| Backbone | #Params (M) | FLOPs (G) | \\( {\\mathrm{{AP}}}^{b} \\) | \\( {\\mathrm{{AP}}}_{50}^{b} \\) | \\( {\\mathrm{{AP}}}_{75}^{b} \\) | \\( {\\mathrm{{AP}}}^{m} \\) | \\( {\\mathrm{{AP}}}_{50}^{m} \\) | \\( {\\mathrm{{AP}}}_{75}^{m} \\) |
| PVT-T [48] | 32.9 | - | 39.8 | 62.2 | 43.0 | 37.4 | 59.3 | 39.9 |
| PVTv2-B1 [47] | 33.7 | \\( {259}^{ * } \\) | 41.8 | 64.3 | 45.9 | 38.8 | 61.2 | 41.6 |
| PaCa-Tiny (ours) | 32.0 | \\( {252}^{ * } \\) | 43.3 | 66.0 | 47.5 | 39.6 | 62.9 | 42.4 |
| ResNet-50 [22] | 44.2 | 260 | 41.0 | 61.7 | 44.9 | 37.1 | 58.4 | 40.1 |
| SWin-T [32] | 47.8 | 264 | 43.7 | 66.6 | 47.7 | 39.8 | 63.3 | 42.7 |
| Twins-SVT-S [9] | 44.0 | 228 | 43.4 | 66.0 | 47.3 | 40.3 | 63.2 | 43.4 |
| FocalAtt-T [56] | 48.8 | 291 | 44.8 | 67.7 | 49.2 | 41.0 | 64.7 | 44.2 |
| PVT-S [48] | 44.1 | 245 | 43.0 | 65.3 | 46.9 | 39.9 | 62.5 | 42.8 |
| PVTv2-B2 [47] | 45.0 | \\( {325}^{ * } \\) | 45.3 | 67.1 | 49.6 | 41.2 | 64.2 | 44.4 |
| PaCa-Small (ours) | 41.8 | \\( {296}^{ * } \\) | 46.4 | 68.7 | 50.9 | 41.8 | 65.5 | 45.0 |
| \\( {\\mathrm{{PaCa}}}^{mlp} \\) -Small (ours) | 42.4 | \\( {303}^{ * } \\) | 46.6 | 69.0 | 51.3 | 41.9 | 65.7 | 45.0 |
| \\( {\\mathrm{{PaCa}}}^{ec} \\) -Small (ours) | 40.9 | \\( {292}^{ * } \\) | 45.8 | 68.0 | 50.3 | 41.4 | 64.9 | 44.5 |
| SWin-S [32] | 69.1 | 354 | 46.5 | 68.7 | 51.3 | 42.1 | 65.8 | 45.2 |
| SWin-B [32] | 107.1 | 497 | 46.9 | 69.2 | 51.6 | 42.3 | 66.0 | 45.5 |
| FocalAtt-S [56] | 71.2 | 401 | 47.4 | 69.8 | 51.9 | 42.8 | 66.6 | 46.1 |
| FocalAtt-B [56] | 110.0 | 533 | 47.8 | 70.2 | 52.5 | 43.2 | 67.3 | 46.5 |
| Twins-SVT-B [9] | 76.3 | 340 | 45.2 | 67.6 | 49.3 | 41.5 | 64.5 | 44.8 |
| PVT-M [48] | 63.9 | 302 | 42.0 | 64.4 | 45.6 | 39.0 | 61.6 | 42.1 |
| PVT-L [48] | 81.0 | 364 | 42.9 | 65.0 | 46.6 | 39.5 | 61.9 | 42.5 |
| PVTv2-B3 [47] | 64.9 | 413* | 47.0 | 68.1 | 51.7 | 42.5 | 65.7 | 45.7 |
| PVTv2-B4 [47] | 82.2 | 516* | 47.5 | 68.7 | 52.0 | 42.7 | 66.1 | 46.1 |
| PVTv2-B5 [47] | 101.6 | 573* | 47.4 | 68.6 | 51.9 | 42.5 | 65.7 | 46.0 |
| PaCa-Base (ours) | 66.6 | \\( {373}^{ * } \\) | 48.0 | 69.7 | 52.1 | 42.9 | 66.6 | 45.6 |
| \\( {\\mathrm{{PaCa}}}^{cc} \\) -Base (ours) | 61.4 | \\( {372}^{ * } \\) | 48.3 | 70.5 | 52.6 | 43.3 | 67.2 | 46.6 |
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+ "Table 3. Semantic segmentation on MIT-ADE20k [64] with the crop size $512 \\times 512$ using the IN1K pretrained backbones. FLOPs are computed at the input resolution of $512 \\times 512$ . *computed using the torchprofile package."
+ ],
+ "table_body": "| Backbone | #Params (M) | FLOPs (G) | \\( {\\mathrm{{AP}}}^{b} \\) | \\( {\\mathrm{{AP}}}_{50}^{b} \\) | \\( {\\mathrm{{AP}}}_{75}^{b} \\) | \\( {\\mathrm{{AP}}}^{m} \\) | \\( {\\mathrm{{AP}}}_{50}^{m} \\) | \\( {\\mathrm{{AP}}}_{75}^{m} \\) |
| PVT-T [48] | 32.9 | - | 39.8 | 62.2 | 43.0 | 37.4 | 59.3 | 39.9 |
| PVTv2-B1 [47] | 33.7 | \\( {259}^{ * } \\) | 41.8 | 64.3 | 45.9 | 38.8 | 61.2 | 41.6 |
| PaCa-Tiny (ours) | 32.0 | \\( {252}^{ * } \\) | 43.3 | 66.0 | 47.5 | 39.6 | 62.9 | 42.4 |
| ResNet-50 [22] | 44.2 | 260 | 41.0 | 61.7 | 44.9 | 37.1 | 58.4 | 40.1 |
| SWin-T [32] | 47.8 | 264 | 43.7 | 66.6 | 47.7 | 39.8 | 63.3 | 42.7 |
| Twins-SVT-S [9] | 44.0 | 228 | 43.4 | 66.0 | 47.3 | 40.3 | 63.2 | 43.4 |
| FocalAtt-T [56] | 48.8 | 291 | 44.8 | 67.7 | 49.2 | 41.0 | 64.7 | 44.2 |
| PVT-S [48] | 44.1 | 245 | 43.0 | 65.3 | 46.9 | 39.9 | 62.5 | 42.8 |
| PVTv2-B2 [47] | 45.0 | \\( {325}^{ * } \\) | 45.3 | 67.1 | 49.6 | 41.2 | 64.2 | 44.4 |
| PaCa-Small (ours) | 41.8 | \\( {296}^{ * } \\) | 46.4 | 68.7 | 50.9 | 41.8 | 65.5 | 45.0 |
| \\( {\\mathrm{{PaCa}}}^{mlp} \\) -Small (ours) | 42.4 | \\( {303}^{ * } \\) | 46.6 | 69.0 | 51.3 | 41.9 | 65.7 | 45.0 |
| \\( {\\mathrm{{PaCa}}}^{ec} \\) -Small (ours) | 40.9 | \\( {292}^{ * } \\) | 45.8 | 68.0 | 50.3 | 41.4 | 64.9 | 44.5 |
| SWin-S [32] | 69.1 | 354 | 46.5 | 68.7 | 51.3 | 42.1 | 65.8 | 45.2 |
| SWin-B [32] | 107.1 | 497 | 46.9 | 69.2 | 51.6 | 42.3 | 66.0 | 45.5 |
| FocalAtt-S [56] | 71.2 | 401 | 47.4 | 69.8 | 51.9 | 42.8 | 66.6 | 46.1 |
| FocalAtt-B [56] | 110.0 | 533 | 47.8 | 70.2 | 52.5 | 43.2 | 67.3 | 46.5 |
| Twins-SVT-B [9] | 76.3 | 340 | 45.2 | 67.6 | 49.3 | 41.5 | 64.5 | 44.8 |
| PVT-M [48] | 63.9 | 302 | 42.0 | 64.4 | 45.6 | 39.0 | 61.6 | 42.1 |
| PVT-L [48] | 81.0 | 364 | 42.9 | 65.0 | 46.6 | 39.5 | 61.9 | 42.5 |
| PVTv2-B3 [47] | 64.9 | 413* | 47.0 | 68.1 | 51.7 | 42.5 | 65.7 | 45.7 |
| PVTv2-B4 [47] | 82.2 | 516* | 47.5 | 68.7 | 52.0 | 42.7 | 66.1 | 46.1 |
| PVTv2-B5 [47] | 101.6 | 573* | 47.4 | 68.6 | 51.9 | 42.5 | 65.7 | 46.0 |
| PaCa-Base (ours) | 66.6 | \\( {373}^{ * } \\) | 48.0 | 69.7 | 52.1 | 42.9 | 66.6 | 45.6 |
| \\( {\\mathrm{{PaCa}}}^{cc} \\) -Base (ours) | 61.4 | \\( {372}^{ * } \\) | 48.3 | 70.5 | 52.6 | 43.3 | 67.2 | 46.6 |
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+ "content": "Table 2. Object detection and instance segmentation on MS-COCO val2017 [31] using the IN1K pretrained backbones and the Mask R-CNN [21] with the 1x (12-epoch) training schedule in training. FLOPs are computed at the input resolution of \\(1280 \\times 800\\). *computed using the torchprofile package."
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+ "content": "| Backbone | #Params (M) | FLOPs (G) | \( {\mathrm{{AP}}}^{b} \) | \( {\mathrm{{AP}}}_{50}^{b} \) | \( {\mathrm{{AP}}}_{75}^{b} \) | \( {\mathrm{{AP}}}^{m} \) | \( {\mathrm{{AP}}}_{50}^{m} \) | \( {\mathrm{{AP}}}_{75}^{m} \) |
| PVT-T [48] | 32.9 | - | 39.8 | 62.2 | 43.0 | 37.4 | 59.3 | 39.9 |
| PVTv2-B1 [47] | 33.7 | \( {259}^{ * } \) | 41.8 | 64.3 | 45.9 | 38.8 | 61.2 | 41.6 |
| PaCa-Tiny (ours) | 32.0 | \( {252}^{ * } \) | 43.3 | 66.0 | 47.5 | 39.6 | 62.9 | 42.4 |
| ResNet-50 [22] | 44.2 | 260 | 41.0 | 61.7 | 44.9 | 37.1 | 58.4 | 40.1 |
| SWin-T [32] | 47.8 | 264 | 43.7 | 66.6 | 47.7 | 39.8 | 63.3 | 42.7 |
| Twins-SVT-S [9] | 44.0 | 228 | 43.4 | 66.0 | 47.3 | 40.3 | 63.2 | 43.4 |
| FocalAtt-T [56] | 48.8 | 291 | 44.8 | 67.7 | 49.2 | 41.0 | 64.7 | 44.2 |
| PVT-S [48] | 44.1 | 245 | 43.0 | 65.3 | 46.9 | 39.9 | 62.5 | 42.8 |
| PVTv2-B2 [47] | 45.0 | \( {325}^{ * } \) | 45.3 | 67.1 | 49.6 | 41.2 | 64.2 | 44.4 |
| PaCa-Small (ours) | 41.8 | \( {296}^{ * } \) | 46.4 | 68.7 | 50.9 | 41.8 | 65.5 | 45.0 |
| \( {\mathrm{{PaCa}}}^{mlp} \) -Small (ours) | 42.4 | \( {303}^{ * } \) | 46.6 | 69.0 | 51.3 | 41.9 | 65.7 | 45.0 |
| \( {\mathrm{{PaCa}}}^{ec} \) -Small (ours) | 40.9 | \( {292}^{ * } \) | 45.8 | 68.0 | 50.3 | 41.4 | 64.9 | 44.5 |
| SWin-S [32] | 69.1 | 354 | 46.5 | 68.7 | 51.3 | 42.1 | 65.8 | 45.2 |
| SWin-B [32] | 107.1 | 497 | 46.9 | 69.2 | 51.6 | 42.3 | 66.0 | 45.5 |
| FocalAtt-S [56] | 71.2 | 401 | 47.4 | 69.8 | 51.9 | 42.8 | 66.6 | 46.1 |
| FocalAtt-B [56] | 110.0 | 533 | 47.8 | 70.2 | 52.5 | 43.2 | 67.3 | 46.5 |
| Twins-SVT-B [9] | 76.3 | 340 | 45.2 | 67.6 | 49.3 | 41.5 | 64.5 | 44.8 |
| PVT-M [48] | 63.9 | 302 | 42.0 | 64.4 | 45.6 | 39.0 | 61.6 | 42.1 |
| PVT-L [48] | 81.0 | 364 | 42.9 | 65.0 | 46.6 | 39.5 | 61.9 | 42.5 |
| PVTv2-B3 [47] | 64.9 | 413* | 47.0 | 68.1 | 51.7 | 42.5 | 65.7 | 45.7 |
| PVTv2-B4 [47] | 82.2 | 516* | 47.5 | 68.7 | 52.0 | 42.7 | 66.1 | 46.1 |
| PVTv2-B5 [47] | 101.6 | 573* | 47.4 | 68.6 | 51.9 | 42.5 | 65.7 | 46.0 |
| PaCa-Base (ours) | 66.6 | \( {373}^{ * } \) | 48.0 | 69.7 | 52.1 | 42.9 | 66.6 | 45.6 |
| \( {\mathrm{{PaCa}}}^{cc} \) -Base (ours) | 61.4 | \( {372}^{ * } \) | 48.3 | 70.5 | 52.6 | 43.3 | 67.2 | 46.6 |
+
+Table 2. Object detection and instance segmentation on MS-COCO val2017 [31] using the IN1K pretrained backbones and the Mask R-CNN [21] with the 1x (12-epoch) training schedule in training. FLOPs are computed at the input resolution of $1280 \times 800$ . *computed using the torchprofile package.
+
+| Backbone | #Params (M) | FLOPs (G) | \\( {\\mathrm{{AP}}}^{b} \\) | \\( {\\mathrm{{AP}}}_{50}^{b} \\) | \\( {\\mathrm{{AP}}}_{75}^{b} \\) | \\( {\\mathrm{{AP}}}^{m} \\) | \\( {\\mathrm{{AP}}}_{50}^{m} \\) | \\( {\\mathrm{{AP}}}_{75}^{m} \\) |
| PVT-T [48] | 32.9 | - | 39.8 | 62.2 | 43.0 | 37.4 | 59.3 | 39.9 |
| PVTv2-B1 [47] | 33.7 | \\( {259}^{ * } \\) | 41.8 | 64.3 | 45.9 | 38.8 | 61.2 | 41.6 |
| PaCa-Tiny (ours) | 32.0 | \\( {252}^{ * } \\) | 43.3 | 66.0 | 47.5 | 39.6 | 62.9 | 42.4 |
| ResNet-50 [22] | 44.2 | 260 | 41.0 | 61.7 | 44.9 | 37.1 | 58.4 | 40.1 |
| SWin-T [32] | 47.8 | 264 | 43.7 | 66.6 | 47.7 | 39.8 | 63.3 | 42.7 |
| Twins-SVT-S [9] | 44.0 | 228 | 43.4 | 66.0 | 47.3 | 40.3 | 63.2 | 43.4 |
| FocalAtt-T [56] | 48.8 | 291 | 44.8 | 67.7 | 49.2 | 41.0 | 64.7 | 44.2 |
| PVT-S [48] | 44.1 | 245 | 43.0 | 65.3 | 46.9 | 39.9 | 62.5 | 42.8 |
| PVTv2-B2 [47] | 45.0 | \\( {325}^{ * } \\) | 45.3 | 67.1 | 49.6 | 41.2 | 64.2 | 44.4 |
| PaCa-Small (ours) | 41.8 | \\( {296}^{ * } \\) | 46.4 | 68.7 | 50.9 | 41.8 | 65.5 | 45.0 |
| \\( {\\mathrm{{PaCa}}}^{mlp} \\) -Small (ours) | 42.4 | \\( {303}^{ * } \\) | 46.6 | 69.0 | 51.3 | 41.9 | 65.7 | 45.0 |
| \\( {\\mathrm{{PaCa}}}^{ec} \\) -Small (ours) | 40.9 | \\( {292}^{ * } \\) | 45.8 | 68.0 | 50.3 | 41.4 | 64.9 | 44.5 |
| SWin-S [32] | 69.1 | 354 | 46.5 | 68.7 | 51.3 | 42.1 | 65.8 | 45.2 |
| SWin-B [32] | 107.1 | 497 | 46.9 | 69.2 | 51.6 | 42.3 | 66.0 | 45.5 |
| FocalAtt-S [56] | 71.2 | 401 | 47.4 | 69.8 | 51.9 | 42.8 | 66.6 | 46.1 |
| FocalAtt-B [56] | 110.0 | 533 | 47.8 | 70.2 | 52.5 | 43.2 | 67.3 | 46.5 |
| Twins-SVT-B [9] | 76.3 | 340 | 45.2 | 67.6 | 49.3 | 41.5 | 64.5 | 44.8 |
| PVT-M [48] | 63.9 | 302 | 42.0 | 64.4 | 45.6 | 39.0 | 61.6 | 42.1 |
| PVT-L [48] | 81.0 | 364 | 42.9 | 65.0 | 46.6 | 39.5 | 61.9 | 42.5 |
| PVTv2-B3 [47] | 64.9 | 413* | 47.0 | 68.1 | 51.7 | 42.5 | 65.7 | 45.7 |
| PVTv2-B4 [47] | 82.2 | 516* | 47.5 | 68.7 | 52.0 | 42.7 | 66.1 | 46.1 |
| PVTv2-B5 [47] | 101.6 | 573* | 47.4 | 68.6 | 51.9 | 42.5 | 65.7 | 46.0 |
| PaCa-Base (ours) | 66.6 | \\( {373}^{ * } \\) | 48.0 | 69.7 | 52.1 | 42.9 | 66.6 | 45.6 |
| \\( {\\mathrm{{PaCa}}}^{cc} \\) -Base (ours) | 61.4 | \\( {372}^{ * } \\) | 48.3 | 70.5 | 52.6 | 43.3 | 67.2 | 46.6 |
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+ "html": "| Dataset | Energy landscape [44] | Cambridge [15] |
| Scene representation | PC | OLC | PPL | PPL+ | PC | OLC | PPL | PPL+ |
| Minimal solver | P3P | P6L | P6L | P6L | P3P | P6L | P6L | P6L |
| Original point used (%) | 100 | 100 | 50 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |
| Line cloud used (%) | - | 100 | 50 | 50 | 50 | 50 | N/A | 100 | 50 | 50 | 50 | 50 |
| Peak finding algorithm used | - | SPF | SPF | SPF | TPF | SPF | N/A | SPF | SPF | SPF | TPF | SPF |
| Proportion of revealed points (%) | 100 | 100 | 50 | 50 | 100 | 50 | 100 | 100 | 50 | 50 | 100 | 100 |
| Median 3D point error (m, ↑) | - | 0.046 | 0.055 | 0.056 | 0.224 | 0.056 | 0.227 | - | 0.752 | 0.854 | 0.973 | 2.845 |
| Image quality (PSNR ↓) | 15.70 | 13.30 | 12.84 | 10.42 | 11.21 | 10.44 | 11.22 | 14.00 | 12.67 | 12.40 | 11.20 | 11.43 |
| Image quality (SSIM ↓) | 0.514 | 0.402 | 0.388 | 0.356 | 0.325 | 0.355 | 0.323 | 0.433 | 0.331 | 0.320 | 0.296 | 0.283 |
| Image quality (MAE ↑) | 33.58 | 43.62 | 45.83 | 62.40 | 56.99 | 62.11 | 56.93 | 39.41 | 46.21 | 47.93 | 55.75 | 54.01 |
| Mean rotation error (°, ↓) | 0.178 | 0.272 | 0.294 | 0.283 | 0.287 | 0.700 | 0.807 | 0.833 | 0.789 |
| Mean translation error (m, ↓) | 0.0071 | 0.0100 | 0.0108 | 0.0105 | 0.0106 | 0.141 | 0.184 | 0.195 | 0.193 |
| Median rotation error (°, ↓) | 0.031 | 0.104 | 0.116 | 0.112 | 0.116 | 0.100 | 0.194 | 0.200 | 0.196 |
| Median translation error (m, ↓) | 0.0010 | 0.0032 | 0.0036 | 0.0035 | 0.0037 | 0.042 | 0.072 | 0.078 | 0.085 |
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+ "text": "Table 1. Results obtained from different scene representations on two public datasets (PC: point cloud, OLC: original line cloud, PPL: paired-point lifting and PPL+: PPL with rejection sampling). $\\uparrow$ denotes higher values imply better privacy-preserving behavior, and vice versa for $\\downarrow$ . Bold text denotes lowest image quality for each metric. Mean and median values are averaged across all views and sequences.",
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+ "img_path": "images/91063d67b0a229e05d80ff0f91a48e9124c20a0df43b174dc5d710b2e53487fe.jpg",
+ "image_caption": [
+ "Figure 8. Pose estimation error versus image quality across different levels of point cloud sparsity for the scene 'Office1_manolis'. The size of the marker in the graph represents the proportion of the sampled points in the following order: $100\\%$ $50\\%$ $25\\%$ $10\\%$ $5\\%$ cloud density. The PPL class of approaches achieve lower PSNR and SSIM values and higher MAE values than those of OLC with comparable camera pose estimation errors, suggesting PPL/PPL+ enhance the privacy-preserving visual localization performance."
