td>43.0</td></tr><tr><td>Cutie-base† [14] CVPR&#x27;24</td><td>✗</td><td>RN-50</td><td>RN-18</td><td>46.8</td><td>43.1</td><td>50.6</td><td>668M</td><td>45.5</td><td>45.6</td><td>41.6</td><td>49.7</td><td>748M</td><td>43.0</td></tr><tr><td>LiVOS</td><td>✗</td><td>RN-50</td><td>RN-18</td><td>50.6</td><td>46.5</td><td>54.7</td><td>503M</td><td>47.3</td><td>44.6</td><td>41.2</td><td>47.9</td><td>575M</td><td>45.2</td></tr><tr><td>LiVOS*</td><td>✗</td><td>RN-50</td><td>RN-18</td><td>51.2</td><td>46.8</td><td>55.6</td><td>503M</td><td>47.3</td><td>50.9</td><td>47.0</td><td>54.7</td><td>575M</td><td>45.2</td></tr><tr><td>LiVOS</td><td>✗</td><td>RN-50</td><td>RN-18</td><td>51.2</td><td>47.3</td><td>55.1</td><td>503M</td><td>47.3</td><td>47.0</td><td>44.0</td><td>50.0</td><td>575M</td><td>45.2</td></tr></table>
+
+Table 2. Quantitative comparisons on long-term videos (480p). We present the same model variants and notations as in Tab. 1. We additionally report FPS and the maximum GPU memory usage.  ${}^{ \ddagger  }$  unexpectedly large GPU memory consumption for RDE, likely due to implementation issues in its released code. LiVOS consistently achieves the best performance across non-STM methods on both LVOS validation and test sets while using less GPU memory.
+
+Short Videos. Tab. 1 shows results on standard VOS benchmarks: MOSE [18], DAVIS [42], and YouTube VOS [56]. Our method achieves a score of 64.8  $\mathcal{J}\&\mathcal{F}$  on MOSE [18], trailing the state-of-the-art method Cutie [14] by just 3.5  $\mathcal{J}\&\mathcal{F}$ . Note that MOSE is very challenging because of the complexity of multi-object interactions and dynamic
+
+environments. By default, Cutie [14] uses five memory frames. When limited to one memory frame, in a variant labeled Cutie†, its performance drops significantly, falling below ours. Moreover, our method consistently outperforms other non-STM methods, including MobileVOS [34] and RDE [29], across most benchmarks.
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">with STM</td><td colspan="3">1024P</td><td colspan="3">2048P</td><td colspan="3">3072P</td><td colspan="3">4096P</td></tr><tr><td>Mem↓</td><td>FPS↑</td><td>J&amp;F</td><td>Mem↓</td><td>FPS↑</td><td>J&amp;F</td><td>Mem↓</td><td>FPS↑</td><td>J&amp;F</td><td>Mem↓</td><td>FPS↑</td><td>J&amp;F</td></tr><tr><td>STCN [12] NeurIPS&#x27;21</td><td>✓</td><td>22.6G</td><td>3.7</td><td>83.1</td><td>OOM</td><td>N/A</td><td>N/A</td><td>OOM</td><td>N/A</td><td>N/A</td><td>OOM</td><td>N/A</td><td>N/A</td></tr><tr><td>AOT [61] NeurIPS&#x27;21</td><td>✓</td><td>OOM</td><td>N/A</td><td>N/A</td><td>OOM</td><td>N/A</td><td>N/A</td><td>OOM</td><td>N/A</td><td>N/A</td><td>OOM</td><td>N/A</td><td>N/A</td></tr><tr><td>XMem [10] ECCV&#x27;22</td><td>✓</td><td>12.5G</td><td>7.3</td><td>86.8</td><td>OOM</td><td>N/A</td><td>N/A</td><td>OOM</td><td>N/A</td><td>N/A</td><td>OOM</td><td>N/A</td><td>N/A</td></tr><tr><td>DeAOT [59] NeurIPS&#x27;22</td><td>✓</td><td>13.0G</td><td>4.5</td><td>86.9</td><td>OOM</td><td>N/A</td><td>N/A</td><td>OOM</td><td>N/A</td><td>N/A</td><td>OOM</td><td>N/A</td><td>N/A</td></tr><tr><td>DEVA [13] ICCV&#x27;23</td><td>✓</td><td>15.7G</td><td>5.1</td><td>90.0</td><td>OOM</td><td>N/A</td><td>N/A</td><td>OOM</td><td>N/A</td><td>N/A</td><td>OOM</td><td>N/A</td><td>N/A</td></tr><tr><td>Cutie-small [14] CVPR&#x27;24</td><td>✓</td><td>9.7G</td><td>7.6</td><td>89.3</td><td>OOM‡</td><td>N/A</td><td>N/A</td><td>OOM</td><td>N/A</td><td>N/A</td><td>OOM</td><td>N/A</td><td>N/A</td></tr><tr><td>Cutie-base [14] CVPR&#x27;24</td><td>✓</td><td>9.9G</td><td>6.6</td><td>89.5</td><td>150G‡</td><td>N/A</td><td>N/A</td><td>735G‡</td><td>N/A</td><td>N/A</td><td>2815G‡</td><td>N/A</td><td>N/A</td></tr><tr><td>RDE [29] CVPR&#x27;22</td><td>✗</td><td>14.4G</td><td>10.6</td><td>76.3</td><td>OOM</td><td>N/A</td><td>N/A</td><td>OOM</td><td>N/A</td><td>N/A</td><td>OOM</td><td>N/A</td><td>N/A</td></tr><tr><td>Cutie-small† [14] CVPR&#x27;24</td><td>✗</td><td>2.3G</td><td>11.9</td><td>83.7</td><td>30.3G</td><td>2.1</td><td>79.8</td><td>OOM</td><td>N/A</td><td>N/A</td><td>OOM</td><td>N/A</td><td>N/A</td></tr><tr><td>Cutie-base† [14] CVPR&#x27;24</td><td>✗</td><td>2.6G</td><td>10.2</td><td>86.0</td><td>31.1G</td><td>1.9</td><td>79.6</td><td>147G‡</td><td>N/A</td><td>N/A</td><td>563G‡</td><td>N/A</td><td>N/A</td></tr><tr><td>LiVOS</td><td>✗</td><td>2.0G</td><td>12.8</td><td>85.0</td><td>7.7G</td><td>3.5</td><td>80.0</td><td>17.2G</td><td>1.5</td><td>73.4</td><td>30.4G</td><td>0.8</td><td>61.5</td></tr></table>
+
+Long-term Videos. Tab. 2 shows results on the long video benchmark LVOS [23]. Compared with the state-of-the-art recurrent memory network RDE [29], our method is better across all benchmarks. Compared with state-of-the-art STM-based methods, our method delivers competitive performance while being faster and more memory efficient. Even with Cutie's memory bank limited to one memory frame, our method requires less memory while achieving better segmentation quality. Note that memory networks such as Cutie and DEVA employ a bounded memory bank (by default, the number is five), so they have no memory issues when video length increases. To highlight our memory efficiency, we also compare our method with baselines on high-resolution videos, introduced below.