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+ "img_path": "images/c290a26295f8c2ef076481c0c9146fca8b711aa5f85392eaff289b568b4890ed.jpg",
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+ "img_path": "images/17b5ec35259c414cb2159d5713acbc11ba4b00639fd1a455ca6626349b367cb1.jpg",
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+ {
+ "type": "text",
+ "text": "those found by TPF, and the results in the supplementary material [18] shows TPF mostly functions as expected.",
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+ "type": "text",
+ "text": "5.2. Comparing quality of revealed images",
+ "text_level": 1,
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+ "type": "text",
+ "text": "We also compared the quality of revealed images from different scene representations.",
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+ "text": "For a quantitative comparison, we reconstructed images of the scenes by projecting a 3D point cloud (revealed via peak-finding for line clouds) to 2D using the ground truth camera poses and feeding this along with feature descriptors to the InvSfM network [30]. We then computed the average PSNR, SSIM and MAE values of the revealed images against the ground truth images.",
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+ "text": "Table 1 shows that the image quality of recovered images from PPL and $\\mathrm{PPL + }$ are much lower than those from OLC (100% and 50%), indicating improved privacy preserving performance even without the effect of reduced cloud density. This trend is maintained even when SPF is replaced by",
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+ "text": "In order to disentangle the effect of feature misassignment and geometric uncertainty (induced by non-uniform distribution of lines), we resort to the qualitative comparison of revealed images from different scene representations and different peak finding algorithms. The comparison includes an oracle setting in which the effect of feature descriptor misallocation in PPL is minimized to only visualize the effect of non-uniformly distributed line directions (mimicking $0\\%$ feature swap) by assigning descriptors based on the two points' proximity to ground truth points.",
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+ "Figure 9. Images revealed from various scene representations using InvSfM [30]. To disentangle the effect of feature swapping and geometric uncertainty in PPL, we provide results for the \"oracle\" case (SP-O and TP-O) where the ground truth feature descriptor is assigned for each revealed point based on the point's proximity to ground truth points thereby minimizing the effect of descriptor misassignment."
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+ "text": "5.3. Comparing camera relocalization accuracy",
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+ "text": "We also compared the camera pose estimation accuracy when using different types of scene representations.",
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+ "text": "For this purpose, we estimated the absolute pose of the query image from the constructed 3D point cloud maps. This was carried out using the P3P solver [29] for point clouds (PC) and the P6L solver [42] for line clouds (OLC, PPL and PPL+). Our code implementation is based on Poselib [17] maintained by Viktor Larsson, and we made a few adjustments to accommodate the point-to-line distance as the objective function, enforce a chirality constraint for P6L and add bundle adjustment for line clouds.",
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+ "type": "text",
+ "text": "Following [40, 41], we evaluated the localization accuracy by computing the rotational error $\\Delta \\mathsf{R} =$ $\\arccos \\left(\\mathrm{Tr}(\\hat{\\mathbf{R}}^{\\top}\\mathsf{R}) - 1\\right) / 2$ and the translation error $\\Delta \\mathbf{t} =$ $\\left\\| \\hat{\\mathbf{R}}^\\top \\hat{\\mathbf{t}} -\\mathbf{R}^\\top \\mathbf{t}\\right\\| _2,$ where $(\\mathbb{R},\\mathfrak{t})$ denote the ground truth absolute rotation and translation of the query image and $(\\hat{\\mathbb{R}},\\hat{\\mathbf{t}})$ are the estimated absolute rotation and translation of the query image. In order to yield translation error in meters, we multiplied a number to all camera translations in a sequence to match the translation scale of the ground truth datasets provided in [14, 15, 44] (see [18] for details).",
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+ "text": "Table 1 shows visual localization on PPL/PPL+-based line clouds show similar pose accuracy when compared with OLC with standard lifting [40]. Specifically, the median rotation and translation errors of PPL/PPL+ are lower or at least similar to those of OLC with $50\\%$ sparsity, which have the same number of lines for pose estimation.",
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+ "text": "For a detailed comparison, we also plot pose estimation accuracy against image reconstruction quality across different scene representations and different peak finding algorithms in Fig. 8. The plots confirm PPL/PPL+ are more robust to inversion attacks than OLC without compromising camera relocalization accuracy.",
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+ "text": "6. Conclusion",
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+ "text": "This work was motivated by the major limitation of the original line cloud (OLC) that the point cloud and the respective scene details can be revealed by utilizing the statistics of the 3D points and lines. To mitigate this issue, we proposed a new lightweight strategy called paired-point lifting (PPL), which creates line clouds by joining random pairs of sparse points thereby concealing two points per line. We illustrated three main benefits of PPL, namely added uncertainty in descriptor assignment for each line, increased sparsity of the cloud representation and non-uniform distribution of line directions, all of which were experimentally demonstrated to enhance the privacy-preserving nature of the line clouds without trading off camera localization performance. We also proposed an extension of PPL $(\\mathrm{PPL}+)$ to avoid theoretical corner cases. We put effort into comparing between different scene representations on a level playground by implementing a two-peak finding algorithm to handle PPL-based line clouds.",
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+ "type": "text",
+ "text": "An interesting avenue for future work includes devising a more protective lifting approach or developing a faster re-localization algorithm for line clouds (e.g. by combining homotopy and deep learning such as in [11]) for real-time applications in need of privacy-preserving measures.",
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+ "text": "Acknowledgement This work was partly supported by the National Research Foundation of Korea(NRF) grants funded by the Korea government(MSIT) (No. 2022R1C1C1004907, No. 2022R1A5A1022977), Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government(MSIT) (No. 2020-0-01373, Artificial Intelligence Graduate School Program(Hanyang University)) and Hanyang University (HY-202100000003084).",
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+ "text": "References",
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diff --git a/2023/Paired-Point Lifting for Enhanced Privacy-Preserving Visual Localization/15df0ee8-2b51-4a6f-ae53-ee0a888b663e_model.json b/2023/Paired-Point Lifting for Enhanced Privacy-Preserving Visual Localization/15df0ee8-2b51-4a6f-ae53-ee0a888b663e_model.json
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+ "content": "Chunghwan Lee| Dataset | Energy landscape [44] | Cambridge [15] |
| Scene representation | PC | OLC | PPL | PPL+ | PC | OLC | PPL | PPL+ |
| Minimal solver | P3P | P6L | P6L | P6L | P3P | P6L | P6L | P6L |
| Original point used (%) | 100 | 100 | 50 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |
| Line cloud used (%) | - | 100 | 50 | 50 | 50 | 50 | N/A | 100 | 50 | 50 | 50 | 50 |
| Peak finding algorithm used | - | SPF | SPF | SPF | TPF | SPF | N/A | SPF | SPF | SPF | TPF | SPF |
| Proportion of revealed points (%) | 100 | 100 | 50 | 50 | 100 | 50 | 100 | 100 | 50 | 50 | 100 | 100 |
| Median 3D point error (m, ↑) | - | 0.046 | 0.055 | 0.056 | 0.224 | 0.056 | 0.227 | - | 0.752 | 0.854 | 0.973 | 2.845 |
| Image quality (PSNR ↓) | 15.70 | 13.30 | 12.84 | 10.42 | 11.21 | 10.44 | 11.22 | 14.00 | 12.67 | 12.40 | 11.20 | 11.43 |
| Image quality (SSIM ↓) | 0.514 | 0.402 | 0.388 | 0.356 | 0.325 | 0.355 | 0.323 | 0.433 | 0.331 | 0.320 | 0.296 | 0.283 |
| Image quality (MAE ↑) | 33.58 | 43.62 | 45.83 | 62.40 | 56.99 | 62.11 | 56.93 | 39.41 | 46.21 | 47.93 | 55.75 | 54.01 |
| Mean rotation error (°, ↓) | 0.178 | 0.272 | 0.294 | 0.283 | 0.287 | 0.700 | 0.807 | 0.833 | 0.789 |
| Mean translation error (m, ↓) | 0.0071 | 0.0100 | 0.0108 | 0.0105 | 0.0106 | 0.141 | 0.184 | 0.195 | 0.193 |
| Median rotation error (°, ↓) | 0.031 | 0.104 | 0.116 | 0.112 | 0.116 | 0.100 | 0.194 | 0.200 | 0.196 |
| Median translation error (m, ↓) | 0.0010 | 0.0032 | 0.0036 | 0.0035 | 0.0037 | 0.042 | 0.072 | 0.078 | 0.085 |
"
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+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 1. Results obtained from different scene representations on two public datasets (PC: point cloud, OLC: original line cloud, PPL: paired-point lifting and PPL+: PPL with rejection sampling). \\(\\uparrow\\) denotes higher values imply better privacy-preserving behavior, and vice versa for \\(\\downarrow\\). Bold text denotes lowest image quality for each metric. Mean and median values are averaged across all views and sequences."
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+ "type": "image",
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+ "content": null
+ },
+ {
+ "type": "image",
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+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Figure 8. Pose estimation error versus image quality across different levels of point cloud sparsity for the scene 'Office1_manolis'. The size of the marker in the graph represents the proportion of the sampled points in the following order: \\(100\\%\\) \\(50\\%\\) \\(25\\%\\) \\(10\\%\\) \\(5\\%\\) cloud density. The PPL class of approaches achieve lower PSNR and SSIM values and higher MAE values than those of OLC with comparable camera pose estimation errors, suggesting PPL/PPL+ enhance the privacy-preserving visual localization performance."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "those found by TPF, and the results in the supplementary material [18] shows TPF mostly functions as expected."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "5.2. Comparing quality of revealed images"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "We also compared the quality of revealed images from different scene representations."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "For a quantitative comparison, we reconstructed images of the scenes by projecting a 3D point cloud (revealed via peak-finding for line clouds) to 2D using the ground truth camera poses and feeding this along with feature descriptors to the InvSfM network [30]. We then computed the average PSNR, SSIM and MAE values of the revealed images against the ground truth images."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 1 shows that the image quality of recovered images from PPL and \\(\\mathrm{PPL + }\\) are much lower than those from OLC (100% and 50%), indicating improved privacy preserving performance even without the effect of reduced cloud density. This trend is maintained even when SPF is replaced by"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "TPF, demonstrating the potential errors due to misassignment of descriptors also affect image quality."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "In order to disentangle the effect of feature misassignment and geometric uncertainty (induced by non-uniform distribution of lines), we resort to the qualitative comparison of revealed images from different scene representations and different peak finding algorithms. The comparison includes an oracle setting in which the effect of feature descriptor misallocation in PPL is minimized to only visualize the effect of non-uniformly distributed line directions (mimicking \\(0\\%\\) feature swap) by assigning descriptors based on the two points' proximity to ground truth points."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "As shown in Fig. 9, image quality is disimproved by both the effect of feature swap and non-uniformly distributed line directions. Additionally, Fig. 9h and 9i demonstrate PPL+ further degrades the image reconstruction quality, enhancing the privacy preserving performance."
+ },
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+ }
+ ],
+ [
+ {
+ "type": "image",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "(a) Ground truth"
+ },
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+ "bbox": [
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+ "angle": 0,
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+ {
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+ "bbox": [
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+ "angle": 0,
+ "content": "(b) Point cloud"
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+ {
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+ "angle": 0,
+ "content": "(c) OLC [40]"
+ },
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+ "content": null
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+ {
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+ "angle": 0,
+ "content": "(d) PPL (SP-O)"
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+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "(e) PPL (TP-O)"
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+ {
+ "type": "image",
+ "bbox": [
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+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "(f) \\(\\mathrm{PPL + (TP - }\\)"
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+ {
+ "type": "image",
+ "bbox": [
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+ "angle": 0,
+ "content": null
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+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "g) PPL(SPF [3])"
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+ {
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+ "angle": 0,
+ "content": "(h) PPL (TPF)"
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+ {
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+ "angle": 0,
+ "content": "(i) PPL+ (TPF)"
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Figure 9. Images revealed from various scene representations using InvSfM [30]. To disentangle the effect of feature swapping and geometric uncertainty in PPL, we provide results for the \"oracle\" case (SP-O and TP-O) where the ground truth feature descriptor is assigned for each revealed point based on the point's proximity to ground truth points thereby minimizing the effect of descriptor misassignment."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.077,
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+ ],
+ "angle": 0,
+ "content": "5.3. Comparing camera relocalization accuracy"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.077,
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+ ],
+ "angle": 0,
+ "content": "We also compared the camera pose estimation accuracy when using different types of scene representations."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.076,
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+ ],
+ "angle": 0,
+ "content": "For this purpose, we estimated the absolute pose of the query image from the constructed 3D point cloud maps. This was carried out using the P3P solver [29] for point clouds (PC) and the P6L solver [42] for line clouds (OLC, PPL and PPL+). Our code implementation is based on Poselib [17] maintained by Viktor Larsson, and we made a few adjustments to accommodate the point-to-line distance as the objective function, enforce a chirality constraint for P6L and add bundle adjustment for line clouds."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.076,
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+ ],
+ "angle": 0,
+ "content": "Following [40, 41], we evaluated the localization accuracy by computing the rotational error \\(\\Delta \\mathsf{R} =\\) \\(\\arccos \\left(\\mathrm{Tr}(\\hat{\\mathbf{R}}^{\\top}\\mathsf{R}) - 1\\right) / 2\\) and the translation error \\(\\Delta \\mathbf{t} =\\) \\(\\left\\| \\hat{\\mathbf{R}}^\\top \\hat{\\mathbf{t}} -\\mathbf{R}^\\top \\mathbf{t}\\right\\| _2,\\) where \\((\\mathbb{R},\\mathfrak{t})\\) denote the ground truth absolute rotation and translation of the query image and \\((\\hat{\\mathbb{R}},\\hat{\\mathbf{t}})\\) are the estimated absolute rotation and translation of the query image. In order to yield translation error in meters, we multiplied a number to all camera translations in a sequence to match the translation scale of the ground truth datasets provided in [14, 15, 44] (see [18] for details)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.076,
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+ 0.808
+ ],
+ "angle": 0,
+ "content": "Table 1 shows visual localization on PPL/PPL+-based line clouds show similar pose accuracy when compared with OLC with standard lifting [40]. Specifically, the median rotation and translation errors of PPL/PPL+ are lower or at least similar to those of OLC with \\(50\\%\\) sparsity, which have the same number of lines for pose estimation."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.076,
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+ ],
+ "angle": 0,
+ "content": "For a detailed comparison, we also plot pose estimation accuracy against image reconstruction quality across different scene representations and different peak finding algorithms in Fig. 8. The plots confirm PPL/PPL+ are more robust to inversion attacks than OLC without compromising camera relocalization accuracy."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "6. Conclusion"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.498,
+ 0.389,
+ 0.893,
+ 0.661
+ ],
+ "angle": 0,
+ "content": "This work was motivated by the major limitation of the original line cloud (OLC) that the point cloud and the respective scene details can be revealed by utilizing the statistics of the 3D points and lines. To mitigate this issue, we proposed a new lightweight strategy called paired-point lifting (PPL), which creates line clouds by joining random pairs of sparse points thereby concealing two points per line. We illustrated three main benefits of PPL, namely added uncertainty in descriptor assignment for each line, increased sparsity of the cloud representation and non-uniform distribution of line directions, all of which were experimentally demonstrated to enhance the privacy-preserving nature of the line clouds without trading off camera localization performance. We also proposed an extension of PPL \\((\\mathrm{PPL}+)\\) to avoid theoretical corner cases. We put effort into comparing between different scene representations on a level playground by implementing a two-peak finding algorithm to handle PPL-based line clouds."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.498,
+ 0.666,
+ 0.892,
+ 0.743
+ ],
+ "angle": 0,
+ "content": "An interesting avenue for future work includes devising a more protective lifting approach or developing a faster re-localization algorithm for line clouds (e.g. by combining homotopy and deep learning such as in [11]) for real-time applications in need of privacy-preserving measures."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.498,
+ 0.765,
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+ ],
+ "angle": 0,
+ "content": "Acknowledgement This work was partly supported by the National Research Foundation of Korea(NRF) grants funded by the Korea government(MSIT) (No. 2022R1C1C1004907, No. 2022R1A5A1022977), Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government(MSIT) (No. 2020-0-01373, Artificial Intelligence Graduate School Program(Hanyang University)) and Hanyang University (HY-202100000003084)."
+ },
+ {
+ "type": "page_number",
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+ "angle": 0,
+ "content": "17273"
+ }
+ ],
+ [
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "References"
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+# Paired-Point Lifting for Enhanced Privacy-Preserving Visual Localization
+
+Chunghwan Lee| Dataset | Energy landscape [44] | Cambridge [15] |
| Scene representation | PC | OLC | PPL | PPL+ | PC | OLC | PPL | PPL+ |
| Minimal solver | P3P | P6L | P6L | P6L | P3P | P6L | P6L | P6L |
| Original point used (%) | 100 | 100 | 50 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |
| Line cloud used (%) | - | 100 | 50 | 50 | 50 | 50 | N/A | 100 | 50 | 50 | 50 | 50 |
| Peak finding algorithm used | - | SPF | SPF | SPF | TPF | SPF | N/A | SPF | SPF | SPF | TPF | SPF |
| Proportion of revealed points (%) | 100 | 100 | 50 | 50 | 100 | 50 | 100 | 100 | 50 | 50 | 100 | 100 |
| Median 3D point error (m, ↑) | - | 0.046 | 0.055 | 0.056 | 0.224 | 0.056 | 0.227 | - | 0.752 | 0.854 | 0.973 | 2.845 |
| Image quality (PSNR ↓) | 15.70 | 13.30 | 12.84 | 10.42 | 11.21 | 10.44 | 11.22 | 14.00 | 12.67 | 12.40 | 11.20 | 11.43 |
| Image quality (SSIM ↓) | 0.514 | 0.402 | 0.388 | 0.356 | 0.325 | 0.355 | 0.323 | 0.433 | 0.331 | 0.320 | 0.296 | 0.283 |
| Image quality (MAE ↑) | 33.58 | 43.62 | 45.83 | 62.40 | 56.99 | 62.11 | 56.93 | 39.41 | 46.21 | 47.93 | 55.75 | 54.01 |
| Mean rotation error (°, ↓) | 0.178 | 0.272 | 0.294 | 0.283 | 0.287 | 0.700 | 0.807 | 0.833 | 0.789 |
| Mean translation error (m, ↓) | 0.0071 | 0.0100 | 0.0108 | 0.0105 | 0.0106 | 0.141 | 0.184 | 0.195 | 0.193 |
| Median rotation error (°, ↓) | 0.031 | 0.104 | 0.116 | 0.112 | 0.116 | 0.100 | 0.194 | 0.200 | 0.196 |
| Median translation error (m, ↓) | 0.0010 | 0.0032 | 0.0036 | 0.0035 | 0.0037 | 0.042 | 0.072 | 0.078 | 0.085 |
+
+Table 1. Results obtained from different scene representations on two public datasets (PC: point cloud, OLC: original line cloud, PPL: paired-point lifting and PPL+: PPL with rejection sampling). $\uparrow$ denotes higher values imply better privacy-preserving behavior, and vice versa for $\downarrow$ . Bold text denotes lowest image quality for each metric. Mean and median values are averaged across all views and sequences.
+
+
+
+
+
+
+
+
+Figure 8. Pose estimation error versus image quality across different levels of point cloud sparsity for the scene 'Office1_manolis'. The size of the marker in the graph represents the proportion of the sampled points in the following order: $100\%$ $50\%$ $25\%$ $10\%$ $5\%$ cloud density. The PPL class of approaches achieve lower PSNR and SSIM values and higher MAE values than those of OLC with comparable camera pose estimation errors, suggesting PPL/PPL+ enhance the privacy-preserving visual localization performance.
+
+
+
+
+
+those found by TPF, and the results in the supplementary material [18] shows TPF mostly functions as expected.
+
+# 5.2. Comparing quality of revealed images
+
+We also compared the quality of revealed images from different scene representations.
+
+For a quantitative comparison, we reconstructed images of the scenes by projecting a 3D point cloud (revealed via peak-finding for line clouds) to 2D using the ground truth camera poses and feeding this along with feature descriptors to the InvSfM network [30]. We then computed the average PSNR, SSIM and MAE values of the revealed images against the ground truth images.
+
+Table 1 shows that the image quality of recovered images from PPL and $\mathrm{PPL + }$ are much lower than those from OLC (100% and 50%), indicating improved privacy preserving performance even without the effect of reduced cloud density. This trend is maintained even when SPF is replaced by
+
+TPF, demonstrating the potential errors due to misassignment of descriptors also affect image quality.
+
+In order to disentangle the effect of feature misassignment and geometric uncertainty (induced by non-uniform distribution of lines), we resort to the qualitative comparison of revealed images from different scene representations and different peak finding algorithms. The comparison includes an oracle setting in which the effect of feature descriptor misallocation in PPL is minimized to only visualize the effect of non-uniformly distributed line directions (mimicking $0\%$ feature swap) by assigning descriptors based on the two points' proximity to ground truth points.
+
+As shown in Fig. 9, image quality is disimproved by both the effect of feature swap and non-uniformly distributed line directions. Additionally, Fig. 9h and 9i demonstrate PPL+ further degrades the image reconstruction quality, enhancing the privacy preserving performance.
+
+
+(a) Ground truth
+
+
+(b) Point cloud
+
+
+(c) OLC [40]
+
+
+(d) PPL (SP-O)
+Figure 9. Images revealed from various scene representations using InvSfM [30]. To disentangle the effect of feature swapping and geometric uncertainty in PPL, we provide results for the "oracle" case (SP-O and TP-O) where the ground truth feature descriptor is assigned for each revealed point based on the point's proximity to ground truth points thereby minimizing the effect of descriptor misassignment.
+
+
+(e) PPL (TP-O)
+
+
+(f) $\mathrm{PPL + (TP - }$
+
+
+g) PPL(SPF [3])
+
+
+(h) PPL (TPF)
+
+
+(i) PPL+ (TPF)
+
+# 5.3. Comparing camera relocalization accuracy
+
+We also compared the camera pose estimation accuracy when using different types of scene representations.