+
+High-resolution Videos. Tab. 3 shows the comparisons on high-resolution videos upsampled from the DAVIS dataset. All space-time memory networks encounter out-of-memory issues at  $2048\mathrm{p}$ . For example, Cutie-base requires approximately 150GB of memory to run inference at  $2048\mathrm{p}$ , far exceeding the capabilities of consumer-grade GPUs. In contrast, our method requires only 7.7GB for  $2048\mathrm{p}$  inference and is the only one capable of inference at  $4096\mathrm{p}$ . While not specifically optimized for high-resolution videos, our method sets the stage for developing foundation models suited to high-resolution regimes. More comparisons with downsampling baselines are shown in the appendix.
+
+# 4.4. Ablations
+
+Tab. 4 shows the results of an ablation study to validate our design choices. The models are trained on YouTube-VOS and DAVIS and evaluated on the DAVIS validation set. No gate is a model variant that disables the gate mechanism in linear matching. No sensory memory is a model variant that disables the sensory memory. No object memory is a model variant that disables the object memory. The gate mechanism in linear matching improves  $1.4\%$ $\mathcal{J}\& \mathcal{F}$ , with only
+
+Table 3. Quantitative comparisons on high-resolution videos (≥1024p). These videos are upsampled from DAVIS 2017 validation set (480p). All models were tested with an NVIDIA A6000 GPU. OOM indicates out-of-memory, exceeding the A6000's 48G limit. ‡ denotes estimated memory usage. Note that LiVOS utilizes no modules dedicated for high-res segmentation, leaving room for future improvements.  
+
+<table><tr><td>Method</td><td>J&amp;F</td><td>J</td><td>F</td><td>FPS ↑</td><td>Mem ↓</td></tr><tr><td>No gate</td><td>83.0</td><td>80.0</td><td>86.0</td><td>40.8</td><td>573M</td></tr><tr><td>No object memory</td><td>80.4</td><td>77.4</td><td>83.4</td><td>70.5</td><td>565M</td></tr><tr><td>No sensory memory</td><td>79.1</td><td>76.3</td><td>81.9</td><td>52.6</td><td>538M</td></tr><tr><td>Full</td><td>84.4</td><td>81.2</td><td>87.6</td><td>40.3</td><td>574M</td></tr></table>
+
+Table 4. Ablation study for LiVOS on DAVIS 2017 val [39].
+
+a minor trade-off in speed and memory usage. The integration of sensory and object memories substantially boost performance, though it comes at the cost of reduced speed and higher memory consumption. In this ablation, we retain linear matching instead of swapping it with softmax matching, as that would make our method similar to Cutie [14].
+
+# 5. Limitations
+
+Our method uses a single recurrent state for the challenging VOS task, which works well for short, low-resolution videos but may lead to suboptimal results on longer, high-resolution ones. We believe a more advanced state [21], as well as multi-scale linear attention [8], could improve performance in these cases. We leave these extensions for future work.
+
+# 6. Conclusion
+
+We proposed the first light memory network that employs gated linear matching, instead of softmax matching, for memory efficient video object segmentation. Our method reformulates the memory matching process into a recurrent framework where the large, quadratic attention matrix is reduced to a small, constant-size recurrent state. Our evaluation results on long and high-resolution videos demonstrated the effectiveness and efficiency of our method, opening the door for high-resolution video foundation models.
+
+Acknowledgement. We thank our reviewers and ACs for their insightful suggestions. This research was, in part, funded by the National Institutes of Health (NIH) under other transactions 1OT2OD038045-01 and NIAMS 1R01AR082684. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing official policies, either expressed or implied, of the NIH.
+
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+# Libra-Merging: Importance-redundancy and Pruning-merging Trade-off for Acceleration Plug-in in Large Vision-Language Model
+
+Longrong Yang $^{1*}$ , Dong Shen $^{2*}$ , Chaoxiang Cai $^{3}$ , Kaibing Chen $^{2}$ , Fan Yang $^{2}$ , Tingting Gao $^{2}$ , Di Zhang $^{2}$ , Xi Li $^{1\dagger}$ $^{1}$ College of Computer Science and Technology, Zhejiang University  
+ $^{2}$ Kuaishou Technology  
+ $^{3}$ School of Software Technology, Zhejiang University
+
+# Abstract
+
+Large Vision-Language Models (LVLMs) have achieved significant progress in recent years. However, the expensive inference cost limits the realistic deployment of LVLMs. Some works find that visual tokens are redundant and compress tokens to reduce the inference cost. These works identify important non-redundant tokens as target tokens, then prune the remaining tokens (non-target tokens) or merge them into target tokens. However, target token identification faces the token importance-redundancy dilemma. Besides, token merging and pruning face a dilemma between disrupting target token information and losing non-target token information. To solve these problems, we propose a novel visual token compression scheme, named Libra-Merging. In target token identification, Libra-Merging selects the most important tokens from spatially discrete intervals, achieving a more robust token importance-redundancy trade-off than relying on a hyper-parameter. In token compression, when non-target tokens are dissimilar to target tokens, Libra-Merging does not merge them into the target tokens, thus avoiding disrupting target token information. Meanwhile, Libra-Merging condenses these non-target tokens into an information compensation token to prevent losing important non-target token information. Our method can serve as a plug-in for diverse LVLMs, and extensive experimental results demonstrate its effectiveness. The code will be publicly available at https://github.com/longrongyang/Libra-Merging.
+
+# 1. Introduction
+
+Large Vision-Language Models (LVLMs) have recently shown considerable progress by incorporating visual processing capabilities into Large Language Models (LLMs).
+
+Numerous recent LVLMs [2, 8, 58-60] indicate that both large model size and extensive dataset size are crucial for enhancing intelligence. Even with sufficiently large model sizes, these models demonstrate "Emergent Abilities". As a result, a range of studies [12, 26, 32] have increased the model size of LVLMs, resulting in the state-of-the-art performance across a variety of tasks.
+
+Although LVLMs achieve state-of-the-art performance, they are expensive to employ in realistic applications due to significant inference costs. To reduce inference costs, some recent works [9, 23] propose compressing visual tokens, based on the finding that visual tokens are highly redundant in LVLMs. For example, FastV [9] treats tokens as important when they have high output attention (attention score of output token on visual tokens), and prunes the bottom  $R\%$  tokens with the lowest output attention. Turbo [23] computes the information degree of each token, a weighted average of attention and redundancy (the highest similarity between the token and other tokens), and averagely merges the top  $R\%$  tokens into their most similar tokens.
+
+In LVLMs, the token compression process can be modeled as identifying important non-redundant tokens (named target tokens) and compressing the remaining tokens (named non-target tokens). However, target token identification and token compression face a dilemma respectively. The dilemma in target token identification lies in the importance-redundancy trade-off. FastV selects the most important tokens, but these tokens may be redundant; Turbo balances importance and redundancy with a hyperparameter, but the fixed hyper-parameter is hard to apply universally to diverse scenarios. As shown in Figure 1 (a), they still preserve redundant information, leading to the losing of some important tokens. As shown in Figure 1 (b), the dilemma in token compression lies in the pruning-merging trade-off. Pruning non-target tokens loses information in non-target tokens; averagely merging non-target and target tokens may disrupt information in target tokens.
+
+(a) Importance-redundancy dilemma in token identification  
+![](images/91a2fc149e800441376cc82be9c64fbe2b9f7501516075f03ff766fc02ed3cc2.jpg)  
+A, B, C are target tokens. A and B are redundant, losing D
+
+(b) Pruning-merging dilemma in token compression  
+Figure 1. (a) Target Token identification. We select the most important token in each interval, avoiding selecting redundant tokens by disrupting the spatial continuity of target tokens, for achieving importance-redundancy trade-off. (b) Token compression. Similar tokens are merged based on their importance. When non-target tokens are dissimilar to target tokens, we condense these non-target tokens into a compensation token, for achieving pruning-merging trade-off. In this work, we follow FastV [9] to treat tokens as important when they have high output attention.  
+![](images/fec163d4ac2e676002abc2978389c5dd129e23defad6278b264a675d47ada8ad.jpg)  
+Ours: Select the most important token from each interval  
+A, C, D are target tokens, which are not redundant  
+Pruning lose information in non-target token  
+Merging disrupt information in target token  
+Ours Importance-informed token merging when no tokens are discriminative to stem trees
+
+Facing the two dilemmas, this work proposes a novel training-free token compression scheme Libra-Merging, which consists of two key modules: (i) Position-driven token identification. Adjacent tokens are usually redundant [15, 27]. Thus, we discretize the visual token sequence into different intervals, and within each interval, we select the most important token as the target token. As shown in Fig. 1 (a), we avoid selecting redundant tokens by disrupting the spatial continuity of target tokens. This technique achieves a more robust importance-redundancy trade-off than using a hyper-parameter. (ii) Importance-informed grouped merging. We find that token merging is harmful when dissimilar tokens merge. Thus, we categorize non-target tokens into positive set (high similarity) and negative set (low similarity) based on their similarities
+
+with target tokens. Tokens in positive set directly merge into target tokens, and we use Softmax to convert token importance to merging weight. To avoid disrupting target tokens, tokens in negative set should not merge into target tokens. However, these tokens may still contain important information, so we compute their importance-informed average as an information compensation token. We achieve a good pruning-merging trade-off by striving to preserve important information. Overall, for a visual token sequence, Libra-Merging first uses position-driven token identification to divide it into target and non-target tokens. Then, importance-informed grouped merging merges non-target tokens into target tokens, resulting in an output token sequence.
+
+In addition, since flash-attention 2 does not output attention scores, we design a hybrid attention mechanism. With the hybrid attention mechanism, we can further employ token compression to accelerate the training of LVLMs.
+
+Our contributions are summarized as:
+
+(i) We propose position-driven token identification to avoid selecting redundant target tokens, which achieves a robust importance-redundancy trade-off in target token identification.  
+(ii) We propose importance-informed grouped merging to prevent disrupting target tokens while preserving important information in non-target tokens, which achieves a good pruning-merging trade-off in token compression.  
+(iii) As a plug-in, our method can be easily integrated into LVLMs, including image-text models and video-text models. Extensive experiments on different models have validated that our method Libra-Merging achieves significantly higher performance than existing works.
+
+# 2. Related Works
+
+# 2.1. Large Vision-Language Model
+
+Large Language Models (LLMs) have shown remarkable proficiency in following instructions and generalizing across various tasks. To extend these capabilities to incorporate visual information, Large Vision-Language Models (LVLMs) like GPT-4 and LLaVA employ frozen visual encoders and trainable visual projectors. These models typically transform visual data into visual tokens, which are then used to condition the adaptation of text tokens within LLMs [1, 36, 37, 42–46, 50, 51, 53–56]. Recent advancements in LVLMs have primarily focused on two aspects. The first involves optimizing training strategies, e.g., [2, 6]. The second, and more prevalent, focuses on enhancing visual components. This includes expanding datasets [31, 59], improving image encoders [2, 11], and aligning the input and projection layers [5, 12, 29, 57, 60]. These efforts, particularly the expansion of visual instruction-tuning datasets and the scaling up of model sizes, have significantly boosted the visual understanding capabilities of LVLMs.
+
+# 2.2. Token Compression
+
+There have been studies on improving the efficiency of Vision-Language Models (VLMs) before the era of Large Vision-Language Models (LVLMs). A majority of them focus on token compression for vision transformers (ViTs). Token compression for ViTs can be roughly categorized as token pruning [4, 10, 14, 18, 25, 28, 38, 47] and token merging [3, 4, 10, 13, 15, 17, 19, 24, 27, 35, 39, 49, 61]. EViT [28] extends Top-K pruning by creating a "fused" token. DynamicViT [38] prunes tokens by keep probabilities produced by a small prediction module. ATS [14] and DiffRate [10] design the dynamic compression ratio for token compression. ToMe [3], K-Medoids [35], and DPC-KNN [13] are token merging methods based on similarity, cluster, and density, respectively. SiT [61], Sinkhorn [17], PatchMerger [39] focus on soft merging. More recently, PYRA [52] has enhanced the training and inference of ViTs via a specialized token merging technique. FastV [9] and IVTP [20] are the initial two works to explore visual token compression for Large Vision-Language Models (LVLMs), which uses language as an interface for various vision-language tasks. ToCom [22] discusses the multi-step token compression. HOMER [41] proposes the use of token compression to enlarge the context length. LLaVolta [7] proposes a training token compression scheme. Turbo [23] is a token merging method designed for LVLMs, which uses information degree to sort tokens and merge tokens with the high information degree. Pruning loses important information in non-target tokens, while merging may disrupt target tokens when dissimilar tokens merge. The proposed importance-informed grouped merging is used to prevent disrupting target tokens while preserving important information in non-target tokens.
+
+# 3. Methodology
+
+# 3.1. Overview
+
+Large Vision-Language Model (LVLM): A LVLM is usually designed to integrate a visual model into the pre-trained LLM. Specifically, the input of the vision model is an image or a video, and its output is a visual token sequence  $\mathcal{Z} = [z_1,z_2,\dots ,z_N]\in \mathbb{R}^{N\times C}$ , where  $N$  is the sequence length of visual tokens. Then, a visual projection layer maps  $\mathcal{Z}\in \mathbb{R}^{N\times C}$  to  $\mathcal{V}\in \mathbb{R}^{N\times D}$ , where  $D$  represents the hidden size. Besides, the instruction text is projected as instruction text tokens  $\mathcal{T} = [t_{1},t_{2},\dots ,t_{P}]\in \mathbb{R}^{P\times D}$ , where  $N$  represents the sequence length of text tokens. LLM consists of stacked multi-head self-attention (MSA) and feed-forward neural networks (FFN), with layer normalization (LN) and residual connections:
+
+$$
+\mathbf {x} _ {0} = \left[ v _ {1}, v _ {2}, \dots , v _ {N}, \dots , t _ {1}, t _ {2}, \dots , t _ {P} \right], \tag {1}
+$$
+
+$$
+\mathbf {x} _ {\ell} ^ {\prime} = \operatorname {M S A} (\mathrm {L N} (\mathbf {x} _ {\ell - 1})) + \mathbf {x} _ {\ell - 1}, \ell \in \{1, \dots , L \}, \tag {2}
+$$
+
+$$
+\mathbf {x} _ {\ell} = \operatorname {F F N} \left(\operatorname {L N} \left(\mathbf {x} ^ {\prime} _ {\ell}\right)\right) + \mathbf {x} ^ {\prime} _ {\ell}, \ell \in \{1, \dots , L \}, \tag {3}
+$$
+
+where  $L$  is the layer number of LLM.