+
+For this purpose, we estimated the absolute pose of the query image from the constructed 3D point cloud maps. This was carried out using the P3P solver [29] for point clouds (PC) and the P6L solver [42] for line clouds (OLC, PPL and PPL+). Our code implementation is based on Poselib [17] maintained by Viktor Larsson, and we made a few adjustments to accommodate the point-to-line distance as the objective function, enforce a chirality constraint for P6L and add bundle adjustment for line clouds.
+
+Following [40, 41], we evaluated the localization accuracy by computing the rotational error $\Delta \mathsf{R} =$ $\arccos \left(\mathrm{Tr}(\hat{\mathbf{R}}^{\top}\mathsf{R}) - 1\right) / 2$ and the translation error $\Delta \mathbf{t} =$ $\left\| \hat{\mathbf{R}}^\top \hat{\mathbf{t}} -\mathbf{R}^\top \mathbf{t}\right\| _2,$ where $(\mathbb{R},\mathfrak{t})$ denote the ground truth absolute rotation and translation of the query image and $(\hat{\mathbb{R}},\hat{\mathbf{t}})$ are the estimated absolute rotation and translation of the query image. In order to yield translation error in meters, we multiplied a number to all camera translations in a sequence to match the translation scale of the ground truth datasets provided in [14, 15, 44] (see [18] for details).
+
+Table 1 shows visual localization on PPL/PPL+-based line clouds show similar pose accuracy when compared with OLC with standard lifting [40]. Specifically, the median rotation and translation errors of PPL/PPL+ are lower or at least similar to those of OLC with $50\%$ sparsity, which have the same number of lines for pose estimation.
+
+For a detailed comparison, we also plot pose estimation accuracy against image reconstruction quality across different scene representations and different peak finding algorithms in Fig. 8. The plots confirm PPL/PPL+ are more robust to inversion attacks than OLC without compromising camera relocalization accuracy.
+
+# 6. Conclusion
+
+This work was motivated by the major limitation of the original line cloud (OLC) that the point cloud and the respective scene details can be revealed by utilizing the statistics of the 3D points and lines. To mitigate this issue, we proposed a new lightweight strategy called paired-point lifting (PPL), which creates line clouds by joining random pairs of sparse points thereby concealing two points per line. We illustrated three main benefits of PPL, namely added uncertainty in descriptor assignment for each line, increased sparsity of the cloud representation and non-uniform distribution of line directions, all of which were experimentally demonstrated to enhance the privacy-preserving nature of the line clouds without trading off camera localization performance. We also proposed an extension of PPL $(\mathrm{PPL}+)$ to avoid theoretical corner cases. We put effort into comparing between different scene representations on a level playground by implementing a two-peak finding algorithm to handle PPL-based line clouds.
+
+An interesting avenue for future work includes devising a more protective lifting approach or developing a faster re-localization algorithm for line clouds (e.g. by combining homotopy and deep learning such as in [11]) for real-time applications in need of privacy-preserving measures.
+
+Acknowledgement This work was partly supported by the National Research Foundation of Korea(NRF) grants funded by the Korea government(MSIT) (No. 2022R1C1C1004907, No. 2022R1A5A1022977), Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government(MSIT) (No. 2020-0-01373, Artificial Intelligence Graduate School Program(Hanyang University)) and Hanyang University (HY-202100000003084).
+
+# References
+
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| Scene representation | PC | OLC | PPL | PPL+ | PC | OLC | PPL | PPL+ |
| Minimal solver | P3P | P6L | P6L | P6L | P3P | P6L | P6L | P6L |
| Original point used (%) | 100 | 100 | 50 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |
| Line cloud used (%) | - | 100 | 50 | 50 | 50 | 50 | N/A | 100 | 50 | 50 | 50 | 50 |
| Peak finding algorithm used | - | SPF | SPF | SPF | TPF | SPF | N/A | SPF | SPF | SPF | TPF | SPF |
| Proportion of revealed points (%) | 100 | 100 | 50 | 50 | 100 | 50 | 100 | 100 | 50 | 50 | 100 | 100 |
| Median 3D point error (m, ↑) | - | 0.046 | 0.055 | 0.056 | 0.224 | 0.056 | 0.227 | - | 0.752 | 0.854 | 0.973 | 2.845 |
| Image quality (PSNR ↓) | 15.70 | 13.30 | 12.84 | 10.42 | 11.21 | 10.44 | 11.22 | 14.00 | 12.67 | 12.40 | 11.20 | 11.43 |
| Image quality (SSIM ↓) | 0.514 | 0.402 | 0.388 | 0.356 | 0.325 | 0.355 | 0.323 | 0.433 | 0.331 | 0.320 | 0.296 | 0.283 |
| Image quality (MAE ↑) | 33.58 | 43.62 | 45.83 | 62.40 | 56.99 | 62.11 | 56.93 | 39.41 | 46.21 | 47.93 | 55.75 | 54.01 |
| Mean rotation error (°, ↓) | 0.178 | 0.272 | 0.294 | 0.283 | 0.287 | 0.700 | 0.807 | 0.833 | 0.789 |
| Mean translation error (m, ↓) | 0.0071 | 0.0100 | 0.0108 | 0.0105 | 0.0106 | 0.141 | 0.184 | 0.195 | 0.193 |
| Median rotation error (°, ↓) | 0.031 | 0.104 | 0.116 | 0.112 | 0.116 | 0.100 | 0.194 | 0.200 | 0.196 |
| Median translation error (m, ↓) | 0.0010 | 0.0032 | 0.0036 | 0.0035 | 0.0037 | 0.042 | 0.072 | 0.078 | 0.085 |
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+ "content": " are the estimated absolute rotation and translation of the query image. In order to yield translation error in meters, we multiplied a number to all camera translations in a sequence to match the translation scale of the ground truth datasets provided in [14, 15, 44] (see [18] for details)."
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+ "content": "Table 1 shows visual localization on PPL/PPL+-based line clouds show similar pose accuracy when compared with OLC with standard lifting [40]. Specifically, the median rotation and translation errors of PPL/PPL+ are lower or at least similar to those of OLC with "
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+ "content": "For a detailed comparison, we also plot pose estimation accuracy against image reconstruction quality across different scene representations and different peak finding algorithms in Fig. 8. The plots confirm PPL/PPL+ are more robust to inversion attacks than OLC without compromising camera relocalization accuracy."
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+ "content": "This work was motivated by the major limitation of the original line cloud (OLC) that the point cloud and the respective scene details can be revealed by utilizing the statistics of the 3D points and lines. To mitigate this issue, we proposed a new lightweight strategy called paired-point lifting (PPL), which creates line clouds by joining random pairs of sparse points thereby concealing two points per line. We illustrated three main benefits of PPL, namely added uncertainty in descriptor assignment for each line, increased sparsity of the cloud representation and non-uniform distribution of line directions, all of which were experimentally demonstrated to enhance the privacy-preserving nature of the line clouds without trading off camera localization performance. We also proposed an extension of PPL "
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diff --git a/2023/PaletteNeRF_ Palette-Based Appearance Editing of Neural Radiance Fields/3ad1cf6f-9d28-4a28-8311-c8a82da85967_content_list.json b/2023/PaletteNeRF_ Palette-Based Appearance Editing of Neural Radiance Fields/3ad1cf6f-9d28-4a28-8311-c8a82da85967_content_list.json
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+ "text": "Zhengfei Kuang $^{1}$ , Fujun Luan $^{2}$ , Sai Bi $^{2}$ , Zhixin Shu $^{2}$ , Gordon Wetzstein $^{1}$ , Kalyan Sunkavalli $^{2}$ $^{1}$ Stanford University \n $^{2}$ Adobe Research",
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+ "(a) Training Images",
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+ "Figure 1. We propose PaletteNeRF, a novel method for efficient appearance editing of neural radiance fields (NeRF). Taking (a) multi-view photos as training input, our approach reconstructs a NeRF and decomposes its appearance into a set of (b) 3D palette-based color bases. This enables (c) intuitive and photorealistic recoloring of the scene with 3D consistency across arbitrary views. Further, we show that (d) our method supports various palette-based editing applications such as illumination modification and 3D photorealistic style transfer."
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+ "text": "Recent advances in neural radiance fields have enabled the high-fidelity 3D reconstruction of complex scenes for novel view synthesis. However, it remains underexplored how the appearance of such representations can be efficiently edited while maintaining photorealism. In this work, we present PaletteNeRF, a novel method for photorealistic appearance editing of neural radiance fields (NeRF) based on 3D color decomposition. Our method decomposes the appearance of each 3D point into a linear combination of palette-based bases (i.e., 3D segmentations defined by a group of NeRF-type functions) that are shared across the scene. While our palette-based bases are view-independent, we also predict a view-dependent function to capture the color residual (e.g., specular shading). During training, we jointly optimize the basis functions and the color palettes, and we also introduce novel regularizers to encourage the spatial coherence of the decomposi",
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+ "text": "tion. Our method allows users to efficiently edit the appearance of the 3D scene by modifying the color palettes. We also extend our framework with compressed semantic features for semantic-aware appearance editing. We demonstrate that our technique is superior to baseline methods both quantitatively and qualitatively for appearance editing of complex real-world scenes. Our project page is https://palettenerf.github.io.",
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+ "text": "Neural Radiance Fields (NeRF) [23] and its variants [8, 25, 27, 39] have received increasing attention in recent years for their ability to robustly reconstruct real-world 3D scenes from 2D images and enable high-quality, photorealistic novel view synthesis. However, such volumetric representations are challenging to edit due to the fact that scene appearance is implicitly encoded in neural features and network weights that do not support local manipulation or intuitive modification.",
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+ "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+ "text": "ing of NeRF. One category of methods [4, 18, 41, 45] recover the material properties of the scene so that they can re-render them under novel lighting conditions or adjust the material properties such as surface roughness. Such methods rely on accurate estimation of the scene reflectance, which is typically challenging for real-world complex scenes captured under unconstrained environment. Another category of methods [21,35] learns a latent code on which NeRF can be conditioned to produce the desired appearance. However, these methods often suffer from limited capacity and flexibility and do not support fine-grained editing. In addition, some other methods [40] learn to transfer the appearance of NeRF to match a given style image, but sometimes fail to maintain the same level of photorealism in the original scene.",
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+ "text": "In this paper, we propose PaletteNeRF, a novel method to support flexible and intuitive editing of NeRF. Our method is inspired by previous image-editing methods based on color palettes [7, 31], where a small set of colors are used to represent the full range of colors in the image. We model the radiance of each point using a combination of specular and diffuse components, and we further decompose the diffuse component into a linear combination of view-independent color bases that are shared across the scene. During training, we jointly optimize the perpoint specular component, the global color bases and the per-point linear weights to minimize the difference between the rendered images and the ground truth images. We also introduce novel regularizers on the weights to encourage the sparseness and spatially coherence of the decomposition and achieve more meaningful grouping. With the proposed framework, we can intuitively edit the appearance of NeRF by freely modifying the learned color bases (Fig. 1). We further show that our framework can be combined with semantic features to support semantic-aware editing. Unlike previous palette-based image [1, 31] or video [10] editing methods, our method produces more globally coherent and 3D consistent recoloring results of the scene across arbitrary views. We demonstrate that our method can enable more fine-grained local color editing while faithfully maintaining the photorealism of the 3D scene, and achieves better performance than baseline methods both quantitatively and qualitatively. In summary, our contributions include:",
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+ "list_items": [
+ "- We propose a novel framework to facilitate the editing of NeRF by decomposing the radiance field into a weighted combination of learned color bases.",
+ "- We introduced a robust optimization scheme with novel regularizers to achieve intuitive decompositions.",
+ "- Our approach enables practical palette-based appearance editing, making it possible for novice users to interactively edit NeRF in an intuitive and controllable manner on commodity hardware."
+ ],
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+ {
+ "type": "text",
+ "text": "2. Related Work",
+ "text_level": 1,
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+ "text": "Neural radiance fields. Neural radiance fields in the form of MLPs have been extensively used for neural rendering tasks such as novel view synthesis. Typically, these methods [20, 23, 28, 37] encode the geometry and appearance of the scene into network weights of the MLPs. Many recent works [8, 25, 36, 39, 44] propose to speed up the training and improve the performance of the models by applying a combination of light-weight MLPs and neural feature maps or volumes. However, different from traditional graphics primitives such as triangle meshes, both the neural features and the network weights represent scene appearance in an implicit manner and do not support intuitive editing or controls such as recoloring, thereby greatly limiting their applications in existing graphics pipelines.",
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "Appearance editing with NeRF. Many methods have been proposed to support appearance editing of NeRF. Some methods [4,5,29,45] recover the physical properties of the scene such as albedo, specular roughness, and then they can support rendering the scene under novel lighting conditions or changing its material properties. Some other works [15,21,35] learn a latent code jointly with the NeRF reconstruction so as to control its appearance such as changing the illuminations or colors by taking new latent codes as input, which can be mapped from user input or interpolated from existing latent codes. Moreover, there are also approaches [9,13,40] that try to optimize the NeRF to match its appearance against the provided style images. All these methods do not support fine-grained intuitive color editing of NeRF as ours. Concurrently, Ye et al. [38] introduces a NeRF-based intrinsic decomposition model which enables 3D intuitive recoloring, but it does not support palette-based editing.",
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+ "type": "text",
+ "text": "Palette-based editing. Color palette-based methods [7, 12, 31, 32, 42, 46] have been previously used in 2D image editing tasks such as recoloring. However, it is non-trivial to adapt such methods for NeRF editing and naively performing the editing on each rendered frame cannot guarantee view-consistent results. Instead, we integrate the learning of the color bases and the spatially varying weights into the NeRF optimization process, thereby enabling view-consistent and 3D-aware editing. A recent work [33] proposes a palette-based recoloring method on NeRF. However, it is based on posterization and converts the results to a flat and non-photorealistic style.",
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+ "type": "text",
+ "text": "3. Method",
+ "text_level": 1,
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+ {
+ "type": "text",
+ "text": "Fig. 2 illustrates the overview of our multi-stage pipeline. Given a set of images with known poses from",
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+ "type": "page_number",
+ "text": "20692",
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+ },
+ {
+ "type": "image",
+ "img_path": "images/592e2c9f97a57169ef7d4a598f671ba6f45459fe41ac7bbf0e3a87603606f2ac.jpg",
+ "image_caption": [
+ "(a) Preprocessing",
+ "(b) Rendering & Optimization"
+ ],
+ "image_footnote": [],
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "a scene, we first optimize a NeRF-based model to reconstruct the geometry of the scene. Then, we extract $N_{p}$ color palettes with the input images and the learned scene geometry. Finally, we train a segmentation model to decompose the scene appearance into multiple bases based on the extracted palettes. Our decomposition result is able to drive various downstream applications, such as recoloring, photorealistic style transfer and illuminance modification.",
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+ {
+ "type": "text",
+ "text": "3.1. Volumetric Rendering",
+ "text_level": 1,
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+ {
+ "type": "text",
+ "text": "We build our model on the widely used framework Neural Radiance Fields (NeRF). Typically, a NeRF-based model optimizes two neural functions: a geometry function $\\sigma(\\boldsymbol{x})$ and a color function $\\boldsymbol{c}(\\boldsymbol{x},\\boldsymbol{d})$ . The geometry function takes a 3D position as input and outputs the density at this point. The color function takes a 3D position and a viewing direction as input and output a corresponding RGB color. To render an image from a given camera pose, NeRF samples batches of rays from the camera to render the pixels. For each sampled ray $\\boldsymbol{r} = (\\boldsymbol{o},\\boldsymbol{d})$ , a group of 3D points are sampled along the ray path $x_{1\\dots M}$ with depth $t_{1\\dots M}$ , where $\\boldsymbol{x}_i = \\boldsymbol{o} + t_i\\boldsymbol{d}$ . The color prediction of the ray $\\boldsymbol{r}$ is calculated as:",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\boldsymbol {c} (\\boldsymbol {r}) = \\sum_ {i = 1} ^ {M} \\alpha_ {i} \\left(1 - w _ {i}\\right) \\boldsymbol {c} \\left(\\boldsymbol {x} _ {i}, \\boldsymbol {d}\\right), \\tag {1}\n$$\n",
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+ {
+ "type": "text",
+ "text": "where $w_{i} = \\exp \\left(-\\left(t_{i} - t_{i - 1}\\right)\\sigma (\\pmb{x}_{i})\\right)$ is the transmittance of the ray between the $i$ th sample point and the $(i + 1)$ th sample point, and $\\alpha_{i} = \\prod_{j = 1}^{i - 1}w_{i}$ is the ray attenuation from the ray's origin to the $i$ th sample point.",
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+ },
+ {
+ "type": "image",
+ "img_path": "images/ac3a1aaadb90171fd2aeb5d6f188939bcba0c2d21abb05036d093e9e7bc4c6e1.jpg",
+ "image_caption": [
+ "Figure 2. The overview of our pipeline. Given a set of training images, we first (a) reconstruct the scene geometry and build the color palettes with existing methods. Then, our PaletteNeRF (b) decomposes the scene appearance into multiple palette-based bases and the view-dependent color. We deploy a series of losses on the palette-based base's functions, the view-dependent color, and the final output.",
+ "Figure 3. Left: Reference image; Middle: Comparison between the recoloring result of our model trained with extracted palettes and model trained with random initialized palettes; Right: Normalized training image and the extracted palettes from normalization of different levels."
+ ],
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+ {
+ "type": "text",
+ "text": "3.2. Palette Extraction",
+ "text_level": 1,
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+ },
+ {
+ "type": "text",
+ "text": "Although it is possible to directly train our model with randomly initialized color palettes, doing this will bring excessive ambiguity to the problem and may produces irregular results as shown in Fig. 3(b). Thankfully, the problem of extracting color palettes from images has been extensively researched over the past years, thus we use the extraction method from a state-of-the-art image recoloring work [31] as our initialization. In general, this method extracts color palettes from the 3D convex hull of the clustered image colors in the RGB space. In our scenario, we simply select all training image pixels with valid depth from NeRF's depth maps and concatenate their color as input.",
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+ {
+ "type": "text",
+ "text": "We notice that with input from multiple images, the extraction method may produce palettes that are chromatically",
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+ "type": "page_number",
+ "text": "20693",
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+ {
+ "type": "image",
+ "img_path": "images/7001e77836cb064e96919328163504cb1e4501a09adaf0271a30d40d77768b73.jpg",
+ "image_caption": [
+ "Figure 4. Our network structure. As we only show one palette-based basis in the figure, our network generates $N_{p}$ bases in parallel and they are summed up in the final step."