+
+Token Compression: Given an input visual token sequence  $\mathcal{V} = \{v_{1}, v_{2}, \dots, v_{N}\}$ . The token compression usually consists of two steps: (i) Target token identification. Important non-redundant tokens should be selected as target tokens, forming a target set  $T = \{v_{1}^{t}, \dots, v_{N_{t}}^{t}\}$ . The remaining tokens are named as non-target tokens, forming a non-target set  $S = \{v_{1}^{s}, \dots, v_{N_{s}}^{s}\}$ . Suppose the compression ratio is  $R$ .  $N_{t} = (1 - R)\cdot N$ .  $N_{s} = R\cdot N$ . (ii) Token compression. FastV [9] is a token pruning technique, which directly prunes non-target tokens, resulting in the final token sequence  $\mathcal{V}' = \{v_1', \dots, v_{N_t}'\}$ , where  $v_{i}' = v_{i}^{t}$ . Turbo [9] is a token merging technique, which merges non-target tokens into target tokens, resulting in the final token sequence  $\mathcal{V}' = \{v_1', \dots, v_{N_t}'\}$ , where  $v_{i}' = \frac{v_{i}^{t} + v_{i}^{s}}{2}$ .
+
+Libra-Merging: In this work, we follow FastV [9] to treat tokens as important when they have high output attention (response-related tokens). The importance metric  $\alpha$  is defined as the attention score of output token on visual input tokens during the decoding process of one response:
+
+$$
+\alpha = \operatorname {s o f t m a x} \left(\frac {\mathbf {Q} _ {\text {o u t p u t}} \mathbf {K} ^ {T}}{\sqrt {D}}\right) \in \mathbb {R} ^ {1 \times N _ {a l l}}, \quad \sum_ {i = 1} ^ {N _ {a l l}} \alpha_ {1, i} = 1, \tag {4}
+$$
+
+where  $\mathbf{Q}_{\mathrm{output}}$  refers to the output token,  $\mathbf{K}$  refers to all tokens, and  $N_{all} = N + P$ . For convenience, we denote  $\alpha_{1,i}$  as  $\alpha_{i}$ . As shown in Figure 2, given a sequence of visual tokens and the importance  $\alpha$  of each token, we first use position-driven token identification to identify important and nonredundant tokens as target tokens. The remaining tokens serve as non-target tokens. Then, when non-target tokens are similar to target tokens, we merge non-target tokens into target tokens, where merging weighting results from token importance. When non-target tokens are dissimilar to target tokens, we compute their importance-informed average as an information compensation token. Furthermore, we select different layers and perform the above two operations on each layer to achieve higher token compression efficiency. The details of these modules will be introduced in the subsequent sections.
+
+# 3.2. Position-driven Token Identification
+
+Generally, important and non-redundant tokens should be selected as target tokens. However, it is challenging to achieve a robust importance-redundancy trade-off during selecting tokens. In this work, we assume that the redundancy of visual tokens is mainly reflected in spatially contiguous visual tokens. Thus, as shown in Figure 2, we divide the visual token sequence into several intervals and select important tokens from different intervals, to disrupt the spatial continuity of target tokens. This technique achieves
+
+![](images/ba4591cf2669f37b39aa684e932d22fefd6b791a6c7771ce07b0cd946b420fbc.jpg)  
+Figure 2. The pipeline of Libra-Merging. Hierarchical Merging indicates that we perform token merging operations at different layers. The token merging per layer consists of two steps: (i) Position-driven Token Identification. We divide the input visual token sequence into multiple intervals, and within each interval, we select the token with the highest importance as the target token. The remaining tokens serve as non-target tokens. (ii) Importance-informed Grouped Merging. We divide non-target tokens into positive set (high similarity) and negative set (low similarity) based on their similarities  $s^{max}$  with target tokens. To prevent disrupting target tokens, tokens in negative set do not merge into target tokens. To preserve important information in negative set tokens, we merge these tokens as an information compensation token rather than discarding them. All merging weights are generated from token importance.
+
+a robust importance-redundancy trade-off based on a common property of visual tokens rather than a manually designed fixed hyperparameter.
+
+Specifically,  $(i)$  we evenly divide the visual token sequence into several intervals. To avoid selecting adjacent tokens, we only select one token from each interval. Thus, the number of intervals should be  $N_{t}$ . Given a compression ratio  $R$ , we calculate the length of the visual token sequence  $l_{interval}$  in each interval as  $l_{interval} = \frac{1}{1 - R}$ . We have different intervals  $I = \{I_1,\dots ,I_{N_t}\}$ . For example, when  $R = 75\%$ , the length of the visual token sequence in each interval is 4. This means that every four tokens form an interval, and one token is selected from every four tokens as the target token.  $(ii)$  After dividing the intervals, we extract the token with the highest importance from each interval as the target token. For example, for the interval  $I_{1} = \{v_{1},\dots ,v_{l}\}$ , we select  $v_{n}$  as  $v_{1}^{t}$  when  $n = \operatorname{argmax}_{n = \{1,\dots ,l\}}(\alpha_n)$ .
+
+# 3.3. Importance-informed Grouped Merging
+
+Token pruning and merging face a dilemma. Directly pruning non-target tokens loses information in non-target tokens. Token merging prevents losing information in nontarget tokens by merging non-target tokens into target tokens. However, it may disrupt important information in target tokens. When an especially important target token merges with a dissimilar non-target token, the result can be catastrophic. Therefore, as shown in Figure 2, we propose importance-informed grouped merging to achieve the
+
+pruning-merging trade-off.