+ ],
+ "image_footnote": [],
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "similar (e.g., palettes including a light yellow and a dark yellow), due to the varying shading of the captured scene. This may result in unrealistic appearance editing. Inspired by image illumination decomposition works [6,22], we normalize the input colors of the training images by their intensity, to narrow down the search space of color palettes. Conventionally, the intensity of a color is represented by the L1 norm of its RGB value. However, normalizing with L1 norm projects the colors to a plane, which is a highly ill-posed edge case for 3D convex hull calculation. These problems can be addressed by replacing the norm with a higher order one. Empirically, we find that palettes extracted from L2 normalized images work well in our next decomposition stage, and use them in all of our experiments.",
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+ {
+ "type": "text",
+ "text": "In addition to the extracted palettes $\\bar{\\mathcal{P}}$ , we also keep the blending weights $\\bar{\\omega}$ of the input pixel colors, calculated from the method of the same work. These weights act as an additional supervision in the next stage.",
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+ {
+ "type": "text",
+ "text": "3.3. Color Decomposition",
+ "text_level": 1,
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+ {
+ "type": "text",
+ "text": "To introduce our color decomposition model, we first explain our target outputs, then describe the structure of our decomposition network.",
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+ "type": "text",
+ "text": "As shown in Fig. 2, given the color palettes of size $N_{p}$ , our model aims to reconstruct $N_{p}$ view-independent palette-based bases and an additional view-dependent color function representing all view-dependent shading such as specular reflections. The palette-based bases correspond to the extracted color palettes, and are defined by two functions of $x$ : A color offset function $\\delta : \\mathbb{R}^3 \\to \\mathbb{R}^3$ , and a weight function $\\omega : \\mathbb{R}^3 \\to [0,1]$ . Observing that realistic image captures usually consists of a huge variety of colors, we allow the basis color of each point shift from the palette color with an offset (inspired by image-based soft color segmentation methods [1, 2]). This design increases the capacity of the bases and benefits the segmentation quality on complex scenes. We also introduce an intensity function $I: \\mathbb{R}^3 \\to [0,1]$ that is shared among all palette-based bases, due to the normalization of the extracted palettes. While",
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+ "type": "text",
+ "text": "the aforementioned functions only take position as input, our model also contains a view-dependent color function $s: \\mathbb{R}^5 \\to [0,1]^3$ that takes viewing direction as input, too. We compose all of these bases into a color output $c \\in \\mathbb{R}^3$ by the following equation:",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\boldsymbol {c} (\\boldsymbol {x}, \\boldsymbol {d}) = \\boldsymbol {s} (\\boldsymbol {x}, \\boldsymbol {d}) + I (\\boldsymbol {x}) \\sum_ {i = 1} ^ {N _ {p}} \\omega_ {i} (\\boldsymbol {x}) \\left(\\boldsymbol {\\mathcal {P}} _ {i} + \\boldsymbol {\\delta} _ {i} (\\boldsymbol {x})\\right), \\tag {2}\n$$\n",
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+ "type": "text",
+ "text": "where $\\omega_{i}(\\pmb{x})$ are normalized by their sum. We clamp the summed-up color $c$ to [0, 1] as the final output. We also optimize the palette color $\\mathcal{P}_i$ during the training. As shown in Fig. 4, Our network consists of three MLPs: the Diffuse MLP predicts the diffuse color $c_{d}(\\pmb{x})$ , i.e., the sum of all palette-based bases; the View-Dependent MLP generates view-dependent color $s(\\pmb{x}, \\pmb{d})$ ; Finally, the Palette MLP predicts the function values of the palette-based bases: $\\omega_{i}(\\pmb{x}), \\delta_{i}(\\pmb{x})$ and $I(\\pmb{x})$ , where $c_{d}$ is also fed as an input prior. We compose all of the network outputs to the final color using Eq. 2.",
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+ "type": "text",
+ "text": "3.4. Optimization",
+ "text_level": 1,
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+ "type": "text",
+ "text": "Given the fact that separating multiple bases from the scene appearance is a considerably ill-posed task, a lot of cautions should be taken in designing the optimization scheme. Hence, we develop a series of losses to regulate the optimized parameters and to avoid undesirable results such as local-minimum.",
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+ "type": "text",
+ "text": "To begin with, we deploy the image reconstruction loss defined as:",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} _ {\\text {r e c o n}} = \\left\\| \\boldsymbol {c} ^ {\\text {r e f}} - \\boldsymbol {c} (\\boldsymbol {r}) \\right\\| _ {2} ^ {2} + \\left\\| \\boldsymbol {c} ^ {\\text {r e f}} - \\left(\\boldsymbol {c} _ {d} (\\boldsymbol {r}) + \\boldsymbol {s} (\\boldsymbol {r})\\right) \\right\\| _ {2} ^ {2}, \\tag {3}\n$$\n",
+ "text_format": "latex",
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+ "type": "text",
+ "text": "where $c^{\\mathrm{ref}}$ is the ground truth color, $c(\\boldsymbol{r}), c_d(\\boldsymbol{r}), s(\\boldsymbol{r})$ are calculated from the volume rendering equation at Eq. 1. The second term of this loss can also be considered as the L2 distance between $c_d(\\boldsymbol{r})$ and the sum of palette-based bases. We also add a regularization loss $\\mathcal{L}_s$ to the view-dependent color function $s(\\boldsymbol{x}, \\boldsymbol{r})$ , to prevent the particular situation where $s$ dominates the appearance and pushes all palette-based bases to 0. This loss is defined as:",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} _ {\\mathrm {s}} = \\| \\boldsymbol {s} (\\boldsymbol {x}, \\boldsymbol {d}) \\| _ {2} ^ {2}. \\tag {4}\n$$\n",
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+ "type": "text",
+ "text": "While our model uses color offsets to shift the basis color, it is necessary to restrict the blending weights and color offset to avoid extreme solutions. Hence, we adapt the sparsity loss $\\mathcal{L}_{\\mathrm{sp}}$ and the color offset loss $\\mathcal{L}_{\\mathrm{offset}}$ from the image soft segmentation method [2]. They are defined as:",
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+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} _ {\\mathrm {s p}} = \\frac {\\sum_ {i = 1} ^ {N _ {p}} \\omega_ {i} (\\boldsymbol {x})}{\\sum_ {i = 1} ^ {N _ {p}} \\omega_ {i} ^ {2} (\\boldsymbol {x})} - 1, \\tag {5}\n$$\n",
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+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} _ {\\text {o f f s e t}} = \\| \\boldsymbol {\\delta} (\\boldsymbol {x}) \\| _ {2} ^ {2}. \\tag {6}\n$$\n",
+ "text_format": "latex",
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+ {
+ "type": "page_number",
+ "text": "20694",
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+ "type": "text",
+ "text": "The sparsity loss aims to make the blending weights sparser (e.g., segmenting each point $x$ to fewer bases), which will eventually increase the capacity of the bases by increasing the color offset. On the other hand, the color offset loss directly suppresses the magnitude of color offsets, preventing them from deviating from the palettes too much. Intuitively, these two losses act as two adversarial roles, and finding a good balance between them will lead to neat segmentation results with reasonable basis color. In our experiments, however, we observe that these two losses may lead to harsh segmentation results, which will drastically affect the quality of the following editing (see our qualitative ablation study). Thus we introduce a novel 3D-aware smooth loss to smooth the weight function based on the NeRF's output. It is given by:",
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+ "page_idx": 4
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} _ {\\mathrm {s m}} = \\xi (\\boldsymbol {x}, \\boldsymbol {x} + \\varepsilon) \\| \\boldsymbol {\\omega} (\\boldsymbol {x}) - \\boldsymbol {\\omega} (\\boldsymbol {x} + \\varepsilon) \\| ^ {2}, \\tag {7}\n$$\n",
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+ "type": "text",
+ "text": "where $\\omega = \\omega_{1\\dots N_p},\\varepsilon$ is a random position offset sampled from a Gaussian distribution, and $\\xi (\\cdot)$ is the similarity between two points. Here, we adapt the Gaussian kernel used in the bilateral filter, and define the similarity function as:",
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+ "type": "equation",
+ "text": "\n$$\n\\xi (\\boldsymbol {x}, \\boldsymbol {y}) = \\exp \\left(- \\frac {\\| \\boldsymbol {x} - \\boldsymbol {y} \\| ^ {2}}{\\sigma_ {x}} - \\frac {\\| \\boldsymbol {c} _ {d} (\\boldsymbol {x}) - \\boldsymbol {c} _ {d} (\\boldsymbol {y}) \\| ^ {2}}{\\sigma_ {c}}\\right), \\tag {8}\n$$\n",
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+ "type": "text",
+ "text": "where $\\sigma_{x}$ and $\\sigma_{c}$ are smoothing parameters. While the diffuse color $c_{d}$ is used in the smooth loss, we cut off their gradients during the training.",
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+ "type": "text",
+ "text": "Finally, we add two more losses that incorporate the supervisions from the palette extraction model. They are:",
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+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} _ {\\text {p a l e t t e}} = \\| \\boldsymbol {\\mathcal {P}} - \\hat {\\boldsymbol {\\mathcal {P}}} \\| _ {2} ^ {2}, \\tag {9}\n$$\n",
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+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} _ {\\text {w e i g h t}} = \\| \\omega - \\bar {\\omega} \\| _ {2} ^ {2}. \\tag {10}\n$$\n",
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+ "type": "text",
+ "text": "As a summary, the overall loss of our optimization is the weighted sum defined as:",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\begin{array}{l} \\mathcal {L} = \\mathcal {L} _ {\\text {r e c o n}} + \\lambda_ {\\mathrm {s}} \\mathcal {L} _ {\\mathrm {s}} + \\lambda_ {\\mathrm {s p}} \\mathcal {L} _ {\\mathrm {s p}} \\\\ + \\lambda_ {\\text {o f f s e t}} \\mathcal {L} _ {\\text {o f f s e t}} + \\lambda_ {\\mathrm {s m}} \\mathcal {L} _ {\\mathrm {s m}} \\tag {11} \\\\ + \\lambda_ {\\text {p a l e t e}} \\mathcal {L} _ {\\text {p a l e t e}} + \\lambda_ {\\text {w e i g h t}} \\mathcal {L} _ {\\text {w e i g h t}}, \\\\ \\end{array}\n$$\n",
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+ "type": "text",
+ "text": "where $\\lambda_{\\mathrm{s}}, \\lambda_{\\mathrm{sp}}, \\lambda_{\\mathrm{offset}}, \\lambda_{\\mathrm{sm}}, \\lambda_{\\mathrm{palette}}, \\lambda_{\\mathrm{weight}}$ are all loss weights.",
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+ "type": "text",
+ "text": "3.5. Appearance Editing",
+ "text_level": 1,
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+ "text": "With the bases predicted from the model, we can simply tune the value of the functions to support appearance editing, such as recoloring and photorealistic style transfer. When deployed with recent fast NeRF models, our method is able to achieve real-time interactive editing.",
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+ "text": "Since our basis functions are defined on the whole scene, they do not directly support local editing (e.g., edit a single object in the scene). To achieve that, we follow one recent work [17] that learns a 3D feature field from the semantic feature maps predicted from state-of-the-art image-based",
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+ "text": "segmentation models (e.g., Lang-Seg [19]), and use the feature field to guide the editing. However, directly adding high dimensional semantic features to our model may decrease its efficiency, making it impractical to edit in real-time. As the objects captured from a scene are often limited to a small set (e.g., in an indoor scene, chairs, walls and floor are the most likely appeared objects), the semantic features extracted from the scene are often a limited subset of the whole feature space. Therefore, we apply PCA to compress the extracted features to a lower dimension (16 in our experiments) before feeding them to the network. Please find more details in terms of implementation, usage and results on editing in the supplemental materials.",
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+ "text": "Training. To support real-time appearance editing, we use Instant-NGP [25] as our backbone. For the geometry learning stage, we keep all original configurations, except adding a per-point rgb loss introduced by Sun et al. [30] to make the density field sparser and avoid floaters. For the segmentation learning stage, we fix the extracted palettes for the first 100 epochs. After that, we unleash the palettes and remove $\\mathcal{L}_{\\mathrm{weight}}$ to fine-tune the model. Moreover, since our smooth loss $\\mathcal{L}_{\\mathrm{sm}}$ employs the diffuse color $c_{d}$ to calculate the smoothing weight, we do not apply $\\mathcal{L}_{\\mathrm{sm}}$ for the first 30 epochs to avoid unconverged $c_{d}$ as input.",
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+ "text": "Our training and testing experiments are implemented using PyTorch [26], and run on a single NVIDIA RTX 3090 GPU. For both stages, we train our model for 300-600 epochs (depending on the number of training images) using the Adam Optimizer [16] with learning rate set to 0.01, which takes no more than 2 hours in total.",
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+ "text": "Datasets. We conduct experiments on scenes from three sources: Lego, Ficus, Ship and Hotdog from the NeRF Blender dataset [23], Fern, Horns, Flower, Orchids from the the forward-facing LLFF dataset [24] and Bonsai, Kitchen and Room from the 360-degree Mip-NeRF360 dataset [3].",
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+ "text": "4.2. Comparisons",
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+ "text": "Recoloring. We use the HSV color space for recoloring in all experiments. Given a group of modified color palettes $\\mathcal{P}'$ , we calculate the difference between the original palettes $\\mathcal{P}$ and $\\mathcal{P}'$ in HSV, then directly apply the change to all points' soft color, i.e. $\\mathcal{P} + \\delta(x)$ .",
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+ "text": "We compare our model with the state-of-the-art NeRF-based recoloring method PosterNeRF [34] on the Blender Dataset in Fig. 5. Compared to PosterNeRF, our model achieves better reconstruction quality, and produces more photorealistic results with fewer artifacts, and requires fewer palette edits.",
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+ "img_path": "images/421274e51689e8e783429bf3425b65ce6d88c3a5bfb7465aca77b33bbe487831.jpg",
+ "image_caption": [
+ "Figure 5. Qualitative comparison with PosterNeRF [33]. We show reconstruction results in the first row and recolor results in the second row."
+ ],
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+ "img_path": "images/ef656ea4564841d65e22701c64d59e53b63b15297de219ab57058d59017b3eee.jpg",
+ "image_caption": [
+ "Figure 6. Qualitative comparison with video palette-based recoloring method [11]. Unlike Du et al. [11] that either only modifies the lego color (Edit 1) or introduces view-inconsistency when also modifying the gloves (Edit 2), our method recolors the 3D scene consistently while maintaining photorealism across views."
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+ "text": "We also compare our model with a state-of-the-art palette-based video recoloring model [10] in Fig. 6 and image recoloring models [1, 31] in Fig. 7. Since our model consists of color offsets and radiance functions that extend the palette color to basis, it requires fewer palettes to reconstruct the images than other methods, which improves usability and benefits the quality of recoloring results. Also, with the help of the scene geometry, our results are more plausible in 3D. Particularly, we show recoloring results on two different views in the Kitchen scene, where we set the same recoloring goal for each of them: changing the light on the excavator to purple. While the image-based methods failed to keep the other objects looking the same from the two views, our model is able to produce view-consistent results for the whole scene.",
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+ "text": "User-Guided Photorealistic style transfer. We can apply our decomposition model to achieve photorealistic style transfer on the captured scenes with sparse user guidance. Given a style image, users may define a series of correspondences between the image pixels and 3D points, that our system uses to transform our palette-based bases to align the point colors to the pixel colors; more details in the supplementary. We compare our model with three state-of-the-art methods: UPST-NeRF [9], ARF [40] and image-based",
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+ "text": "stylization with AdaIN [14] (Fig. 9). Our results are more photorealistic than ARF and AdaIN, and comparable with UPST-NeRF. However, UPST-NeRF takes much more time to train (tens of hours) than ours.",
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+ "text": "User study. To better demonstrate the effectiveness of our model, we also conduct a user study on these two applications. The study was taken on the Amazon Mechanical Turk platform, where we dispatched 162 questions 30 times to the crowd (4860 in total), and received 4496 answers. In each question, the user watches images/videos generated from our model and another randomly selected baseline and was asked to decide which one is more view-consistent and/or photorealistic. Fig. 8 summarizes our study's results. We outperform image-based recoloring baselines [1, 31], and are considered more photorealistic than posterNeRF [34]. For the style transfer task, our model received better feedback than ARF [40] and AdaIN [14] and is rated better than UPST-NeRF [9] for view-consistency. More details are in the supplementary.",
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+ "text": "4.3. Ablations",
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+ "text": "We conduct three ablative evaluations on the LLFF dataset to show the effectiveness of our model design. We first compare our model with the original vanilla Instant-NGP with two metrics: the Peak Signal-to-Noise Ratio (PSNR $\\uparrow$ ), the Learned Perceptual Image Patch Similarity [43] (LPIPS). Our model achieves the same PSNR score from the Instant-NGP (24.50), and has a slightly higher LPIPS score (0.152 compared to 0.145). This shows our model has little effect on the reconstruction quality.",
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+ "text": "We then compare the reconstruction results of our model with two variants on the LPIPS metric: Model without color offsets and Model without view-dependent function. Both of the variants get higher LPIPS scores (0.160 for removing the color offset, and 0.155 for removing the view-dependent function), showing that adding the color offsets and view-dependent function increases the capability of our model to reconstruct real scenes.",
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+ "text": "We also compare the palette decomposition results of our model with three variants: Model without color offset (Ours w/o $\\delta$ ), model without the sparsity loss (Ours w/o $\\mathcal{L}_{\\mathrm{sp}}$ ) and model without the smooth loss (Ours w/o $\\mathcal{L}_{\\mathrm{sm}}$ ) both quantitatively and qualitatively. Quantitative results are shown in Tab. 1, and qualitative comparisons are shown in Fig. 10. Removing the smooth loss will downgrade the smoothness of the blending weights, and leads to critical artifacts on the fern; Removing the sparsity loss will decrease the sparseness of the weights, and hence leads to unwanted red-dish tint in the whole image; Removing the color offset also reduces the sparsity of the weights, and leads to unwanted tint for some area (e.g. the wall behind the fern). This",
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+ "Figure 7. Qualitative comparison with image palette-based recoloring methods. We compare our method with Tan et al. [31] and Akimoto et al. [1]. For each recolored image, we also show the corresponding palettes editing on its left side, and a zoom-in view on its right side."
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+ "Figure 8. User study results. For each comparison we demonstrate the percentage of users who prefer our method, users who prefer the baseline method, and users who do not lean towards anyone."
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+ "text": "shows that our designed components are essential to generating clean recoloring results.",
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+ "text": "4.4. More Results",
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+ "text": "In Fig. 11, we show several results of feature-guided editing. Although our optimized segmentations are shared",
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+ "Table 1. Quantitative ablation study results. We compare our model with variants on two metrics: The sparsity error defined by Eq. 5 and the total variation of the weight images (TV) which measures their smoothness."
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+ "table_body": "| structure alias | embedding dim | structure | para. |
| PanoSwinT8 | 8 | [W, PSW, PA], PM, [W, PSW, PA], PM, [W, PSW, PA], PM, [W, PSW] | 191k |
| PanoSwinT12 | 12 | [W, PSW, PA], PM, [W, PSW] | 66k |
| SwinT13 [19] | 13 | [W, PSW, W], PM, [W, PSW] | 67k |
| PanoSwinT92 | 92 | [W,PSW,PA],PM,[W,PSW,PA],PM,[(W,PSW)*2,W,PA],PM,[W,PSW] | 28M |
| SwinT [19] | 96 | [W,SW],PM,[W,SW],PM,[(W,SW)*3],PM,[W,SW] | 28M |
| PanoSwinT | 96 | [W,PSW,PA],PM,[W,PSW,PA],PM,[(W,PSW)*2,W,PA],PM,[W,PSW] | 30M |
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+ "text": "dataset [39], which is composed of PanoContext and the extended Stanford 2D-3D, consisting of 500 and 571 annotated panoramas respectively. Following HorizonNet [26], we train our model on the LayoutNet training set and test it on Stanford 2D-3D test set. We ONLY enable the panoramic stage in this task.",
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+ "Table 3. PanoSwin architecture variants. W/SW: regular/shift windowing attention [19]. PSW: pano-style shift windowing attention. PA: pitch attention module. PM: patch merging [19]. $(*)^{n}$ denotes repeating n times. Refer to Supplementary for more details."
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| PanoSwinT8 | 8 | [W, PSW, PA], PM, [W, PSW, PA], PM, [W, PSW, PA], PM, [W, PSW] | 191k |
| PanoSwinT12 | 12 | [W, PSW, PA], PM, [W, PSW] | 66k |
| SwinT13 [19] | 13 | [W, PSW, W], PM, [W, PSW] | 67k |
| PanoSwinT92 | 92 | [W,PSW,PA],PM,[W,PSW,PA],PM,[(W,PSW)*2,W,PA],PM,[W,PSW] | 28M |
| SwinT [19] | 96 | [W,SW],PM,[W,SW],PM,[(W,SW)*3],PM,[W,SW] | 28M |
| PanoSwinT | 96 | [W,PSW,PA],PM,[W,PSW,PA],PM,[(W,PSW)*2,W,PA],PM,[W,PSW] | 30M |
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| PanoSwinT8 | 8 | [W, PSW, PA], PM, [W, PSW, PA], PM, [W, PSW, PA], PM, [W, PSW] | 191k |
| PanoSwinT12 | 12 | [W, PSW, PA], PM, [W, PSW] | 66k |
| SwinT13 [19] | 13 | [W, PSW, W], PM, [W, PSW] | 67k |
| PanoSwinT92 | 92 | [W,PSW,PA],PM,[W,PSW,PA],PM,[(W,PSW)*2,W,PA],PM,[W,PSW] | 28M |
| SwinT [19] | 96 | [W,SW],PM,[W,SW],PM,[(W,SW)*3],PM,[W,SW] | 28M |
| PanoSwinT | 96 | [W,PSW,PA],PM,[W,PSW,PA],PM,[(W,PSW)*2,W,PA],PM,[W,PSW] | 30M |
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+Table 3. PanoSwin architecture variants. W/SW: regular/shift windowing attention [19]. PSW: pano-style shift windowing attention. PA: pitch attention module. PM: patch merging [19]. $(*)^{n}$ denotes repeating n times. Refer to Supplementary for more details.
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| PanoSwinT8 | 8 | [W, PSW, PA], PM, [W, PSW, PA], PM, [W, PSW, PA], PM, [W, PSW] | 191k |
| PanoSwinT12 | 12 | [W, PSW, PA], PM, [W, PSW] | 66k |
| SwinT13 [19] | 13 | [W, PSW, W], PM, [W, PSW] | 67k |
| PanoSwinT92 | 92 | [W,PSW,PA],PM,[W,PSW,PA],PM,[(W,PSW)*2,W,PA],PM,[W,PSW] | 28M |
| SwinT [19] | 96 | [W,SW],PM,[W,SW],PM,[(W,SW)*3],PM,[W,SW] | 28M |
| PanoSwinT | 96 | [W,PSW,PA],PM,[W,PSW,PA],PM,[(W,PSW)*2,W,PA],PM,[W,PSW] | 30M |
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+ "html": "| Query Shape | Parts2Words | TriCoLo |
| 1. a wooden oval brown small table . it have a rectangular hole at the middle below the table - top , seem like it have two leg . \n2. a capsule shape wooden table with two half cylinder shape leg . \n3. brown color , oval shape , wood material , and physical appearance table \n4. this be a light brown wooden table , with a flat capsule shape surface at the top , and two thick leg that be vertically tall , and be semicircle shape with the flat side face the middle create an empty space . \n5. brown colored whole wood oval shape coffee table . | 1. this oval light wood topped table is on a dark wood base . \n2. a wooden oval brown small table . it has a rectangular hole at the middle below the table top seems like it has two legs . \n3. an oval shaped table with two legs . it is also wooden and brown . \n4. an brown oval table with three section base \n5. brown color rectangle shape wood material and physical appearance table |
| 1. a red chair with a back . \n2. a red chair . the seat be curved downward and the back have a gap . \n3. red side chair \n4. maroon color chair with four leg and rest at back \n5. it be a wooden chair . it be red in color . | 1. a wooden chair red in color \n2. it is a wooden chair . it is red in color . \n3. a wooden chair with red colour back and seat with spindle and strong four legs \n4. a red wooden kitchen chair with detached back and slightly rounded seat \n5. this is wooden chair with four legs and it is in red texture light weight |
| 1. marble round table with metal leg . table be black color . \n2. black , round metal outdoor table . with long curl leg . \n3. a center - table with black circular top and four curved leg \n4. a stylish black color round table for all - purpose \n5. a circular black table . | 1. the table is circular with three legs . the table is black and the legs stick out from the top . \n2. a black color round shaped wooden table with three legs \n3. a black colored round table with four slim shaped legs \n4. black round metal outdoor table with long curled legs . \n5. black round table three legs wooden material |
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+ "text": "Figure 8. Retrieval result of the proposed Parts2Words and TriCoLo [37], the ground truth description are marked in red. Each retrieval case under our model can match 2 or 3 ground truth sentences, which is more than TriCoLo.",
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+ "Figure 10. Comparison in terms of Recall@1(RR@1), Recall@5(RR@5) and NDCG@5 using different segmentation granularity. S1, S2, and S3 represent the representing different segmentation granularities from coarse to fine, which have 17 classes, 72 classes, and 90 classes separately. The segmentation with the coarsest granularity S1 achieves a better performance."