+
+Firstly, we find the most similar token of each token and group tokens in two sets. Given target tokens  $T = \{v_1^t,\dots ,v_{N_t}^t\}$ , we compute the cosine similarities between target tokens and all tokens  $\mathcal{V} = \{v_{1},v_{2},\dots ,v_{N}\}$ , forming  $S\in R^{N_t\times N}$ . Then, we identify the most similar target token of each token and create a token matching matrix  $M$ :
+
+$$
+M _ {i j} = \mathbb {I} \left(S _ {i j} = \max  _ {k = 1} ^ {N _ {t}} S _ {k j}\right), \tag {5}
+$$
+
+where  $\mathbb{I}(\cdot)$  is the indicator function, which is 1 if the condition inside the parentheses is true, and 0 otherwise. When the maximum value of a column  $j$  in  $S$  is located at row  $i$ , the corresponding element  $M_{ij}$  is set 1, and all other elements in that column of  $M$  are set to 0. The highest similarity between one token and target tokens is masked as  $s^{max}$ . During merging, we follow two principles: (i) merging similar tokens; and (ii) preserving important information. Some non-target tokens have a low  $s^{max}$  with target tokens, directly merging these tokens into target tokens may disrupt target tokens. However, these non-target tokens may still contain important information with relatively high output attention scores. To address this issue, we divide non-target tokens into two groups: when tokens satisfy  $s^{max} > \tau$ , they are grouped in positive set; the remaining tokens are grouped in negative set.
+
+Then, the proposed importance-informed grouped merging operates on two dimensions: (i) Tokens in the positive set are similar to target tokens, so we directly merge
+
+them into target tokens. During the merging, we use importance  $\alpha_{i}$  to generate the merging weight to avoid introducing unimportant noise information. Specifically, we first replace zero elements in the matching matrix with -inf and non-zero elements with importance.
+
+$$
+M _ {i j} ^ {\prime} = - \inf  \cdot \left(1 - M _ {i j}\right) + \alpha_ {j} * M _ {i j}. \tag {6}
+$$
+
+For each  $M_{ij}$  in  $M$ , when  $M_{ij} = 0$ ,  $M_{ij}' = -\inf$ ; when  $M_{ij} = 1$ ,  $M_{ij}' = \alpha_j$ . Then, we use Softmax to achieve the importance-informed merging weighting modeling in each row  $M_i'$ :  $W_i := \text{Softmax}(\frac{M_i'}{\eta})$ , where  $\eta$  is a temperature coefficient. Finally, we use  $W$  to merge tokens into the final visual token sequence  $\mathcal{V}' = \{v_1', \dots, v_{N_t}'\}$ :
+
+$$
+\mathcal {V} ^ {\prime} = W \times \mathcal {V}, \tag {7}
+$$
+
+where  $W \in R^{N_t \times N}$  is the importance-informed merging matrix,  $\mathcal{V} \in R^{N \times D}$  is the input visual token sequence, and  $\mathcal{V}' \in R^{N_t \times D}$  is the output visual token sequence. (ii) To avoid disrupting target tokens, tokens in the negative set cannot merge into target tokens. However, to prevent losing important information, we cannot simply discard them. Thus, we propose to compute their importance-informed average as an information compensation token  $v_c$ , which is appended after the token sequence  $\mathcal{V}'$ .  $N_t \gg 1$ , so the increased Flops can be negligible. The computation of the average weighting is consistent with the computation of  $W$ .
+
+Our method achieves a good pruning-merging trade-off by striving to preserve important information not only in target tokens but also in non-target tokens.
+
+# 3.4. Hierarchical Merging
+
+When the model layer is deeper, the visual token redundancy is higher [61]. Thus, if token compression is only applied in the shallow layers, the tokens in the deep layers remain redundant. To further improve the compression efficiency, we introduce a hierarchical token merging trick to reduce the visual token count layer by layer.
+
+Suppose the layers for visual token compression as  $\{L_1^c, L_2^c, \dots, L_K^c\}$ . As shown in Figure 2, we perform the aforementioned two operations at each layer  $L_k^c$ , i.e., we first use position-driven token identification to divide the visual token sequence into target tokens and non-target tokens; then, we use importance-informed grouped merging to merge non-target tokens into target tokens, resulting in the final token sequence. Suppose the compression ratio per layer is  $R$  and the total count of visual tokens is  $N$ . The visual token count in the layer  $l$  is  $N_l = N \cdot R^k$  when  $L_k^c < l \leq L_{k+1}^c$  ( $k \in \{1, \dots, K-1\}$ ). When  $l \leq L_1^c$ , the visual token count in the layer  $l$  is  $N_l = N$ . When  $l > L_K^c$ , the visual token count in the layer  $l$  is  $N_l = N \cdot R^K$ .
+
+# 4. Experiments
+
+# 4.1. Experimental Setup
+
+Models: We verify the effectiveness of Libra-Merging by experiments on LVLMs with different model sizes and input resolution. In detail, we study LLaVA-1.5-7B [32], LLaVA-1.5-13B [32], and LLaVA-NeXT-8B [30]. LLaVA-1.5 is the most widely used open-source LVLM for research. The visual token sequence length in LLaVA-Next is 576. LLaVA-Next is the extension of LLaVA-1.5, which supports the dynamic input resolution. The visual token sequence length in LLaVA-Next is dynamic. We also conduct experiments on Qwen2-VL [48] in the supplementary material.
+
+**Benchmarks:** We follow LLaVA-1.5 [32] to evaluate the performance of LVLMs. Specifically, GQA [21] evaluates the visual perception capabilities of models through open-ended short answers. ScienceQA [34], a multiple-choice benchmark, evaluates the zero-shot generalization of models on scientific question answering. TextVQA [40] focuses on text-rich visual question answering tasks. MME [16] assesses the visual perception of models with yes/no questions. MMBench [33] evaluates the robustness of model answers with all-round shuffling on multiple choice answers.
+
+Efficiency evaluation: In this paper, to evaluate the inference efficiency, we follow FastV [9] and mainly report the Flops of the image token part. For example, when conducting experiments on LLaVA-1.5-7B, the Flops of MSA and FFN is defined as  $4nd^{2} + 2n^{2}d + 3ndm$ , where  $n$  is the visual token count,  $d$  is the hidden state size, and  $m$  is the intermediate size of the FFN. When the visual token count is  $n'$  in the layer  $l$ , the Flops for the layer  $l$  is computed as  $4n'd^{2} + 2(n')^{2}d + 3n'dm$ . The reported Flops is the sum of Flops for all layers.
+
+Baselines and Libra-Merging: Our main baselines are FastV [9] and Turbo [23]. FastV [9] is a token pruning technique that prunes the  $\mathbb{R}\%$  tokens with the lowest output attention at the layer  $K$ . Turbo [23] is a token merging technique that merges the  $\mathbb{R}\%$  tokens at the layer  $K$ , where a little difference is that we do not use bipartite soft matching because bipartite soft matching may fail to find the most similar token of a token. We set  $K = 3$  and  $R = 50$ . The proposed method is Libra-Merging. Libra-Merging compresses visual tokens in multiple layers. In each compression layer, Libra-Merging uses position-driven token identification to identify target tokens. Then, it uses importance-informed grouped merging to merge non-target tokens. We set the compression ratio as  $\{50\%, 67\%, 80\% \}$ . The compression layers are  $\{7, 15, 23\}$  for LLaVA-1.5-7B (32 layers,  $\{0, 1, \dots, 31\}$ ) and LLaVA-NeXT-8B (32 layers). The compression layers are  $\{9, 19, 29\}$  for LLaVA-1.5-13B (40 layers). In Libra-Merging,  $\tau = 0.7$  and  $\eta = \mathrm{mean}(\alpha)$ . More details please refer to the supplementary material.