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+ "text": "texts for each case. From Figure 4, we can see the top-5 retrieval shapes have a more similar appearance, especially in details such as color and geometry. The results demonstrate that our method could find correspondences in details, such as color and geometric description. In particular, for complex shapes, our model can still achieve superior results.",
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+ "Figure 11. Comparison in terms of Recall@1(RR@1), Recall@5(RR@5) and NDCG@5 using different loss weight $\\beta$ . According to the above result, we choose loss weight $\\beta$ as 40."
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+ "text": "We also compare with with TriCoLo [37] by presenting 3 text-to-shape retrieval results and 3 shape-to-text retrieval results, as shown in Figures 7 and 8. For each query text/shape, we display top-5 retrieval shapes/texts ranked by the similarity scores from the two methods. The ground truth shapes/texts are marked in red. And as shown in Figure 7, our model matches the ground truth shapes within top-2 retrieval shapes. For the S2T retrieval result in Figure 8, our model can match 2 or 3 ground truth sentences within top-5 retrieval results, which is more than the ones that TriCoLo can match.",
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+ "text": "Granularity We explore the impact of part embedding extracted under different segmentation granularities on the matching model. The PartNet dataset contains hierarchical segmentation annotation in three granularities from S1 to S3, representing different segmentation granularities from coarse to fine, which have 17 classes, 72 classes, and 90 classes separately. The ground truths and our semantic predictions are shown in Figure 9. As shown in Figure 10, the results show that our method with coarse part segmentation",
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+ "text": "annotation achieves the best performance. We believe that the parts learned through finer segmentation ground truth are hard to align with the simple plain words. Therefore, the coarsest part segmentation annotation S1 is selected.",
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+ "text": "Loss Weight We adopt the balance weight $\\beta$ to adjust the joint loss to make our network focus more on the retrieval performance than the segmentation result. We present our retrieval performance when selecting different $\\beta$ to select the most suitable parameter settings, as shown in Figure 11. The retrieval performance improves with the increase of the weight of retrieval loss until $\\beta$ is 40.",
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+ "text": "Backbone We analyzed the influence of different network backbones on the retrieval results. We use PointNet and PointNet++ respectively as the backbone for the feature extraction network. As shown in Table 2, the comparison results show that the retrieval result gets worse after replacing the backbone with PointNet++.",
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+ "text": "CD/EMD In Table 2, we replace the EMD for matching similarity calculation by CD (Chamfer Distance), which can be regarded as a local optimal hard matching method. In the Chamfer distance matching flow, each node only corresponds to the node with the most similar individual. The experimental results show that the EMD is better than CD.",
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+ "text": "Sampling We explore the impact of different negative sample learning strategies based on the triplet ranking loss on retrieval. We compared two strategies: hardest negative mining and semi-hard negative mining. As demonstrated in Table 3, we find that the model using the hardest negative mining results in a collapsed model.",
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+ "text": "Training We examine the effectiveness of end-to-end training by joint multi-task learning as shown in Table 3. In comparison, we separately train the shape encoder module and the matching module. Our results demonstrate that the end-to-end model outperforms the separate training approach.",
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+ "text": "Color and Segmentation As shown in Table 4, we separately evaluate the influence of integrating the point cloud color into the feature fusion step and supervising the training with the segmentation loss. The results demonstrate that, after removing these two components (w/o color and w/o seg loss), it is hard for the network to learn to establish a local alignment between color and geometry, which will lead to a significant decrease in accuracy. It indicates that color and part information are crucial for multi-modal retrieval.",
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+ "text": "4.3. Visualization",
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+ "text": "We visualized two examples of the best matching pair between the shape and the text, as shown in Figure 12. The normalized similarity matrix is colored by calculating each pairwise distance $D = \\{1 - c_{ij}\\}$ between parts and words. We can see that our model can accurately find the correspondence (dark red) between parts and words. For the first",
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+ "Figure 12. Visualization of the similarity between parts and words. We display a normalized similarity matrix between parts and words. The place with darker color indicates the higher relationship between corresponding parts and words."
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+ "text": "example, the chair is firstly segmented into 4 parts, then the black seat matches the words \"black\" and \"seat\" in the text well, and the rest also attends the words \"yellow\", \"black\" and \"rest\". Besides, the similarity weight between the part of blue legs and the word \"blue\" obtained the highest score.",
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+ "text": "We introduce a method to learn the joint embedding of 3D point clouds and text. Our method successively increases the ability of a joint understanding of 3D point clouds and text by learning to bidirectionally match 3D parts to words in an optimized space. We obtain the 3D parts by leveraging a 3D segmentation prior, which effectively resolves the self-occlusion issue of parts that is suffered by current multi-view based methods. We also demonstrate that matching 3D parts to words using the optimal transport is an efficient way to merge different modalities including 3D shapes and text in a common space, where the proposed cross-modal earth mover's distance is also justified to effectively capture the relationship of part-word in this matching procedure. Experimental results show that our method significantly outperforms other state-of-the-art methods.",
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+ "text": "Acknowledgement. This work is supported by the Young Scientists Fund of the National Natural Science Foundation of China (Grant No.62206106).",
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+ "content": "| Query Shape | Parts2Words | TriCoLo |
| 1. a wooden oval brown small table . it have a rectangular hole at the middle below the table - top , seem like it have two leg . \n2. a capsule shape wooden table with two half cylinder shape leg . \n3. brown color , oval shape , wood material , and physical appearance table \n4. this be a light brown wooden table , with a flat capsule shape surface at the top , and two thick leg that be vertically tall , and be semicircle shape with the flat side face the middle create an empty space . \n5. brown colored whole wood oval shape coffee table . | 1. this oval light wood topped table is on a dark wood base . \n2. a wooden oval brown small table . it has a rectangular hole at the middle below the table top seems like it has two legs . \n3. an oval shaped table with two legs . it is also wooden and brown . \n4. an brown oval table with three section base \n5. brown color rectangle shape wood material and physical appearance table |
| 1. a red chair with a back . \n2. a red chair . the seat be curved downward and the back have a gap . \n3. red side chair \n4. maroon color chair with four leg and rest at back \n5. it be a wooden chair . it be red in color . | 1. a wooden chair red in color \n2. it is a wooden chair . it is red in color . \n3. a wooden chair with red colour back and seat with spindle and strong four legs \n4. a red wooden kitchen chair with detached back and slightly rounded seat \n5. this is wooden chair with four legs and it is in red texture light weight |
| 1. marble round table with metal leg . table be black color . \n2. black , round metal outdoor table . with long curl leg . \n3. a center - table with black circular top and four curved leg \n4. a stylish black color round table for all - purpose \n5. a circular black table . | 1. the table is circular with three legs . the table is black and the legs stick out from the top . \n2. a black color round shaped wooden table with three legs \n3. a black colored round table with four slim shaped legs \n4. black round metal outdoor table with long curled legs . \n5. black round table three legs wooden material |
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+ "content": "Figure 9. Segmentation results in three different granularity."
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+ {
+ "type": "image",
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+ "content": "Figure 10. Comparison in terms of Recall@1(RR@1), Recall@5(RR@5) and NDCG@5 using different segmentation granularity. S1, S2, and S3 represent the representing different segmentation granularities from coarse to fine, which have 17 classes, 72 classes, and 90 classes separately. The segmentation with the coarsest granularity S1 achieves a better performance."
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+ "angle": 0,
+ "content": "texts for each case. From Figure 4, we can see the top-5 retrieval shapes have a more similar appearance, especially in details such as color and geometry. The results demonstrate that our method could find correspondences in details, such as color and geometric description. In particular, for complex shapes, our model can still achieve superior results."
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+ {
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+ "angle": 0,
+ "content": "Figure 11. Comparison in terms of Recall@1(RR@1), Recall@5(RR@5) and NDCG@5 using different loss weight \\(\\beta\\). According to the above result, we choose loss weight \\(\\beta\\) as 40."
+ },
+ {
+ "type": "text",
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+ "angle": 0,
+ "content": "We also compare with with TriCoLo [37] by presenting 3 text-to-shape retrieval results and 3 shape-to-text retrieval results, as shown in Figures 7 and 8. For each query text/shape, we display top-5 retrieval shapes/texts ranked by the similarity scores from the two methods. The ground truth shapes/texts are marked in red. And as shown in Figure 7, our model matches the ground truth shapes within top-2 retrieval shapes. For the S2T retrieval result in Figure 8, our model can match 2 or 3 ground truth sentences within top-5 retrieval results, which is more than the ones that TriCoLo can match."
+ },
+ {
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+ "content": "4.2. Ablation Study"
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+ "content": "Granularity We explore the impact of part embedding extracted under different segmentation granularities on the matching model. The PartNet dataset contains hierarchical segmentation annotation in three granularities from S1 to S3, representing different segmentation granularities from coarse to fine, which have 17 classes, 72 classes, and 90 classes separately. The ground truths and our semantic predictions are shown in Figure 9. As shown in Figure 10, the results show that our method with coarse part segmentation"
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+ "content": "annotation achieves the best performance. We believe that the parts learned through finer segmentation ground truth are hard to align with the simple plain words. Therefore, the coarsest part segmentation annotation S1 is selected."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "content": "Loss Weight We adopt the balance weight \\(\\beta\\) to adjust the joint loss to make our network focus more on the retrieval performance than the segmentation result. We present our retrieval performance when selecting different \\(\\beta\\) to select the most suitable parameter settings, as shown in Figure 11. The retrieval performance improves with the increase of the weight of retrieval loss until \\(\\beta\\) is 40."
+ },
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+ "type": "text",
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+ "content": "Backbone We analyzed the influence of different network backbones on the retrieval results. We use PointNet and PointNet++ respectively as the backbone for the feature extraction network. As shown in Table 2, the comparison results show that the retrieval result gets worse after replacing the backbone with PointNet++."
+ },
+ {
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+ "angle": 0,
+ "content": "CD/EMD In Table 2, we replace the EMD for matching similarity calculation by CD (Chamfer Distance), which can be regarded as a local optimal hard matching method. In the Chamfer distance matching flow, each node only corresponds to the node with the most similar individual. The experimental results show that the EMD is better than CD."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Sampling We explore the impact of different negative sample learning strategies based on the triplet ranking loss on retrieval. We compared two strategies: hardest negative mining and semi-hard negative mining. As demonstrated in Table 3, we find that the model using the hardest negative mining results in a collapsed model."
+ },
+ {
+ "type": "text",
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+ "angle": 0,
+ "content": "Training We examine the effectiveness of end-to-end training by joint multi-task learning as shown in Table 3. In comparison, we separately train the shape encoder module and the matching module. Our results demonstrate that the end-to-end model outperforms the separate training approach."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Color and Segmentation As shown in Table 4, we separately evaluate the influence of integrating the point cloud color into the feature fusion step and supervising the training with the segmentation loss. The results demonstrate that, after removing these two components (w/o color and w/o seg loss), it is hard for the network to learn to establish a local alignment between color and geometry, which will lead to a significant decrease in accuracy. It indicates that color and part information are crucial for multi-modal retrieval."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.3. Visualization"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "We visualized two examples of the best matching pair between the shape and the text, as shown in Figure 12. The normalized similarity matrix is colored by calculating each pairwise distance \\( D = \\{1 - c_{ij}\\} \\) between parts and words. We can see that our model can accurately find the correspondence (dark red) between parts and words. For the first"
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 12. Visualization of the similarity between parts and words. We display a normalized similarity matrix between parts and words. The place with darker color indicates the higher relationship between corresponding parts and words."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "content": "example, the chair is firstly segmented into 4 parts, then the black seat matches the words \"black\" and \"seat\" in the text well, and the rest also attends the words \"yellow\", \"black\" and \"rest\". Besides, the similarity weight between the part of blue legs and the word \"blue\" obtained the highest score."
+ },
+ {
+ "type": "title",
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+ "angle": 0,
+ "content": "5. Conclusion"
+ },
+ {
+ "type": "text",
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+ "angle": 0,
+ "content": "We introduce a method to learn the joint embedding of 3D point clouds and text. Our method successively increases the ability of a joint understanding of 3D point clouds and text by learning to bidirectionally match 3D parts to words in an optimized space. We obtain the 3D parts by leveraging a 3D segmentation prior, which effectively resolves the self-occlusion issue of parts that is suffered by current multi-view based methods. We also demonstrate that matching 3D parts to words using the optimal transport is an efficient way to merge different modalities including 3D shapes and text in a common space, where the proposed cross-modal earth mover's distance is also justified to effectively capture the relationship of part-word in this matching procedure. Experimental results show that our method significantly outperforms other state-of-the-art methods."
+ },
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+ "type": "text",
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+ "angle": 0,
+ "content": "Acknowledgement. This work is supported by the Young Scientists Fund of the National Natural Science Foundation of China (Grant No.62206106)."
+ },
+ {
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+ [
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+ "angle": 0,
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+# Parts2Words: Learning Joint Embedding of Point Clouds and Texts by Bidirectional Matching between Parts and Words
+
+Chuan Tang
+
+Xi Yang $^{1,4*}$
+
+Bojian $\mathbf{W}\mathbf{u}^{2}$
+
+Zhizhong Han
+
+Yi Chang $^{1,4*}$
+
+$^{1}$ School of Artificial Intelligence, Jilin University, China $^{2}$ Zhejiang University
+
+| Query Shape | Parts2Words | TriCoLo |
| 1. a wooden oval brown small table . it have a rectangular hole at the middle below the table - top , seem like it have two leg .
+2. a capsule shape wooden table with two half cylinder shape leg .
+3. brown color , oval shape , wood material , and physical appearance table
+4. this be a light brown wooden table , with a flat capsule shape surface at the top , and two thick leg that be vertically tall , and be semicircle shape with the flat side face the middle create an empty space .
+5. brown colored whole wood oval shape coffee table . | 1. this oval light wood topped table is on a dark wood base .
+2. a wooden oval brown small table . it has a rectangular hole at the middle below the table top seems like it has two legs .
+3. an oval shaped table with two legs . it is also wooden and brown .
+4. an brown oval table with three section base
+5. brown color rectangle shape wood material and physical appearance table |
| 1. a red chair with a back .
+2. a red chair . the seat be curved downward and the back have a gap .
+3. red side chair
+4. maroon color chair with four leg and rest at back
+5. it be a wooden chair . it be red in color . | 1. a wooden chair red in color
+2. it is a wooden chair . it is red in color .
+3. a wooden chair with red colour back and seat with spindle and strong four legs
+4. a red wooden kitchen chair with detached back and slightly rounded seat
+5. this is wooden chair with four legs and it is in red texture light weight |
| 1. marble round table with metal leg . table be black color .
+2. black , round metal outdoor table . with long curl leg .
+3. a center - table with black circular top and four curved leg
+4. a stylish black color round table for all - purpose
+5. a circular black table . | 1. the table is circular with three legs . the table is black and the legs stick out from the top .
+2. a black color round shaped wooden table with three legs
+3. a black colored round table with four slim shaped legs
+4. black round metal outdoor table with long curled legs .
+5. black round table three legs wooden material |
+
+Figure 8. Retrieval result of the proposed Parts2Words and TriCoLo [37], the ground truth description are marked in red. Each retrieval case under our model can match 2 or 3 ground truth sentences, which is more than TriCoLo.
+
+
+Figure 9. Segmentation results in three different granularity.
+
+
+Figure 10. Comparison in terms of Recall@1(RR@1), Recall@5(RR@5) and NDCG@5 using different segmentation granularity. S1, S2, and S3 represent the representing different segmentation granularities from coarse to fine, which have 17 classes, 72 classes, and 90 classes separately. The segmentation with the coarsest granularity S1 achieves a better performance.
+
+texts for each case. From Figure 4, we can see the top-5 retrieval shapes have a more similar appearance, especially in details such as color and geometry. The results demonstrate that our method could find correspondences in details, such as color and geometric description. In particular, for complex shapes, our model can still achieve superior results.
+
+
+Figure 11. Comparison in terms of Recall@1(RR@1), Recall@5(RR@5) and NDCG@5 using different loss weight $\beta$ . According to the above result, we choose loss weight $\beta$ as 40.
+
+We also compare with with TriCoLo [37] by presenting 3 text-to-shape retrieval results and 3 shape-to-text retrieval results, as shown in Figures 7 and 8. For each query text/shape, we display top-5 retrieval shapes/texts ranked by the similarity scores from the two methods. The ground truth shapes/texts are marked in red. And as shown in Figure 7, our model matches the ground truth shapes within top-2 retrieval shapes. For the S2T retrieval result in Figure 8, our model can match 2 or 3 ground truth sentences within top-5 retrieval results, which is more than the ones that TriCoLo can match.
+
+# 4.2. Ablation Study
+
+Granularity We explore the impact of part embedding extracted under different segmentation granularities on the matching model. The PartNet dataset contains hierarchical segmentation annotation in three granularities from S1 to S3, representing different segmentation granularities from coarse to fine, which have 17 classes, 72 classes, and 90 classes separately. The ground truths and our semantic predictions are shown in Figure 9. As shown in Figure 10, the results show that our method with coarse part segmentation
+
+annotation achieves the best performance. We believe that the parts learned through finer segmentation ground truth are hard to align with the simple plain words. Therefore, the coarsest part segmentation annotation S1 is selected.
+
+Loss Weight We adopt the balance weight $\beta$ to adjust the joint loss to make our network focus more on the retrieval performance than the segmentation result. We present our retrieval performance when selecting different $\beta$ to select the most suitable parameter settings, as shown in Figure 11. The retrieval performance improves with the increase of the weight of retrieval loss until $\beta$ is 40.
+
+Backbone We analyzed the influence of different network backbones on the retrieval results. We use PointNet and PointNet++ respectively as the backbone for the feature extraction network. As shown in Table 2, the comparison results show that the retrieval result gets worse after replacing the backbone with PointNet++.
+
+CD/EMD In Table 2, we replace the EMD for matching similarity calculation by CD (Chamfer Distance), which can be regarded as a local optimal hard matching method. In the Chamfer distance matching flow, each node only corresponds to the node with the most similar individual. The experimental results show that the EMD is better than CD.
+
+Sampling We explore the impact of different negative sample learning strategies based on the triplet ranking loss on retrieval. We compared two strategies: hardest negative mining and semi-hard negative mining. As demonstrated in Table 3, we find that the model using the hardest negative mining results in a collapsed model.
+
+Training We examine the effectiveness of end-to-end training by joint multi-task learning as shown in Table 3. In comparison, we separately train the shape encoder module and the matching module. Our results demonstrate that the end-to-end model outperforms the separate training approach.
+
+Color and Segmentation As shown in Table 4, we separately evaluate the influence of integrating the point cloud color into the feature fusion step and supervising the training with the segmentation loss. The results demonstrate that, after removing these two components (w/o color and w/o seg loss), it is hard for the network to learn to establish a local alignment between color and geometry, which will lead to a significant decrease in accuracy. It indicates that color and part information are crucial for multi-modal retrieval.
+
+# 4.3. Visualization
+
+We visualized two examples of the best matching pair between the shape and the text, as shown in Figure 12. The normalized similarity matrix is colored by calculating each pairwise distance $D = \{1 - c_{ij}\}$ between parts and words. We can see that our model can accurately find the correspondence (dark red) between parts and words. For the first
+
+
+Figure 12. Visualization of the similarity between parts and words. We display a normalized similarity matrix between parts and words. The place with darker color indicates the higher relationship between corresponding parts and words.
+
+example, the chair is firstly segmented into 4 parts, then the black seat matches the words "black" and "seat" in the text well, and the rest also attends the words "yellow", "black" and "rest". Besides, the similarity weight between the part of blue legs and the word "blue" obtained the highest score.
+
+# 5. Conclusion
+
+We introduce a method to learn the joint embedding of 3D point clouds and text. Our method successively increases the ability of a joint understanding of 3D point clouds and text by learning to bidirectionally match 3D parts to words in an optimized space. We obtain the 3D parts by leveraging a 3D segmentation prior, which effectively resolves the self-occlusion issue of parts that is suffered by current multi-view based methods. We also demonstrate that matching 3D parts to words using the optimal transport is an efficient way to merge different modalities including 3D shapes and text in a common space, where the proposed cross-modal earth mover's distance is also justified to effectively capture the relationship of part-word in this matching procedure. Experimental results show that our method significantly outperforms other state-of-the-art methods.
+
+Acknowledgement. This work is supported by the Young Scientists Fund of the National Natural Science Foundation of China (Grant No.62206106).
+
+# References
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+
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| 1. a wooden oval brown small table . it have a rectangular hole at the middle below the table - top , seem like it have two leg . \n2. a capsule shape wooden table with two half cylinder shape leg . \n3. brown color , oval shape , wood material , and physical appearance table \n4. this be a light brown wooden table , with a flat capsule shape surface at the top , and two thick leg that be vertically tall , and be semicircle shape with the flat side face the middle create an empty space . \n5. brown colored whole wood oval shape coffee table . | 1. this oval light wood topped table is on a dark wood base . \n2. a wooden oval brown small table . it has a rectangular hole at the middle below the table top seems like it has two legs . \n3. an oval shaped table with two legs . it is also wooden and brown . \n4. an brown oval table with three section base \n5. brown color rectangle shape wood material and physical appearance table |
| 1. a red chair with a back . \n2. a red chair . the seat be curved downward and the back have a gap . \n3. red side chair \n4. maroon color chair with four leg and rest at back \n5. it be a wooden chair . it be red in color . | 1. a wooden chair red in color \n2. it is a wooden chair . it is red in color . \n3. a wooden chair with red colour back and seat with spindle and strong four legs \n4. a red wooden kitchen chair with detached back and slightly rounded seat \n5. this is wooden chair with four legs and it is in red texture light weight |
| 1. marble round table with metal leg . table be black color . \n2. black , round metal outdoor table . with long curl leg . \n3. a center - table with black circular top and four curved leg \n4. a stylish black color round table for all - purpose \n5. a circular black table . | 1. the table is circular with three legs . the table is black and the legs stick out from the top . \n2. a black color round shaped wooden table with three legs \n3. a black colored round table with four slim shaped legs \n4. black round metal outdoor table with long curled legs . \n5. black round table three legs wooden material |
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+ "content": "Color and Segmentation As shown in Table 4, we separately evaluate the influence of integrating the point cloud color into the feature fusion step and supervising the training with the segmentation loss. The results demonstrate that, after removing these two components (w/o color and w/o seg loss), it is hard for the network to learn to establish a local alignment between color and geometry, which will lead to a significant decrease in accuracy. It indicates that color and part information are crucial for multi-modal retrieval."
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+ "content": " between parts and words. We can see that our model can accurately find the correspondence (dark red) between parts and words. For the first"
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+ "content": "Figure 12. Visualization of the similarity between parts and words. We display a normalized similarity matrix between parts and words. The place with darker color indicates the higher relationship between corresponding parts and words."
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+ "content": "example, the chair is firstly segmented into 4 parts, then the black seat matches the words \"black\" and \"seat\" in the text well, and the rest also attends the words \"yellow\", \"black\" and \"rest\". Besides, the similarity weight between the part of blue legs and the word \"blue\" obtained the highest score."
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+ "content": "We introduce a method to learn the joint embedding of 3D point clouds and text. Our method successively increases the ability of a joint understanding of 3D point clouds and text by learning to bidirectionally match 3D parts to words in an optimized space. We obtain the 3D parts by leveraging a 3D segmentation prior, which effectively resolves the self-occlusion issue of parts that is suffered by current multi-view based methods. We also demonstrate that matching 3D parts to words using the optimal transport is an efficient way to merge different modalities including 3D shapes and text in a common space, where the proposed cross-modal earth mover's distance is also justified to effectively capture the relationship of part-word in this matching procedure. Experimental results show that our method significantly outperforms other state-of-the-art methods."
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+ "content": "Acknowledgement. This work is supported by the Young Scientists Fund of the National Natural Science Foundation of China (Grant No.62206106)."
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diff --git a/2023/Passive Micron-Scale Time-of-Flight With Sunlight Interferometry/a55c2f92-6092-4982-9cc5-a6760ffdb739_content_list.json b/2023/Passive Micron-Scale Time-of-Flight With Sunlight Interferometry/a55c2f92-6092-4982-9cc5-a6760ffdb739_content_list.json
new file mode 100644
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+ "text": "Passive Micron-scale Time-of-Flight with Sunlight Interferometry",
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+ "text": "Alankar Kotwal| Set | objec-tive | λper[λV12,λV22,λV34,λV44,λV54] | Normalized LperlLV12LV22LV34LV44LV54 | MetricPSNR|LPIPS |
| [0.0, 0.0, 0.0, 0.0, 0.0, 0.0] | [0.00, 0.00, 1.00, 1.00, 1.00] | [0.1960] |
| A | λ0 | [1.0, 0.0, 0.0, 0.0, 0.0] | 0.71 | 0.53 | 0.76 | 0.38 | 0.25 | 23.95 |
| λ1 | [1.0, 0.0, 0.0, 0.0, 0.0] | 0.72 | 0.26 | 0.35 | 0.22 | 0.15 | 23.84 |
| λ2 | [0.0, 0.0, 1.0, 0.0, 0.0] | 0.81 | 0.51 | 0.00 | 0.02 | 0.04 | 23.66 |
| λ3 | [0.0, 0.0, 0.0, 1.0, 0.0] | 0.92 | 0.78 | 0.51 | 0.11 | 0.05 | 23.28 |
| λ4 | [0.0, 0.0, 0.0, 0.0, 1.0] | 1.00 | 1.00 | 0.93 | 0.32 | 0.12 | 23.00 |
| B | λ1 | [1.0, 0.0, 0.0, 0.0, 0.0] | 0.71 | 0.53 | 0.76 | 0.38 | 0.25 | 23.95 |
| λ1-2 | [1/2, 1/2, 0.0, 0.0, 0.0] | 0.64 | 0.23 | 0.34 | 0.20 | 0.13 | 24.08 |
| λ1-3 | [1/3, 1/3, 1/3, 0.0, 0.0] | 0.78 | 0.42 | 0.10 | 0.04 | 0.03 | 23.81 |
| λ1-4 | [1/4, 1/4, 1/4, 1/4, 0.0] | 0.78 | 0.46 | 0.18 | 0.02 | 0.01 | 23.68 |
| ESRGAN-OOSA | [24.03, 0.0848] |
| ESRGAN-OOSB | [24.21, 0.0848] |
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+ "img_path": "images/edfa9d443877046e1c31196eb5b82730c77ed2eb16ec61da3bd6a86af61d7442.jpg",
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+ "Figure 3. Set $A$ (left) and set $B$ (right) in the objective space. The objectives in set $B$ are closer each other than those in set $A$ ."
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+ "text": "To find an effective set of objectives, we define an SR objective space. Since the objective for SR is a weighted sum of seven loss terms, as in Eqn. 3, an objective space is spanned by these basis loss terms, and any objective can be expressed by a seven-dimensional vector of weighting parameters, $\\lambda_{i} \\in \\mathbb{R}^{7}$ as $\\lambda_{i} = [\\lambda_{rec}, \\lambda_{adv}, \\lambda_{per}]$ , where $\\lambda_{per} \\in \\mathbb{R}^{5}$ is a weight vector for perceptual loss.",
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+ "text": "Table 1 compares two objective sets, $A$ and $B$ , defined as shown in Fig. 3. Because ESRGAN [46] is the base model for this comparison, for all objectives in the table, except for $\\lambda_0$ , $\\lambda_{rec}$ and $\\lambda_{adv}$ are set to $1 \\times 10^{-2}$ and $5 \\times 10^{-3}$ , respectively. These are the same as those for ESRGAN, except that $\\lambda_{per}$ changes, where $\\| \\lambda_{per} \\|_1 = 1$ . In particular, in terms of $\\lambda_{per}$ , whereas each objective $\\lambda_i$ in set $A$ has weights for only one of the five VGG feature spaces, each objective in set $B$ has equal weights for each loss in the feature space lower than the target vision level. Therefore, an objective corresponding to a high vision level also includes the losses for the lower-level feature spaces. Meanwhile, because $\\lambda_0$ corresponds to a distortion-oriented RRDB model [46], its $\\lambda_{rec}$ and $\\lambda_{adv}$ are set to $1 \\times 10^{-2}$ and 0, respectively. Note that $\\lambda_0$ is included in both sets $A$ and $B$ .",
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+ "$\\mathrm{OOS}_B$",
+ "Figure 4. The $\\mathrm{OOS}_A$ and $\\mathrm{OOS}_B$ results using Sets $A$ and $B$ (top), their SR results, ESRGAN- $\\mathrm{OOS}_A$ and ESRGAN- $\\mathrm{OOS}_B$ (bottom)."
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+ "intensity of each $\\lambda_{i}$"
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+ "text": "In Table 1, the normalized versions (min-max feature scaling) of the averaged $L_{per_l}$ from Eqn. 4 for five datasets (BSD100 [32], General100 [9], Urban100 [17], Manga109 [33], and DIV2K [1]) are reported. For all feature spaces, including the targeted V12 and V22 feature spaces, $\\lambda_{1-2}$ in set $B$ has smaller L1 errors than those of $\\lambda_1$ and $\\lambda_2$ in set $A$ . Moreover, $\\lambda_{1-4}$ exhibits smaller errors than those of $\\lambda_4$ and $\\lambda_5$ . Although $\\lambda_{1-3}$ has slightly more errors in the V34 feature space than that of $\\lambda_3$ , it has less errors in the V12 and V22 feature spaces therefore, $\\lambda_{1-3}$ has relatively less distortion than $\\lambda_3$ overfitted to the V34 feature space. That is supported by the fact that most of the objectives in set $B$ , including $\\lambda_{1-3}$ , have better PSNR and LPIPS on Urban100 [17] than those in set $A$ . $\\lambda_{1-5}$ showing relatively poor performance compared to $\\lambda_{1-4}$ is not used.",
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+ "type": "text",
+ "text": "To examine the SR result with locally appropriate objectives applied using set $A$ , we mix the six SR results of ESRGAN- $\\lambda_{a}$ , where $\\lambda_{a} \\in A$ , by selecting the SR result with the lowest LPIPS for each pixel position, as follows:",
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+ "type": "equation",
+ "text": "\n$$\ny _ {A} ^ {*} (i, j) = \\hat {y} _ {\\mathbf {T} _ {A} ^ {*} (i, j)} (i, j), \\tag {6}\n$$\n",
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+ "type": "equation",
+ "text": "\n$$\n\\mathbf {T} _ {A} ^ {*} (i, j) = \\arg \\min _ {\\boldsymbol {\\lambda} _ {a} \\in A} \\mathbf {L P I P S} _ {\\boldsymbol {\\lambda} _ {a}} (i, j), \\tag {7}\n$$\n",
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+ "type": "equation",
+ "text": "\n$$\n\\mathbf {L P I P S} _ {\\lambda_ {a}} = L P I P S \\left(y, \\hat {y} _ {\\lambda_ {a}}\\right), \\tag {8}\n$$\n",
+ "text_format": "latex",
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+ "type": "text",
+ "text": "where $\\hat{y}_{\\lambda_a}$ is the SR result of ESRGAN- $\\lambda_a$ . The LPIPS function computes the perceptual distance between two image patches for each pixel position, producing an LPIPS map, LPIPS, of the input image size [28, 35]. The LPIPS metric in Table 1 is the average of this map. Since $\\mathbf{T}_A^*$ is the optimal objective selection (OOS), $\\mathbf{T}_A^*$ and its SR model for mixing are denoted as OOS $_A$ and ESRGAN-OOS $_A$ , respectively. The upper part of Fig. 4 shows an example of OOS $_A$ and OOS $_B$ based on set $A$ and $B$ . PSNR and LPIPS [52] of ESRGAN-OOS $_A$ and ESRGAN-OOS $_B$ are reported in Table 1, where ESRGAN-OOS $_B$ is superior to any single objective model, demonstrating the potential for performance improvement of the locally suitable objective application. The lower part of Fig. 4 shows the side effects caused by mixing the SR results for set $A$ with lower proximities between objectives than those in set $B$ , as shown in Fig. 3. Since ESRGAN-OOS $_B$ in Fig. 4 has less artifact and better PSNR than those of ESRGAN-OOS $_A$ , the proposed set $B$ is more suitable for applying locally appropriate objectives.",
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+ "(a)",
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+ "image_caption": [
+ "(d)",
+ "Figure 5. The proposed vector functions for loss weights, (a) $\\lambda(t)$ in Eqn. 9 when $\\alpha = 1$ and $\\beta = 0$ , (b) its $\\lambda_{per}(t)$ and (c) the weighting functions for $\\lambda_{per}(t)$ . (d) $\\lambda_{per}(t)$ used for FxSR [35]."
+ ],
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+ "type": "text",
+ "text": "Learning Objective Trajectory. We train our generative model on a set of objectives over the trajectory rather than a single objective, $\\lambda_{i}$ . The objective trajectory is formed by connecting the selected objectives, i.e. the five objectives of set $B$ , starting with an objective for a low-vision level and progressing through objectives for higher levels, i.e. from $\\lambda_0$ to $\\lambda_{1-4}$ . It is parameterized by a single variable $t$ , $\\lambda(t) = \\langle \\lambda_{rec}(t), \\lambda_{adv}(t), \\lambda_{per}(t) \\rangle$ , as follow:",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\boldsymbol {\\lambda} (t) = \\boldsymbol {\\alpha} \\cdot \\boldsymbol {f} _ {\\lambda} (t) + \\boldsymbol {\\beta}, \\tag {9}\n$$\n",
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+ "type": "equation",
+ "text": "\n$$\n\\boldsymbol {f} _ {\\lambda} (t) = \\left\\langle f _ {\\lambda_ {r e c}} (t), f _ {\\lambda_ {a d v}} (t), \\boldsymbol {f} _ {\\lambda_ {p e r}} (t) \\right\\rangle , \\tag {10}\n$$\n",
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+ "type": "text",
+ "text": "where $f_{\\lambda_{per}}(t) \\in \\mathbb{R}^5$ , $f_{\\lambda_{rec}}(t)$ , $f_{\\lambda_{adv}}(t)$ are weighting functions, $\\alpha$ and $\\beta$ are the scaling and offset vectors. As $f_{\\lambda}:\\mathbb{R}\\to \\mathbb{R}^7$ , this vector function enables the replacement of high-dimensional weight-vector manipulation with one-dimensional tracking, simplifying the training process.",
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+ "type": "text",
+ "text": "Specifically, the trajectory design is based on the observation in Table 1 that the distortion-oriented RRDB model using $\\lambda_0$ has smaller L1 errors than those of all ESRGAN models for low-level feature spaces, such as V12 and V22, whereas ESRGAN models have smaller L1 errors for higher-level feature spaces, such as V34, V44, and V54. Thus, we design the weight functions $f_{\\lambda_{rec}}$ , $f_{\\lambda_{adv}}$ and $f_{\\lambda_{per}}$ such that when $t$ approaches 0, $f_{\\lambda_{rec}}$ increases and $\\{f_{\\lambda_{adv}}, \\sum_{per_l} f_{\\lambda_{per_l}}\\}$ decrease to go to $\\lambda_0$ , and conversely to go to $\\lambda_{1-4}$ when $t$ increases to 1, as shown in Fig. 5(a).",
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+ "type": "text",
+ "text": "In relation to the change in $\\sum_{per_l}f_{\\lambda_{per_l}}(t)$ , we design each of five component functions, $f_{\\lambda_{per_l}}(t)$ of $f_{\\lambda_{per}}(t)$ , as shown in Fig. 5(c), to obtain the objective trajectory from $\\lambda_0$ to $\\lambda_{1 - 4}$ of set $B$ as shown in Fig. 5(b), illustrating only three out of five components because of the limitations of 3-dimensional visualization. Thus, as we progress through the trajectory by increasing $t$ from 0 to 1, the weighting parameters for the objective start with the distortion-oriented objective, $\\lambda_0$ , and then the losses of higher-vision-level feature",
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+ "type": "image",
+ "img_path": "images/081a6bec3d8eb6021e1cb4e23257fd97f4ad44cb249077c6b4af384fb4030db3.jpg",
+ "image_caption": [],
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+ {
+ "type": "image",
+ "img_path": "images/5171e6a92fc046313227a5b2ab8793cde13b1ec4f82b1a909c607fa06016e448.jpg",
+ "image_caption": [
+ "Figure 6. Changes in detail in the SROT results according to $t$ -value (top) and changes in PSNR and LPIPS for test DBs (bottom)."
+ ],
+ "image_footnote": [],
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+ {
+ "type": "image",
+ "img_path": "images/8d1afdde1551c029019b05d864c3fa1eae5d5eb0d0fa90f50a7c166e4df8a191.jpg",
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+ "type": "text",
+ "text": "spaces and adversarial loss are progressively added, making slight transitions on the objective toward $\\lambda_{1-4}$ . Fig. 5(d) shows the objective trajectory used for FxSR [35], which uses only the V22 feature space, limiting the performance of the perceptually accurate restoration.",
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+ "type": "text",
+ "text": "The proposed objective trajectory can efficiently improve the accuracy and consistency of the SR results. First, we can use any objective on the continuous trajectory from low to high-level vision, which allows the application of more accurate objectives to each region. Second, with regard to consistency, high-level objectives on our proposed trajectory include both low-level and high-level losses, thus also accounting for the low-level objectives. This weighting method allows the sharing of the structural components reconstructed mainly by low-vision-level objectives between all SR results on the trajectory. Finally, we need to train a single SR model only once, reducing the number of models required to produce diverse HR outputs [10, 35].",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "Fig. 6 shows the changes in the result of the generative SR model trained on the objective trajectory in Fig. 5(b), called SROT, as $t$ changes from 0 to 1. The graphs in the bottom of Fig. 6 show the trade-off curves in the perception-distortion plane according to the change of $t$ where $t$ increases by 0.05 from 0.0 to 1.0 and has 21 sample points. Each SR result on the curve is obtained by inputting $\\mathbf{T}$ with the same $t$ throughout the image, as $\\mathbf{T}_t = \\mathbf{1} \\times t$ , into the condition branch of the generative model, as follows:",
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+ "type": "equation",
+ "text": "\n$$\n\\hat {y} _ {\\mathbf {T} _ {t}} = G _ {\\theta} \\left(x \\mid \\mathbf {T} _ {t}\\right). \\tag {11}\n$$\n",
+ "text_format": "latex",
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+ "type": "text",
+ "text": "The horizontal and vertical dotted lines of the graphs in Fig. 6 indicate the lowest LPIPS values of the model and the corresponding PSNR values, respectively. The $t$ values at that time are written next to the vertical lines. However, applying a specific $t$ to the entire image still limits SR performance, and optimal $t$ depending on images is unknown at inference time. We take this one step further and present later how to estimate and apply locally optimal objectives.",
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+ "text": "1729",
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+ "img_path": "images/dd229896298d17e0f2b6ce8d87626d9a7d1ae5dd96c2a7cfd9c4fdafb660b808.jpg",
+ "image_caption": [
+ "image (0824)"
+ ],
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+ "img_path": "images/501382bb58623aaa09adfe6c20e2fd5266c51e46371342e3f7fe93142d7935b8.jpg",
+ "image_caption": [
+ "OOS $\\mathbf{T}_S^*$",
+ "Figure 7. The input image, the optimal objective selection $\\mathbf{T}_S^*$ obtained by parameter sweeping, and $\\hat{\\mathbf{T}}_B$ estimated by $C_{\\psi}$ ."