+
+Table 1. LVLMs (image-text models) with different token compression methods on six benchmarks. We conduct experiments on three different LVLMs to verify the scalability of our method across different model sizes (7b vs. 13b) and visual token count (llava-1.5 vs. llava-last). The Flops ratio  $47\%$  ( $37\%$ ) corresponds to compression ratio  $50\%$  ( $67\%$ ). T means trillion. Experiments about more datasets please refer to the supplementary material.  
+
+<table><tr><td>Model</td><td></td><td>Flops (T)</td><td>Ratio</td><td>GQA</td><td>\( SQA^I \)</td><td>MME</td><td>MMB</td><td>\( MMBC^{CN} \)</td><td>TextVQA</td><td>Avg</td></tr><tr><td rowspan="5">LLaVA-1.5-7B</td><td>vanilla</td><td>3.82</td><td>100%</td><td>62.0</td><td>69.5</td><td>1512.0</td><td>64.7</td><td>58.2</td><td>58.2</td><td>62.5</td></tr><tr><td>FastV</td><td>2.13</td><td>56%</td><td>60.4</td><td>68.8</td><td>1511.7</td><td>64.2</td><td>58.0</td><td>57.6</td><td>61.8</td></tr><tr><td>Turbo</td><td>2.13</td><td>56%</td><td>61.6</td><td>68.7</td><td>1471.7</td><td>63.7</td><td>57.5</td><td>57.4</td><td>61.8</td></tr><tr><td>Libra-Merging</td><td>1.78</td><td>47%</td><td>61.3</td><td>68.9</td><td>1502.5</td><td>64.3</td><td>58.5</td><td>57.4</td><td>62.1</td></tr><tr><td>Libra-Merging</td><td>1.41</td><td>37%</td><td>60.7</td><td>69.2</td><td>1480.1</td><td>63.9</td><td>58.2</td><td>57.4</td><td>61.9</td></tr><tr><td rowspan="5">LLaVA-1.5-13B</td><td>vanilla</td><td>7.44</td><td>100%</td><td>63.2</td><td>72.8</td><td>1531.3</td><td>68.5</td><td>63.6</td><td>61.2</td><td>65.9</td></tr><tr><td>FastV</td><td>4.06</td><td>55%</td><td>62.7</td><td>73.0</td><td>1549.8</td><td>68.3</td><td>63.5</td><td>60.8</td><td>65.7</td></tr><tr><td>Turbo</td><td>4.06</td><td>55%</td><td>62.8</td><td>72.7</td><td>1561.0</td><td>68.1</td><td>63.2</td><td>60.7</td><td>65.5</td></tr><tr><td>Libra-Merging</td><td>3.47</td><td>47%</td><td>63.3</td><td>73.1</td><td>1531.1</td><td>68.4</td><td>63.7</td><td>61.1</td><td>65.9</td></tr><tr><td>Libra-Merging</td><td>2.74</td><td>37%</td><td>62.5</td><td>72.4</td><td>1512.3</td><td>68.4</td><td>63.1</td><td>60.4</td><td>65.4</td></tr><tr><td rowspan="5">LLaVA-NeXT-8B</td><td>vanilla</td><td>17.17</td><td>100%</td><td>65.9</td><td>77.3</td><td>1552.1</td><td>74.4</td><td>70.4</td><td>69.8</td><td>71.6</td></tr><tr><td>FastV</td><td>9.36</td><td>55%</td><td>65.5</td><td>77.2</td><td>1572.6</td><td>74.5</td><td>70.6</td><td>69.5</td><td>71.5</td></tr><tr><td>Turbo</td><td>9.36</td><td>55%</td><td>64.7</td><td>77.7</td><td>1505.3</td><td>73.4</td><td>69.1</td><td>65.0</td><td>70.0</td></tr><tr><td>Libra-Merging</td><td>7.86</td><td>47%</td><td>65.7</td><td>77.6</td><td>1565.8</td><td>74.7</td><td>70.8</td><td>69.7</td><td>71.7</td></tr><tr><td>Libra-Merging</td><td>6.24</td><td>37%</td><td>65.6</td><td>77.2</td><td>1565.7</td><td>73.9</td><td>70.2</td><td>69.4</td><td>71.3</td></tr></table>
+
+# 4.2. Image Understanding Evaluation
+
+We study the inference efficiency on six image-text benchmarks. As shown in Table 1, on LLaVA-1.5-7B, Libra-Merging reduces the inference Flops from 3.82 to 1.78, while maintaining a comparable average performance. Compared to FastV and Turbo, Libra-Merging has a higher average performance and lower Flops. The conclusion is scalable on LLaVA-1.5-13B and LLaVA-NeXT-8B. An exciting phenomenon is that the stronger the LVLM, the more effective the token compression becomes. The average performance of using  $47\%$  tokens even surpasses that of using  $100\%$  tokens on LLaVA-NeXT-8B (71.7 vs. 71.6).
+
+# 4.3. Video Understanding Evaluation
+
+We extend Libra-Merging to VideoLLaMA-2 [29] and the results in Table 2 reveal that the proposed inference scheme significantly surpasses FastV and Turbo.
+
+# 4.4. Ablation Study
+
+Component ablation: In this study, we mainly discuss:  $(i)$  Merging. Refers to Turbo [23], merging tokens in one layer (the layer 3).  $(ii)$  Hierarchical merging, merging tokens in multiple layers (the layers  $\{7,15,23\}$ ).  $(iii)$  Position-driven Token Identification (PTI), aiming to achieve the importance-redundancy trade-off in target token identification.  $(iv)$  Importance-informed Grouped Merging (IGM), aiming to achieve the pruning-merging trade-off in target token identification.
+
+As shown in the Table 3, the experimental results verify: (i) Hierarchical merging works. For example, when  $R = 50\%$ , compared to merging, hierarchical merging improves the performance from 62.9 to 63.1. (ii) Both PTI and IGM contribute to the average performance increase. For example, when  $R = 67\%$ , PTI improves the performance from 62.5 to 62.7, and IGM improves the performance from 62.7 to 63.0. (iii) PTI+IGM brings a more significant average performance increase under a larger compression ratio. For example, when  $R = 67\%$ , PTI+IGM improves the performance by  $0.5\%$ . When  $R = 80\%$ , PTI+IGM improves the performance by  $0.7\%$ . A possible reason is that when the compression ratio is larger, selecting redundant tokens is more likely to discard important tokens and more nonredundant tokens disrupt target tokens during merging.
+
+Study about pruning-merging trade-off: The premise of token merging is that tokens should be similar. When a nontarget token is dissimilar to a target token, token pruning should be preferred, as token merging disrupts the target token; on the contrary, token merging should be preferred. We explore the pruning-merging trade-off from the perspective of different layers. Specifically, we select layers  $\{3,15\}$  to conduct the experiments.
+
+As shown in Table 4, Pruning refers to pruning  $75\%$  visual tokens at layer 3 or layer 15, Merging refers to averaging non-target tokens with the most similar target token, and IGM refers to Importance-informed Grouped Merging. To focus on the token compression study, we only use importance to identify target tokens for all experiments in Ta
+
+Table 2. LVLMs (video-text models) with different token compression methods on Video-MME. VideoLLaMA-2 is the state-of-the-art Large Video-Language Model. We compress  $75\%$  visual tokens at layer 3. More details please refer to the supplementary material.  
+
+<table><tr><td>Model</td><td colspan="3">Flops (T) Ratio</td><td colspan="2">Overall w/o subs w subs</td><td colspan="2">Short w/o subs w subs</td><td colspan="2">Medium w/o subs w subs</td><td colspan="2">Long w/o subs w subs</td></tr><tr><td rowspan="4">VideoLLaMA-2 (7B)</td><td>vanilla</td><td>23.96</td><td>100%</td><td>49.8</td><td>54.7</td><td>58.0</td><td>63.6</td><td>47.0</td><td>53.1</td><td>44.3</td><td>47.3</td></tr><tr><td>FastV</td><td>8.20</td><td>34%</td><td>46.5</td><td>51.4</td><td>52.1</td><td>57.3</td><td>45.2</td><td>50.4</td><td>42.1</td><td>46.5</td></tr><tr><td>Turbo</td><td>8.20</td><td>34%</td><td>47.9</td><td>52.1</td><td>54.0</td><td>59.6</td><td>46.9</td><td>50.1</td><td>42.7</td><td>46.5</td></tr><tr><td>Libra-Merging</td><td>8.20</td><td>34%</td><td>48.8</td><td>52.9</td><td>55.3</td><td>59.0</td><td>46.4</td><td>52.6</td><td>44.7</td><td>47.0</td></tr></table>
+
+Table 3. Component ablation on five benchmarks. "Merging" refers to Turbo [23], merging tokens in one layer (3). "Hierarchical" refers to merging tokens in multiple layers (\{7, 15, 23\}). "PTI" refers to position-driven token identification. "IGM" refers to importance-informed grouped merging.  $R$  refers to the compression ratio.  
+
+<table><tr><td></td><td>Merging</td><td>Hierarchical</td><td>PTI</td><td>IGM</td><td>R</td><td>Flops (T)</td><td>GQA</td><td>\( SQA^I \)</td><td>MME</td><td>MMB</td><td>\( MMB^{CN} \)</td><td>Avg</td></tr><tr><td rowspan="3">LLaVA-1.5-7B</td><td>✓</td><td></td><td></td><td></td><td>50%</td><td>2.13</td><td>61.6</td><td>68.7</td><td>1471.7</td><td>63.7</td><td>57.5</td><td>62.9</td></tr><tr><td></td><td>✓</td><td></td><td></td><td>50%</td><td>1.78</td><td>61.2</td><td>69.3</td><td>1482.9</td><td>63.8</td><td>57.9</td><td>63.1</td></tr><tr><td></td><td>✓</td><td>✓</td><td>✓</td><td>50%</td><td>1.78</td><td>61.3</td><td>68.9</td><td>1502.5</td><td>64.3</td><td>58.5</td><td>63.3</td></tr><tr><td rowspan="3">LLaVA-1.5-7B</td><td></td><td>✓</td><td></td><td></td><td>67%</td><td>1.41</td><td>60.0</td><td>69.4</td><td>1443.2</td><td>63.8</td><td>56.7</td><td>62.5</td></tr><tr><td></td><td>✓</td><td>✓</td><td></td><td>67%</td><td>1.41</td><td>60.7</td><td>68.7</td><td>1487.8</td><td>63.4</td><td>57.8</td><td>62.7</td></tr><tr><td></td><td>✓</td><td>✓</td><td>✓</td><td>67%</td><td>1.41</td><td>60.7</td><td>69.2</td><td>1480.1</td><td>63.9</td><td>58.2</td><td>63.0</td></tr><tr><td rowspan="3">LLaVA-1.5-7B</td><td></td><td>✓</td><td></td><td></td><td>80%</td><td>1.19</td><td>58.1</td><td>69.7</td><td>1419.9</td><td>62.6</td><td>55.6</td><td>61.5</td></tr><tr><td></td><td>✓</td><td>✓</td><td></td><td>80%</td><td>1.19</td><td>58.7</td><td>69.6</td><td>1478.2</td><td>63.1</td><td>56.3</td><td>61.9</td></tr><tr><td></td><td>✓</td><td>✓</td><td>✓</td><td>80%</td><td>1.19</td><td>59.3</td><td>69.7</td><td>1465.8</td><td>63.3</td><td>56.5</td><td>62.2</td></tr></table>
+
+Table 4. Study about pruning-merging trade-off. Token importance is used to identify target tokens, and the only change is token compression technique. Sim indicates the mean of  $s^{max}$ .  
+
+<table><tr><td></td><td>R</td><td>Layer</td><td>GQA</td><td>R</td><td>Layer</td><td>GQA</td></tr><tr><td>Pruning</td><td>80%</td><td>3</td><td>56.57</td><td>80%</td><td>15</td><td>61.78</td></tr><tr><td>Merging</td><td>80%</td><td>3</td><td>57.96</td><td>80%</td><td>15</td><td>61.73</td></tr><tr><td>IGM</td><td>80%</td><td>3</td><td>57.27</td><td>80%</td><td>15</td><td>61.82</td></tr><tr><td colspan="3">Sim</td><td colspan="3">0.8433</td><td>0.5955</td></tr></table>
+
+Table 5. Study about different variants of IGM. IGM-pos means that all non-redundant tokens are used for merging (importance-informed). IGM-neg means that all non-redundant tokens are used for generating the information compensation token.  
+
+<table><tr><td></td><td>R</td><td>Layer</td><td>GQA</td><td>MME</td><td>MMB</td></tr><tr><td>IGM-pos</td><td>80%</td><td>15</td><td>61.79</td><td>1506.3</td><td>64.79</td></tr><tr><td>IGM-neg</td><td>80%</td><td>15</td><td>61.77</td><td>1505.1</td><td>64.69</td></tr><tr><td>IGM</td><td>80%</td><td>15</td><td>61.82</td><td>1525.7</td><td>65.07</td></tr></table>
+
+ble 4. Sim represents the mean of  $s^{max}$ ; a smaller Sim means the lower mean similarity between target tokens and
+
+non-target tokens. Table 4 indicates:  $(i)$  When the Sim is low (high), token pruning is better than merging. When the Sim is high, token merging is better than pruning.  $(ii)$  Importance-informed Grouped Merging (IGM) achieves a good trade-off for different scenarios.
+
+Study about importance-informed grouped merging: In importance-informed grouped merging, we want to preserve the important information in non-target tokens while avoiding the disruption of important information in target tokens due to merging. Thus, we divide non-target tokens into positive set and negative set. To verify the necessity of this division, we set: (i) IGM-pos, all non-target tokens merge into target tokens; (ii) IGM-neg, all non-target tokens merge as an information compensation token, which is similar to EViT [28]. As shown in Table 5, IGM outperforms both IGM-pos and IGM-neg.