+ ],
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+ {
+ "type": "image",
+ "img_path": "images/ffcea8a66a4ea42866bdd0ca0278fbad36319d7129d70a790a17e65b671e0e43.jpg",
+ "image_caption": [
+ "OOE $\\hat{\\mathbf{T}}_B$"
+ ],
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+ {
+ "type": "text",
+ "text": "Network Architecture and Training. The outline of the generator network is adopted from [35], i.e., $G_{\\theta}$ consists of two streams, an SR branch with 23 basic blocks and a condition branch as shown in Fig. 2. The condition branch takes an LR-sized target objective map $\\mathbf{T}$ and produces shared intermediate conditions that can be transferred to all the SFT layers in the SR branch. Since the SFT layers [44] modulate feature maps by applying affine transformation, they learn a mapping function that outputs a modulation parameter based on $\\mathbf{T}$ . Specifically, $\\mathbf{T}_t$ , with $t$ randomly changing in the pre-defined range, is fed into the condition branch during training, and this modulation layer allows the SR branch to optimize the changing objective by $t$ . As a result, $G_{\\theta}$ learns all the objectives on the trajectory and generates SR results with spatially different objectives according to the map at inference time. $G_{\\theta}$ is optimized on the training samples $\\mathcal{Z} = (x,y)$ with the distribution $P_{\\mathcal{Z}}$ , as follows:",
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+ "type": "equation",
+ "text": "\n$$\n\\theta^ {*} = \\arg \\min _ {\\theta} \\mathbb {E} _ {\\mathcal {Z} \\sim \\mathcal {P} _ {\\mathcal {Z}}} \\left[ \\mathcal {L} \\left(\\hat {y} _ {\\mathbf {T} _ {t}}, y | t\\right) \\right], \\tag {12}\n$$\n",
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+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} (t) = \\lambda_ {\\text {r e c}} (t) \\cdot \\mathcal {L} _ {\\text {r e c}} + \\lambda_ {\\text {a d v}} (t) \\cdot \\mathcal {L} _ {\\text {a d v}} + \\sum_ {\\text {p e r l}} \\lambda_ {\\text {p e r l}} (t) \\cdot L _ {\\text {p e r l}}. \\tag {13}\n$$\n",
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+ "type": "text",
+ "text": "3.3. Optimal Objective Estimation (OOE)",
+ "text_level": 1,
+ "bbox": [
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+ "type": "text",
+ "text": "To estimate an optimal combination of objectives for each region, we train a predictive model, $C_{\\psi}$ . This model produces an optimal objective map $\\hat{\\mathbf{T}}_B$ estimated for a given LR image, which is then delivered to the generative model in Eqn. 1. Since it is hard to find the ground truth map for $C_{\\psi}$ training, we obtain its approximation $\\mathbf{T}_S^*$ via a simple exhaustive searching to narrow down the range of the best possible values. Specifically, we generate a set of 21 SR results by changing $t$ from 0 to 1 with a step of 0.05, and the optimal objective maps are generated by selecting the $t$ with the lowest LPIPS among them for each pixel, as",
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+ "type": "equation",
+ "text": "\n$$\n\\mathbf {T} _ {S} ^ {*} (i, j) = \\arg \\min _ {t \\in S} \\mathbf {L P I P S} _ {t} (i, j), \\tag {14}\n$$\n",
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+ "type": "equation",
+ "text": "\n$$\n\\mathbf {L P I P S} _ {t} = L P I P S \\left(y, \\hat {y} _ {\\mathbf {T} _ {t}}\\right), \\tag {15}\n$$\n",
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+ "type": "text",
+ "text": "where $\\mathbf{T}_t = \\mathbf{1} \\times t, t \\in S = \\{0.0, 0.05, 0.10, \\dots, 1.0\\}$ . Fig. 7 shows an example of the optimal objective selection (OOS) $\\mathbf{T}_S^*$ . The SR result using $\\mathbf{T}_S^*$ , SROOS, can be an upper-bound approximation for the performance of $G_{\\theta}$ as",
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+ "type": "equation",
+ "text": "\n$$\n\\hat {y} _ {\\mathbf {T} _ {S} ^ {*}} = G _ {\\theta} \\left(x | \\mathbf {T} _ {S} ^ {*}\\right). \\tag {16}\n$$\n",
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+ "type": "text",
+ "text": "Although $\\mathbf{T}_S^*$ is useful for training $C_{\\psi}$ , this pixel-wise objective selection without considering the interference caused by the convolutions of $G_{\\theta}$ is not accurate ground truth. Therefore, $C_{\\psi}$ is optimized with three loss terms: pixel-wise objective map loss, pixel-wise reconstruction loss and perceptual loss, which measures the difference between the reconstructed and HR images, as follows:",
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+ "type": "equation",
+ "text": "\n$$\n\\psi^ {*} = \\arg \\min _ {\\psi} \\mathbb {E} _ {\\mathcal {Z} _ {\\mathbf {T}} \\sim \\mathcal {P} _ {\\mathcal {Z} _ {\\mathbf {T}}}} \\mathcal {L}, \\tag {17}\n$$\n",
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+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} = \\lambda_ {\\mathbf {T}} \\cdot \\mathcal {L} _ {\\mathbf {T}} + \\lambda_ {r e c} ^ {O O E} \\cdot \\mathcal {L} _ {r e c} + \\lambda_ {R} \\cdot \\mathcal {L} _ {R}, \\tag {18}\n$$\n",
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+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} _ {R} = \\mathbb {E} \\left[ L P I P S \\left(y, \\hat {y} _ {\\hat {\\mathbf {T}} _ {B}}\\right) \\right], \\tag {19}\n$$\n",
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+ {
+ "type": "text",
+ "text": "where $\\mathcal{L}_{\\mathbf{T}}$ and $\\mathcal{L}_{rec}$ is the L1 losses between $\\mathbf{T}_S^*$ and $\\hat{\\mathbf{T}}_B$ and between $y$ and $\\hat{y}_{\\hat{\\mathbf{T}}_B}$ , respectively. Meanwhile, $\\mathcal{Z}_{\\mathbf{T}} = (x,y,\\mathbf{T}_S^*)$ is the training dataset, and $\\lambda_{\\mathbf{T}},\\lambda_{rec}^{OOE}$ and $\\lambda_R$ are the weights for each of the loss terms, respectively. During the $C_\\psi$ model training, $C_\\psi$ is combined with the already trained generative model, and the generator parameters are fixed. Therefore, losses for $C_\\psi$ training, including LPIPS, are involved only in estimating locally-appropriate objective maps without changing the generator's parameters.",
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+ "type": "text",
+ "text": "The architecture of $C_{\\psi}$ consists of two separate subnetwork: one is a feature extractor (F.E.) utilizing the VGG-19 [39] and the other is a predictor with the UNet architecture [37], as shown in Fig 2. For better performance, the feature extractor aims to get low to high-level features and delivers them to Unet, which makes the prediction. Since the structure of UNet has a wider receptive field, it is advantageous for predicting objectives in context.",
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+ "type": "text",
+ "text": "4. Experiments",
+ "text_level": 1,
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+ "type": "text",
+ "text": "4.1. Experiment Setup",
+ "text_level": 1,
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+ "text": "Materials, Evaluation Metrics and Training Details. We use either the DIV2K [1] (800 images) or the DF2K [26] (3450 images) dataset to train our models. Our test datasets include BSD100 [32], General100 [9], Urban100 [17], Manga109 [33], and DIV2K validation set [1]. To evaluate the perceptual quality, we report LPIPS [52] and DISTS [6], which are full-reference metrics. DISTS is a perceptual metric that focuses on detail similarity. PSNR and SSIM [47] are also reported as fidelity-oriented metrics. The LR-PSNR metric is the PSNR between the LR input and downscaled SR images. The higher the LR-PSNR, the better the consistency between the SR results and LR images, where 45 dB or more is recommended for good LR consistency as addressed in NTIRE challenge [28]. Because consistency with the LR input images is important, we also report the LR-PSNR. All training parameters are set to be equal to those of ESRGAN [46], except for the",
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+ "text": "1730",
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+ "type": "table",
+ "img_path": "images/83aa96810296f9902036af195d43ecd053ddf1290dea313e84b9a4dd1c2aef86.jpg",
+ "table_caption": [
+ "Table 2. Comparison with state-of-the-art SR methods on benchmarks. The 1st and the 2nd best performances for each group are highlighted in red and blue, respectively. LR-PSNR values greater than 45dB are underlined."
+ ],
+ "table_footnote": [],
+ "table_body": "| Set | objec-tive | λper[λV12,λV22,λV34,λV44,λV54] | Normalized LperlLV12LV22LV34LV44LV54 | MetricPSNR|LPIPS |
| [0.0, 0.0, 0.0, 0.0, 0.0, 0.0] | [0.00, 0.00, 1.00, 1.00, 1.00] | [0.1960] |
| A | λ0 | [1.0, 0.0, 0.0, 0.0, 0.0] | 0.71 | 0.53 | 0.76 | 0.38 | 0.25 | 23.95 |
| λ1 | [1.0, 0.0, 0.0, 0.0, 0.0] | 0.72 | 0.26 | 0.35 | 0.22 | 0.15 | 23.84 |
| λ2 | [0.0, 0.0, 1.0, 0.0, 0.0] | 0.81 | 0.51 | 0.00 | 0.02 | 0.04 | 23.66 |
| λ3 | [0.0, 0.0, 0.0, 1.0, 0.0] | 0.92 | 0.78 | 0.51 | 0.11 | 0.05 | 23.28 |
| λ4 | [0.0, 0.0, 0.0, 0.0, 1.0] | 1.00 | 1.00 | 0.93 | 0.32 | 0.12 | 23.00 |
| B | λ1 | [1.0, 0.0, 0.0, 0.0, 0.0] | 0.71 | 0.53 | 0.76 | 0.38 | 0.25 | 23.95 |
| λ1-2 | [1/2, 1/2, 0.0, 0.0, 0.0] | 0.64 | 0.23 | 0.34 | 0.20 | 0.13 | 24.08 |
| λ1-3 | [1/3, 1/3, 1/3, 0.0, 0.0] | 0.78 | 0.42 | 0.10 | 0.04 | 0.03 | 23.81 |
| λ1-4 | [1/4, 1/4, 1/4, 1/4, 0.0] | 0.78 | 0.46 | 0.18 | 0.02 | 0.01 | 23.68 |
| ESRGAN-OOSA | [24.03, 0.0848] |
| ESRGAN-OOSB | [24.21, 0.0848] |
"
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+ "angle": 0,
+ "content": "Figure 3. Set \\( A \\) (left) and set \\( B \\) (right) in the objective space. The objectives in set \\( B \\) are closer each other than those in set \\( A \\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "features of shallow layers such as V12 and V22 and deeper layers such as V34, V44, and V54 correspond to relatively low-level and higher-level vision, respectively [36]."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "content": "To find an effective set of objectives, we define an SR objective space. Since the objective for SR is a weighted sum of seven loss terms, as in Eqn. 3, an objective space is spanned by these basis loss terms, and any objective can be expressed by a seven-dimensional vector of weighting parameters, \\(\\lambda_{i} \\in \\mathbb{R}^{7}\\) as \\(\\lambda_{i} = [\\lambda_{rec}, \\lambda_{adv}, \\lambda_{per}]\\), where \\(\\lambda_{per} \\in \\mathbb{R}^{5}\\) is a weight vector for perceptual loss."
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 1 compares two objective sets, \\( A \\) and \\( B \\), defined as shown in Fig. 3. Because ESRGAN [46] is the base model for this comparison, for all objectives in the table, except for \\( \\lambda_0 \\), \\( \\lambda_{rec} \\) and \\( \\lambda_{adv} \\) are set to \\( 1 \\times 10^{-2} \\) and \\( 5 \\times 10^{-3} \\), respectively. These are the same as those for ESRGAN, except that \\( \\lambda_{per} \\) changes, where \\( \\| \\lambda_{per} \\|_1 = 1 \\). In particular, in terms of \\( \\lambda_{per} \\), whereas each objective \\( \\lambda_i \\) in set \\( A \\) has weights for only one of the five VGG feature spaces, each objective in set \\( B \\) has equal weights for each loss in the feature space lower than the target vision level. Therefore, an objective corresponding to a high vision level also includes the losses for the lower-level feature spaces. Meanwhile, because \\( \\lambda_0 \\) corresponds to a distortion-oriented RRDB model [46], its \\( \\lambda_{rec} \\) and \\( \\lambda_{adv} \\) are set to \\( 1 \\times 10^{-2} \\) and 0, respectively. Note that \\( \\lambda_0 \\) is included in both sets \\( A \\) and \\( B \\)."
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+ "content": "\\(\\mathrm{OOS}_A\\)"
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+ "content": "\\(\\mathrm{OOS}_B\\)"
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+ "angle": 0,
+ "content": "intensity of each \\(\\lambda_{i}\\)"
+ },
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+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 4. The \\(\\mathrm{OOS}_A\\) and \\(\\mathrm{OOS}_B\\) results using Sets \\(A\\) and \\(B\\) (top), their SR results, ESRGAN-\\(\\mathrm{OOS}_A\\) and ESRGAN-\\(\\mathrm{OOS}_B\\) (bottom)."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "In Table 1, the normalized versions (min-max feature scaling) of the averaged \\( L_{per_l} \\) from Eqn. 4 for five datasets (BSD100 [32], General100 [9], Urban100 [17], Manga109 [33], and DIV2K [1]) are reported. For all feature spaces, including the targeted V12 and V22 feature spaces, \\( \\lambda_{1-2} \\) in set \\( B \\) has smaller L1 errors than those of \\( \\lambda_1 \\) and \\( \\lambda_2 \\) in set \\( A \\). Moreover, \\( \\lambda_{1-4} \\) exhibits smaller errors than those of \\( \\lambda_4 \\) and \\( \\lambda_5 \\). Although \\( \\lambda_{1-3} \\) has slightly more errors in the V34 feature space than that of \\( \\lambda_3 \\), it has less errors in the V12 and V22 feature spaces therefore, \\( \\lambda_{1-3} \\) has relatively less distortion than \\( \\lambda_3 \\) overfitted to the V34 feature space. That is supported by the fact that most of the objectives in set \\( B \\), including \\( \\lambda_{1-3} \\), have better PSNR and LPIPS on Urban100 [17] than those in set \\( A \\). \\( \\lambda_{1-5} \\) showing relatively poor performance compared to \\( \\lambda_{1-4} \\) is not used."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "To examine the SR result with locally appropriate objectives applied using set \\( A \\), we mix the six SR results of ESRGAN-\\(\\lambda_{a}\\), where \\(\\lambda_{a} \\in A\\), by selecting the SR result with the lowest LPIPS for each pixel position, as follows:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
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+ "angle": 0,
+ "content": "\\[\ny _ {A} ^ {*} (i, j) = \\hat {y} _ {\\mathbf {T} _ {A} ^ {*} (i, j)} (i, j), \\tag {6}\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
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+ "angle": 0,
+ "content": "\\[\n\\mathbf {T} _ {A} ^ {*} (i, j) = \\arg \\min _ {\\boldsymbol {\\lambda} _ {a} \\in A} \\mathbf {L P I P S} _ {\\boldsymbol {\\lambda} _ {a}} (i, j), \\tag {7}\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
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+ "angle": 0,
+ "content": "\\[\n\\mathbf {L P I P S} _ {\\lambda_ {a}} = L P I P S \\left(y, \\hat {y} _ {\\lambda_ {a}}\\right), \\tag {8}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "where \\(\\hat{y}_{\\lambda_a}\\) is the SR result of ESRGAN-\\(\\lambda_a\\). The LPIPS function computes the perceptual distance between two image patches for each pixel position, producing an LPIPS map, LPIPS, of the input image size [28, 35]. The LPIPS metric in Table 1 is the average of this map. Since \\(\\mathbf{T}_A^*\\) is the optimal objective selection (OOS), \\(\\mathbf{T}_A^*\\) and its SR model for mixing are denoted as OOS\\(_A\\) and ESRGAN-OOS\\(_A\\), respectively. The upper part of Fig. 4 shows an example of OOS\\(_A\\) and OOS\\(_B\\) based on set \\(A\\) and \\(B\\). PSNR and LPIPS [52] of ESRGAN-OOS\\(_A\\) and ESRGAN-OOS\\(_B\\) are reported in Table 1, where ESRGAN-OOS\\(_B\\) is superior to any single objective model, demonstrating the potential for performance improvement of the locally suitable objective application. The lower part of Fig. 4 shows the side effects caused by mixing the SR results for set \\(A\\) with lower proximities between objectives than those in set \\(B\\), as shown in Fig. 3. Since ESRGAN-OOS\\(_B\\) in Fig. 4 has less artifact and better PSNR than those of ESRGAN-OOS\\(_A\\), the proposed set \\(B\\) is more suitable for applying locally appropriate objectives."
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+ "content": "(a)"
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+ "type": "image_caption",
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+ "angle": 0,
+ "content": "Figure 5. The proposed vector functions for loss weights, (a) \\(\\lambda(t)\\) in Eqn. 9 when \\(\\alpha = 1\\) and \\(\\beta = 0\\), (b) its \\(\\lambda_{per}(t)\\) and (c) the weighting functions for \\(\\lambda_{per}(t)\\). (d) \\(\\lambda_{per}(t)\\) used for FxSR [35]."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Learning Objective Trajectory. We train our generative model on a set of objectives over the trajectory rather than a single objective, \\(\\lambda_{i}\\). The objective trajectory is formed by connecting the selected objectives, i.e. the five objectives of set \\(B\\), starting with an objective for a low-vision level and progressing through objectives for higher levels, i.e. from \\(\\lambda_0\\) to \\(\\lambda_{1-4}\\). It is parameterized by a single variable \\(t\\), \\(\\lambda(t) = \\langle \\lambda_{rec}(t), \\lambda_{adv}(t), \\lambda_{per}(t) \\rangle\\), as follow:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
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+ "angle": 0,
+ "content": "\\[\n\\boldsymbol {\\lambda} (t) = \\boldsymbol {\\alpha} \\cdot \\boldsymbol {f} _ {\\lambda} (t) + \\boldsymbol {\\beta}, \\tag {9}\n\\]"
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+ "type": "equation",
+ "bbox": [
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+ "angle": 0,
+ "content": "\\[\n\\boldsymbol {f} _ {\\lambda} (t) = \\left\\langle f _ {\\lambda_ {r e c}} (t), f _ {\\lambda_ {a d v}} (t), \\boldsymbol {f} _ {\\lambda_ {p e r}} (t) \\right\\rangle , \\tag {10}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "where \\(f_{\\lambda_{per}}(t) \\in \\mathbb{R}^5\\), \\(f_{\\lambda_{rec}}(t)\\), \\(f_{\\lambda_{adv}}(t)\\) are weighting functions, \\(\\alpha\\) and \\(\\beta\\) are the scaling and offset vectors. As \\(f_{\\lambda}:\\mathbb{R}\\to \\mathbb{R}^7\\), this vector function enables the replacement of high-dimensional weight-vector manipulation with one-dimensional tracking, simplifying the training process."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.076,
+ 0.615,
+ 0.469,
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+ ],
+ "angle": 0,
+ "content": "Specifically, the trajectory design is based on the observation in Table 1 that the distortion-oriented RRDB model using \\(\\lambda_0\\) has smaller L1 errors than those of all ESRGAN models for low-level feature spaces, such as V12 and V22, whereas ESRGAN models have smaller L1 errors for higher-level feature spaces, such as V34, V44, and V54. Thus, we design the weight functions \\(f_{\\lambda_{rec}}\\), \\(f_{\\lambda_{adv}}\\) and \\(f_{\\lambda_{per}}\\) such that when \\(t\\) approaches 0, \\(f_{\\lambda_{rec}}\\) increases and \\(\\{f_{\\lambda_{adv}}, \\sum_{per_l} f_{\\lambda_{per_l}}\\}\\) decrease to go to \\(\\lambda_0\\), and conversely to go to \\(\\lambda_{1-4}\\) when \\(t\\) increases to 1, as shown in Fig. 5(a)."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "In relation to the change in \\(\\sum_{per_l}f_{\\lambda_{per_l}}(t)\\), we design each of five component functions, \\(f_{\\lambda_{per_l}}(t)\\) of \\(f_{\\lambda_{per}}(t)\\), as shown in Fig. 5(c), to obtain the objective trajectory from \\(\\lambda_0\\) to \\(\\lambda_{1 - 4}\\) of set \\(B\\) as shown in Fig. 5(b), illustrating only three out of five components because of the limitations of 3-dimensional visualization. Thus, as we progress through the trajectory by increasing \\(t\\) from 0 to 1, the weighting parameters for the objective start with the distortion-oriented objective, \\(\\lambda_0\\), and then the losses of higher-vision-level feature"
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+ {
+ "type": "image",
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+ {
+ "type": "image",
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+ "content": null
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+ {
+ "type": "image",
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+ "content": null
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+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 6. Changes in detail in the SROT results according to \\( t \\)-value (top) and changes in PSNR and LPIPS for test DBs (bottom)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.498,
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+ "angle": 0,
+ "content": "spaces and adversarial loss are progressively added, making slight transitions on the objective toward \\(\\lambda_{1-4}\\). Fig. 5(d) shows the objective trajectory used for FxSR [35], which uses only the V22 feature space, limiting the performance of the perceptually accurate restoration."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.498,
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+ ],
+ "angle": 0,
+ "content": "The proposed objective trajectory can efficiently improve the accuracy and consistency of the SR results. First, we can use any objective on the continuous trajectory from low to high-level vision, which allows the application of more accurate objectives to each region. Second, with regard to consistency, high-level objectives on our proposed trajectory include both low-level and high-level losses, thus also accounting for the low-level objectives. This weighting method allows the sharing of the structural components reconstructed mainly by low-vision-level objectives between all SR results on the trajectory. Finally, we need to train a single SR model only once, reducing the number of models required to produce diverse HR outputs [10, 35]."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.498,
+ 0.612,
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+ ],
+ "angle": 0,
+ "content": "Fig. 6 shows the changes in the result of the generative SR model trained on the objective trajectory in Fig. 5(b), called SROT, as \\( t \\) changes from 0 to 1. The graphs in the bottom of Fig. 6 show the trade-off curves in the perception-distortion plane according to the change of \\( t \\) where \\( t \\) increases by 0.05 from 0.0 to 1.0 and has 21 sample points. Each SR result on the curve is obtained by inputting \\( \\mathbf{T} \\) with the same \\( t \\) throughout the image, as \\( \\mathbf{T}_t = \\mathbf{1} \\times t \\), into the condition branch of the generative model, as follows:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
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+ "angle": 0,
+ "content": "\\[\n\\hat {y} _ {\\mathbf {T} _ {t}} = G _ {\\theta} \\left(x \\mid \\mathbf {T} _ {t}\\right). \\tag {11}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "The horizontal and vertical dotted lines of the graphs in Fig. 6 indicate the lowest LPIPS values of the model and the corresponding PSNR values, respectively. The \\( t \\) values at that time are written next to the vertical lines. However, applying a specific \\( t \\) to the entire image still limits SR performance, and optimal \\( t \\) depending on images is unknown at inference time. We take this one step further and present later how to estimate and apply locally optimal objectives."