+
+Actual runtime latency and memory usage: To better evaluate inference efficiency, we conduct runtime and GPU memory usage analyses during inference, similar to FastV. We randomly select two datasets (GQA and MME) and perform inference using LLaVA-1.5-7B on an A800 GPU. We measure the end-to-end inference duration including reading/writing, and calculate "Latency/Example" to indicate the average inference time per sample. We comprehensively compare FastV and Libra-Merging. As shown in Tab. 6,
+
+Table 6. Actual runtime latency and memory usage. We directly record the total inference time as "Time", which includes file reading/writing time. "Latency/Example" indicates the average inference time per sample.  
+
+<table><tr><td></td><td>Model</td><td>R</td><td>Layer</td><td>Time (one A800)</td><td>Memory</td><td>Score</td><td>Latency/Example</td></tr><tr><td></td><td>LLaVA-1.5-7B</td><td>-</td><td>-</td><td>21:45</td><td>16.0G</td><td>61.95</td><td>0.104s</td></tr><tr><td rowspan="4">GQA</td><td>+FastV</td><td>50%</td><td>3</td><td>19:36</td><td>15.6G</td><td>60.35</td><td>0.093s</td></tr><tr><td>+Libra-Merging</td><td>50%</td><td>3</td><td>19:48</td><td>15.6G</td><td>61.38</td><td>0.094s</td></tr><tr><td>+FastV</td><td>80%</td><td>3</td><td>17:54</td><td>15.4G</td><td>56.57</td><td>0.085s</td></tr><tr><td>+Libra-Merging</td><td>80%</td><td>3</td><td>17:58</td><td>15.4G</td><td>58.81</td><td>0.086s</td></tr><tr><td></td><td>LLaVA-1.5-7B</td><td>-</td><td>-</td><td>03:59</td><td>16.0G</td><td>1512.0</td><td>0.101s</td></tr><tr><td rowspan="4">MME</td><td>+FastV</td><td>50%</td><td>3</td><td>03:27</td><td>15.6G</td><td>1511.7</td><td>0.087s</td></tr><tr><td>+Libra-Merging</td><td>50%</td><td>3</td><td>03:30</td><td>15.6G</td><td>1513.1</td><td>0.088s</td></tr><tr><td>+FastV</td><td>80%</td><td>3</td><td>03:14</td><td>15.4G</td><td>1427.6</td><td>0.082s</td></tr><tr><td>+Libra-Merging</td><td>80%</td><td>3</td><td>03:16</td><td>15.4G</td><td>1440.0</td><td>0.083s</td></tr></table>
+
+Table 7. The flash-attention compatibility during inference. "hybrid" means the proposed hybrid attention, which is essential for maintaining flash-attention compatibility. The experiments about training are provided in the supplementary material.  
+
+<table><tr><td></td><td>Model</td><td>R</td><td>Layer</td><td>Time (one A800)</td><td>Memory</td><td>Score</td><td>Latency/Example</td></tr><tr><td rowspan="5">MME</td><td>Qwen2-VL-7B</td><td>-</td><td>-</td><td>13:35</td><td>27.7G</td><td>1693.6</td><td>0.343s</td></tr><tr><td>w flash-attention 2</td><td>-</td><td>-</td><td>08:48</td><td>18.5G</td><td>1683.6</td><td>0.222s</td></tr><tr><td>+FastV</td><td>50%</td><td>3</td><td>12:25</td><td>28.6G</td><td>1673.9</td><td>0.314s</td></tr><tr><td>+FastV w hybrid</td><td>50%</td><td>3</td><td>08:12</td><td>17.6G</td><td>1654.9</td><td>0.207s</td></tr><tr><td>+Libra-Merging w hybrid</td><td>50%</td><td>3</td><td>08:19</td><td>17.6G</td><td>1690.3</td><td>0.210s</td></tr><tr><td rowspan="5">MME</td><td>LLaVA-1.5-7B</td><td>-</td><td>-</td><td>03:59</td><td>16.0G</td><td>1512.0</td><td>0.101s</td></tr><tr><td>w flash-attention 2</td><td>-</td><td>-</td><td>03:58</td><td>16.0G</td><td>1507.5</td><td>0.100s</td></tr><tr><td>+FastV</td><td>50%</td><td>3</td><td>03:27</td><td>15.6G</td><td>1511.7</td><td>0.087s</td></tr><tr><td>+FastV w hybrid</td><td>50%</td><td>3</td><td>03:25</td><td>15.5G</td><td>1495.5</td><td>0.086s</td></tr><tr><td>+Libra-Merging w hybrid</td><td>50%</td><td>3</td><td>03:26</td><td>15.5G</td><td>1502.1</td><td>0.087s</td></tr></table>
+
+both methods achieve actual inference acceleration over the baseline. While demonstrating comparable efficiency to FastV, Libra-Merging delivers significantly superior performance, particularly when  $R = 80\%$ .
+
+Flash-attention compatibility: Flash-attention is indispensable for accelerating attention computation, yet it does not output attention scores. Fortunately, our main goal is to preserve response-related visual information, which only requires attention scores between output token and visual tokens. Consequently, we compute only these attention scores, requiring merely  $1 \times N_{t}$  score computations. We term this operation as hybrid attention. Since FLOPs scale quadratically with token length, this introduces approximately  $\frac{1}{N_{t}}$  additional FLOPs, which becomes negligible when  $N_{t} \gg 1$ . As shown in Tab. 7, "Qwen2+flash-attention 2" outperforms "Qwen2+FastV" in speed. Then, with hybrid attention, token compression techniques become fully compatible with flash-attention 2.
+
+With flash-attention compatibility, we successfully extend token compression techniques to model training. Ex
+
+experimental results are detailed in Table E of the supplementary material.
+
+# 5. Conclusion
+
+In this paper, we study the importance-redundancy dilemma and the pruning-merging dilemma in token compression for LVLMs. To solve the two dilemmas, we propose a novel token merging scheme Libra-Merging, which consists of position-driven token identification and importance-informed grouped compression. In target token identification, position-driven token identification is proposed to avoid selecting redundant target tokens, for a robust importance-redundancy trade-off. In token compression, importance-informed grouped compression is proposed to prevent disrupting target tokens while preserving important information in non-target tokens, for a good pruning-merging trade-off. Our method Libra-Merging acts as a plug-in, which can be easily integrated into existing LVLMs. Extensive experiments demonstrate the effectiveness of Libra-Merging across diverse datasets.
+
+# References
+
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+Acknowledgements. This work is supported in part by National Science Foundation for Distinguished Young Scholars under Grant 62225605, Zhejiang Provincial Natural Science Foundation of China under Grant LD24F020016, "Pioneer" and "Leading Goose" R&D Program of Zhejiang (No.2024C01020), Project 12326608 supported by NSFC, the Ningbo Science and Technology Innovation Project (No.2024Z294), and is supported by Kuaishou Technology.  
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