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+ ],
+ "angle": 0,
+ "content": "image (0824)"
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.212,
+ 0.089,
+ 0.336,
+ 0.153
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.249,
+ 0.155,
+ 0.3,
+ 0.169
+ ],
+ "angle": 0,
+ "content": "OOS \\(\\mathbf{T}_S^*\\)"
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.342,
+ 0.089,
+ 0.464,
+ 0.153
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.375,
+ 0.155,
+ 0.429,
+ 0.169
+ ],
+ "angle": 0,
+ "content": "OOE \\(\\hat{\\mathbf{T}}_B\\)"
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.077,
+ 0.171,
+ 0.468,
+ 0.199
+ ],
+ "angle": 0,
+ "content": "Figure 7. The input image, the optimal objective selection \\(\\mathbf{T}_S^*\\) obtained by parameter sweeping, and \\(\\hat{\\mathbf{T}}_B\\) estimated by \\(C_{\\psi}\\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.076,
+ 0.206,
+ 0.47,
+ 0.463
+ ],
+ "angle": 0,
+ "content": "Network Architecture and Training. The outline of the generator network is adopted from [35], i.e., \\( G_{\\theta} \\) consists of two streams, an SR branch with 23 basic blocks and a condition branch as shown in Fig. 2. The condition branch takes an LR-sized target objective map \\( \\mathbf{T} \\) and produces shared intermediate conditions that can be transferred to all the SFT layers in the SR branch. Since the SFT layers [44] modulate feature maps by applying affine transformation, they learn a mapping function that outputs a modulation parameter based on \\( \\mathbf{T} \\). Specifically, \\( \\mathbf{T}_t \\), with \\( t \\) randomly changing in the pre-defined range, is fed into the condition branch during training, and this modulation layer allows the SR branch to optimize the changing objective by \\( t \\). As a result, \\( G_{\\theta} \\) learns all the objectives on the trajectory and generates SR results with spatially different objectives according to the map at inference time. \\( G_{\\theta} \\) is optimized on the training samples \\( \\mathcal{Z} = (x,y) \\) with the distribution \\( P_{\\mathcal{Z}} \\), as follows:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.15,
+ 0.473,
+ 0.469,
+ 0.495
+ ],
+ "angle": 0,
+ "content": "\\[\n\\theta^ {*} = \\arg \\min _ {\\theta} \\mathbb {E} _ {\\mathcal {Z} \\sim \\mathcal {P} _ {\\mathcal {Z}}} \\left[ \\mathcal {L} \\left(\\hat {y} _ {\\mathbf {T} _ {t}}, y | t\\right) \\right], \\tag {12}\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.078,
+ 0.505,
+ 0.469,
+ 0.552
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} (t) = \\lambda_ {\\text {r e c}} (t) \\cdot \\mathcal {L} _ {\\text {r e c}} + \\lambda_ {\\text {a d v}} (t) \\cdot \\mathcal {L} _ {\\text {a d v}} + \\sum_ {\\text {p e r l}} \\lambda_ {\\text {p e r l}} (t) \\cdot L _ {\\text {p e r l}}. \\tag {13}\n\\]"
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.078,
+ 0.56,
+ 0.4,
+ 0.576
+ ],
+ "angle": 0,
+ "content": "3.3. Optimal Objective Estimation (OOE)"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.076,
+ 0.583,
+ 0.47,
+ 0.751
+ ],
+ "angle": 0,
+ "content": "To estimate an optimal combination of objectives for each region, we train a predictive model, \\( C_{\\psi} \\). This model produces an optimal objective map \\( \\hat{\\mathbf{T}}_B \\) estimated for a given LR image, which is then delivered to the generative model in Eqn. 1. Since it is hard to find the ground truth map for \\( C_{\\psi} \\) training, we obtain its approximation \\( \\mathbf{T}_S^* \\) via a simple exhaustive searching to narrow down the range of the best possible values. Specifically, we generate a set of 21 SR results by changing \\( t \\) from 0 to 1 with a step of 0.05, and the optimal objective maps are generated by selecting the \\( t \\) with the lowest LPIPS among them for each pixel, as"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.155,
+ 0.761,
+ 0.469,
+ 0.784
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathbf {T} _ {S} ^ {*} (i, j) = \\arg \\min _ {t \\in S} \\mathbf {L P I P S} _ {t} (i, j), \\tag {14}\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.17,
+ 0.793,
+ 0.469,
+ 0.81
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathbf {L P I P S} _ {t} = L P I P S \\left(y, \\hat {y} _ {\\mathbf {T} _ {t}}\\right), \\tag {15}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.077,
+ 0.814,
+ 0.469,
+ 0.876
+ ],
+ "angle": 0,
+ "content": "where \\(\\mathbf{T}_t = \\mathbf{1} \\times t, t \\in S = \\{0.0, 0.05, 0.10, \\dots, 1.0\\}\\). Fig. 7 shows an example of the optimal objective selection (OOS) \\(\\mathbf{T}_S^*\\). The SR result using \\(\\mathbf{T}_S^*\\), SROOS, can be an upper-bound approximation for the performance of \\(G_{\\theta}\\) as"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.206,
+ 0.886,
+ 0.469,
+ 0.904
+ ],
+ "angle": 0,
+ "content": "\\[\n\\hat {y} _ {\\mathbf {T} _ {S} ^ {*}} = G _ {\\theta} \\left(x | \\mathbf {T} _ {S} ^ {*}\\right). \\tag {16}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.499,
+ 0.092,
+ 0.892,
+ 0.198
+ ],
+ "angle": 0,
+ "content": "Although \\(\\mathbf{T}_S^*\\) is useful for training \\(C_{\\psi}\\), this pixel-wise objective selection without considering the interference caused by the convolutions of \\(G_{\\theta}\\) is not accurate ground truth. Therefore, \\(C_{\\psi}\\) is optimized with three loss terms: pixel-wise objective map loss, pixel-wise reconstruction loss and perceptual loss, which measures the difference between the reconstructed and HR images, as follows:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.603,
+ 0.211,
+ 0.892,
+ 0.234
+ ],
+ "angle": 0,
+ "content": "\\[\n\\psi^ {*} = \\arg \\min _ {\\psi} \\mathbb {E} _ {\\mathcal {Z} _ {\\mathbf {T}} \\sim \\mathcal {P} _ {\\mathcal {Z} _ {\\mathbf {T}}}} \\mathcal {L}, \\tag {17}\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.559,
+ 0.251,
+ 0.892,
+ 0.27
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} = \\lambda_ {\\mathbf {T}} \\cdot \\mathcal {L} _ {\\mathbf {T}} + \\lambda_ {r e c} ^ {O O E} \\cdot \\mathcal {L} _ {r e c} + \\lambda_ {R} \\cdot \\mathcal {L} _ {R}, \\tag {18}\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.593,
+ 0.281,
+ 0.892,
+ 0.307
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {R} = \\mathbb {E} \\left[ L P I P S \\left(y, \\hat {y} _ {\\hat {\\mathbf {T}} _ {B}}\\right) \\right], \\tag {19}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.499,
+ 0.317,
+ 0.892,
+ 0.456
+ ],
+ "angle": 0,
+ "content": "where \\(\\mathcal{L}_{\\mathbf{T}}\\) and \\(\\mathcal{L}_{rec}\\) is the L1 losses between \\(\\mathbf{T}_S^*\\) and \\(\\hat{\\mathbf{T}}_B\\) and between \\(y\\) and \\(\\hat{y}_{\\hat{\\mathbf{T}}_B}\\), respectively. Meanwhile, \\(\\mathcal{Z}_{\\mathbf{T}} = (x,y,\\mathbf{T}_S^*)\\) is the training dataset, and \\(\\lambda_{\\mathbf{T}},\\lambda_{rec}^{OOE}\\) and \\(\\lambda_R\\) are the weights for each of the loss terms, respectively. During the \\(C_\\psi\\) model training, \\(C_\\psi\\) is combined with the already trained generative model, and the generator parameters are fixed. Therefore, losses for \\(C_\\psi\\) training, including LPIPS, are involved only in estimating locally-appropriate objective maps without changing the generator's parameters."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.499,
+ 0.457,
+ 0.892,
+ 0.578
+ ],
+ "angle": 0,
+ "content": "The architecture of \\( C_{\\psi} \\) consists of two separate subnetwork: one is a feature extractor (F.E.) utilizing the VGG-19 [39] and the other is a predictor with the UNet architecture [37], as shown in Fig 2. For better performance, the feature extractor aims to get low to high-level features and delivers them to Unet, which makes the prediction. Since the structure of UNet has a wider receptive field, it is advantageous for predicting objectives in context."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.5,
+ 0.595,
+ 0.633,
+ 0.611
+ ],
+ "angle": 0,
+ "content": "4. Experiments"
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.5,
+ 0.62,
+ 0.676,
+ 0.637
+ ],
+ "angle": 0,
+ "content": "4.1. Experiment Setup"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.498,
+ 0.644,
+ 0.892,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "Materials, Evaluation Metrics and Training Details. We use either the DIV2K [1] (800 images) or the DF2K [26] (3450 images) dataset to train our models. Our test datasets include BSD100 [32], General100 [9], Urban100 [17], Manga109 [33], and DIV2K validation set [1]. To evaluate the perceptual quality, we report LPIPS [52] and DISTS [6], which are full-reference metrics. DISTS is a perceptual metric that focuses on detail similarity. PSNR and SSIM [47] are also reported as fidelity-oriented metrics. The LR-PSNR metric is the PSNR between the LR input and downscaled SR images. The higher the LR-PSNR, the better the consistency between the SR results and LR images, where 45 dB or more is recommended for good LR consistency as addressed in NTIRE challenge [28]. Because consistency with the LR input images is important, we also report the LR-PSNR. All training parameters are set to be equal to those of ESRGAN [46], except for the"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.484,
+ 0.945,
+ 0.516,
+ 0.957
+ ],
+ "angle": 0,
+ "content": "1730"
+ }
+ ],
+ [
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.077,
+ 0.09,
+ 0.893,
+ 0.119
+ ],
+ "angle": 0,
+ "content": "Table 2. Comparison with state-of-the-art SR methods on benchmarks. The 1st and the 2nd best performances for each group are highlighted in red and blue, respectively. LR-PSNR values greater than 45dB are underlined."
+ },
+ {
+ "type": "table",
+ "bbox": [
+ 0.088,
+ 0.127,
+ 0.885,
+ 0.478
+ ],
+ "angle": 0,
+ "content": "| Set | objec-tive | λper[λV12,λV22,λV34,λV44,λV54] | Normalized LperlLV12LV22LV34LV44LV54 | MetricPSNR|LPIPS |
| [0.0, 0.0, 0.0, 0.0, 0.0, 0.0] | [0.00, 0.00, 1.00, 1.00, 1.00] | [0.1960] |
| A | λ0 | [1.0, 0.0, 0.0, 0.0, 0.0] | 0.71 | 0.53 | 0.76 | 0.38 | 0.25 | 23.95 |
| λ1 | [1.0, 0.0, 0.0, 0.0, 0.0] | 0.72 | 0.26 | 0.35 | 0.22 | 0.15 | 23.84 |
| λ2 | [0.0, 0.0, 1.0, 0.0, 0.0] | 0.81 | 0.51 | 0.00 | 0.02 | 0.04 | 23.66 |
| λ3 | [0.0, 0.0, 0.0, 1.0, 0.0] | 0.92 | 0.78 | 0.51 | 0.11 | 0.05 | 23.28 |
| λ4 | [0.0, 0.0, 0.0, 0.0, 1.0] | 1.00 | 1.00 | 0.93 | 0.32 | 0.12 | 23.00 |
| B | λ1 | [1.0, 0.0, 0.0, 0.0, 0.0] | 0.71 | 0.53 | 0.76 | 0.38 | 0.25 | 23.95 |
| λ1-2 | [1/2, 1/2, 0.0, 0.0, 0.0] | 0.64 | 0.23 | 0.34 | 0.20 | 0.13 | 24.08 |
| λ1-3 | [1/3, 1/3, 1/3, 0.0, 0.0] | 0.78 | 0.42 | 0.10 | 0.04 | 0.03 | 23.81 |
| λ1-4 | [1/4, 1/4, 1/4, 1/4, 0.0] | 0.78 | 0.46 | 0.18 | 0.02 | 0.01 | 23.68 |
| ESRGAN-OOSA | [24.03, 0.0848] |
| ESRGAN-OOSB | [24.21, 0.0848] |
+
+
+Figure 3. Set $A$ (left) and set $B$ (right) in the objective space. The objectives in set $B$ are closer each other than those in set $A$ .
+
+
+
+features of shallow layers such as V12 and V22 and deeper layers such as V34, V44, and V54 correspond to relatively low-level and higher-level vision, respectively [36].
+
+To find an effective set of objectives, we define an SR objective space. Since the objective for SR is a weighted sum of seven loss terms, as in Eqn. 3, an objective space is spanned by these basis loss terms, and any objective can be expressed by a seven-dimensional vector of weighting parameters, $\lambda_{i} \in \mathbb{R}^{7}$ as $\lambda_{i} = [\lambda_{rec}, \lambda_{adv}, \lambda_{per}]$ , where $\lambda_{per} \in \mathbb{R}^{5}$ is a weight vector for perceptual loss.
+
+Table 1 compares two objective sets, $A$ and $B$ , defined as shown in Fig. 3. Because ESRGAN [46] is the base model for this comparison, for all objectives in the table, except for $\lambda_0$ , $\lambda_{rec}$ and $\lambda_{adv}$ are set to $1 \times 10^{-2}$ and $5 \times 10^{-3}$ , respectively. These are the same as those for ESRGAN, except that $\lambda_{per}$ changes, where $\| \lambda_{per} \|_1 = 1$ . In particular, in terms of $\lambda_{per}$ , whereas each objective $\lambda_i$ in set $A$ has weights for only one of the five VGG feature spaces, each objective in set $B$ has equal weights for each loss in the feature space lower than the target vision level. Therefore, an objective corresponding to a high vision level also includes the losses for the lower-level feature spaces. Meanwhile, because $\lambda_0$ corresponds to a distortion-oriented RRDB model [46], its $\lambda_{rec}$ and $\lambda_{adv}$ are set to $1 \times 10^{-2}$ and 0, respectively. Note that $\lambda_0$ is included in both sets $A$ and $B$ .
+
+
+
+
+
+
+
+
+
+
+img_073
+
+
+$\mathrm{OOS}_A$
+
+
+$\mathrm{OOS}_B$
+Figure 4. The $\mathrm{OOS}_A$ and $\mathrm{OOS}_B$ results using Sets $A$ and $B$ (top), their SR results, ESRGAN- $\mathrm{OOS}_A$ and ESRGAN- $\mathrm{OOS}_B$ (bottom).
+
+
+intensity of each $\lambda_{i}$
+
+
+
+In Table 1, the normalized versions (min-max feature scaling) of the averaged $L_{per_l}$ from Eqn. 4 for five datasets (BSD100 [32], General100 [9], Urban100 [17], Manga109 [33], and DIV2K [1]) are reported. For all feature spaces, including the targeted V12 and V22 feature spaces, $\lambda_{1-2}$ in set $B$ has smaller L1 errors than those of $\lambda_1$ and $\lambda_2$ in set $A$ . Moreover, $\lambda_{1-4}$ exhibits smaller errors than those of $\lambda_4$ and $\lambda_5$ . Although $\lambda_{1-3}$ has slightly more errors in the V34 feature space than that of $\lambda_3$ , it has less errors in the V12 and V22 feature spaces therefore, $\lambda_{1-3}$ has relatively less distortion than $\lambda_3$ overfitted to the V34 feature space. That is supported by the fact that most of the objectives in set $B$ , including $\lambda_{1-3}$ , have better PSNR and LPIPS on Urban100 [17] than those in set $A$ . $\lambda_{1-5}$ showing relatively poor performance compared to $\lambda_{1-4}$ is not used.
+
+To examine the SR result with locally appropriate objectives applied using set $A$ , we mix the six SR results of ESRGAN- $\lambda_{a}$ , where $\lambda_{a} \in A$ , by selecting the SR result with the lowest LPIPS for each pixel position, as follows:
+
+$$
+y _ {A} ^ {*} (i, j) = \hat {y} _ {\mathbf {T} _ {A} ^ {*} (i, j)} (i, j), \tag {6}
+$$
+
+$$
+\mathbf {T} _ {A} ^ {*} (i, j) = \arg \min _ {\boldsymbol {\lambda} _ {a} \in A} \mathbf {L P I P S} _ {\boldsymbol {\lambda} _ {a}} (i, j), \tag {7}
+$$
+
+$$
+\mathbf {L P I P S} _ {\lambda_ {a}} = L P I P S \left(y, \hat {y} _ {\lambda_ {a}}\right), \tag {8}
+$$
+
+where $\hat{y}_{\lambda_a}$ is the SR result of ESRGAN- $\lambda_a$ . The LPIPS function computes the perceptual distance between two image patches for each pixel position, producing an LPIPS map, LPIPS, of the input image size [28, 35]. The LPIPS metric in Table 1 is the average of this map. Since $\mathbf{T}_A^*$ is the optimal objective selection (OOS), $\mathbf{T}_A^*$ and its SR model for mixing are denoted as OOS $_A$ and ESRGAN-OOS $_A$ , respectively. The upper part of Fig. 4 shows an example of OOS $_A$ and OOS $_B$ based on set $A$ and $B$ . PSNR and LPIPS [52] of ESRGAN-OOS $_A$ and ESRGAN-OOS $_B$ are reported in Table 1, where ESRGAN-OOS $_B$ is superior to any single objective model, demonstrating the potential for performance improvement of the locally suitable objective application. The lower part of Fig. 4 shows the side effects caused by mixing the SR results for set $A$ with lower proximities between objectives than those in set $B$ , as shown in Fig. 3. Since ESRGAN-OOS $_B$ in Fig. 4 has less artifact and better PSNR than those of ESRGAN-OOS $_A$ , the proposed set $B$ is more suitable for applying locally appropriate objectives.
+
+
+
+
+(a)
+(c)
+
+
+(b)
+
+
+(d)
+Figure 5. The proposed vector functions for loss weights, (a) $\lambda(t)$ in Eqn. 9 when $\alpha = 1$ and $\beta = 0$ , (b) its $\lambda_{per}(t)$ and (c) the weighting functions for $\lambda_{per}(t)$ . (d) $\lambda_{per}(t)$ used for FxSR [35].
+
+Learning Objective Trajectory. We train our generative model on a set of objectives over the trajectory rather than a single objective, $\lambda_{i}$ . The objective trajectory is formed by connecting the selected objectives, i.e. the five objectives of set $B$ , starting with an objective for a low-vision level and progressing through objectives for higher levels, i.e. from $\lambda_0$ to $\lambda_{1-4}$ . It is parameterized by a single variable $t$ , $\lambda(t) = \langle \lambda_{rec}(t), \lambda_{adv}(t), \lambda_{per}(t) \rangle$ , as follow:
+
+$$
+\boldsymbol {\lambda} (t) = \boldsymbol {\alpha} \cdot \boldsymbol {f} _ {\lambda} (t) + \boldsymbol {\beta}, \tag {9}
+$$
+
+$$
+\boldsymbol {f} _ {\lambda} (t) = \left\langle f _ {\lambda_ {r e c}} (t), f _ {\lambda_ {a d v}} (t), \boldsymbol {f} _ {\lambda_ {p e r}} (t) \right\rangle , \tag {10}
+$$
+
+where $f_{\lambda_{per}}(t) \in \mathbb{R}^5$ , $f_{\lambda_{rec}}(t)$ , $f_{\lambda_{adv}}(t)$ are weighting functions, $\alpha$ and $\beta$ are the scaling and offset vectors. As $f_{\lambda}:\mathbb{R}\to \mathbb{R}^7$ , this vector function enables the replacement of high-dimensional weight-vector manipulation with one-dimensional tracking, simplifying the training process.
+
+Specifically, the trajectory design is based on the observation in Table 1 that the distortion-oriented RRDB model using $\lambda_0$ has smaller L1 errors than those of all ESRGAN models for low-level feature spaces, such as V12 and V22, whereas ESRGAN models have smaller L1 errors for higher-level feature spaces, such as V34, V44, and V54. Thus, we design the weight functions $f_{\lambda_{rec}}$ , $f_{\lambda_{adv}}$ and $f_{\lambda_{per}}$ such that when $t$ approaches 0, $f_{\lambda_{rec}}$ increases and $\{f_{\lambda_{adv}}, \sum_{per_l} f_{\lambda_{per_l}}\}$ decrease to go to $\lambda_0$ , and conversely to go to $\lambda_{1-4}$ when $t$ increases to 1, as shown in Fig. 5(a).
+
+In relation to the change in $\sum_{per_l}f_{\lambda_{per_l}}(t)$ , we design each of five component functions, $f_{\lambda_{per_l}}(t)$ of $f_{\lambda_{per}}(t)$ , as shown in Fig. 5(c), to obtain the objective trajectory from $\lambda_0$ to $\lambda_{1 - 4}$ of set $B$ as shown in Fig. 5(b), illustrating only three out of five components because of the limitations of 3-dimensional visualization. Thus, as we progress through the trajectory by increasing $t$ from 0 to 1, the weighting parameters for the objective start with the distortion-oriented objective, $\lambda_0$ , and then the losses of higher-vision-level feature
+
+
+
+
+Figure 6. Changes in detail in the SROT results according to $t$ -value (top) and changes in PSNR and LPIPS for test DBs (bottom).
+
+
+
+spaces and adversarial loss are progressively added, making slight transitions on the objective toward $\lambda_{1-4}$ . Fig. 5(d) shows the objective trajectory used for FxSR [35], which uses only the V22 feature space, limiting the performance of the perceptually accurate restoration.
+
+The proposed objective trajectory can efficiently improve the accuracy and consistency of the SR results. First, we can use any objective on the continuous trajectory from low to high-level vision, which allows the application of more accurate objectives to each region. Second, with regard to consistency, high-level objectives on our proposed trajectory include both low-level and high-level losses, thus also accounting for the low-level objectives. This weighting method allows the sharing of the structural components reconstructed mainly by low-vision-level objectives between all SR results on the trajectory. Finally, we need to train a single SR model only once, reducing the number of models required to produce diverse HR outputs [10, 35].
+
+Fig. 6 shows the changes in the result of the generative SR model trained on the objective trajectory in Fig. 5(b), called SROT, as $t$ changes from 0 to 1. The graphs in the bottom of Fig. 6 show the trade-off curves in the perception-distortion plane according to the change of $t$ where $t$ increases by 0.05 from 0.0 to 1.0 and has 21 sample points. Each SR result on the curve is obtained by inputting $\mathbf{T}$ with the same $t$ throughout the image, as $\mathbf{T}_t = \mathbf{1} \times t$ , into the condition branch of the generative model, as follows:
+
+$$
+\hat {y} _ {\mathbf {T} _ {t}} = G _ {\theta} \left(x \mid \mathbf {T} _ {t}\right). \tag {11}
+$$
+
+The horizontal and vertical dotted lines of the graphs in Fig. 6 indicate the lowest LPIPS values of the model and the corresponding PSNR values, respectively. The $t$ values at that time are written next to the vertical lines. However, applying a specific $t$ to the entire image still limits SR performance, and optimal $t$ depending on images is unknown at inference time. We take this one step further and present later how to estimate and apply locally optimal objectives.
+
+
+image (0824)
+
+
+OOS $\mathbf{T}_S^*$
+Figure 7. The input image, the optimal objective selection $\mathbf{T}_S^*$ obtained by parameter sweeping, and $\hat{\mathbf{T}}_B$ estimated by $C_{\psi}$ .
+
+
+OOE $\hat{\mathbf{T}}_B$
+
+Network Architecture and Training. The outline of the generator network is adopted from [35], i.e., $G_{\theta}$ consists of two streams, an SR branch with 23 basic blocks and a condition branch as shown in Fig. 2. The condition branch takes an LR-sized target objective map $\mathbf{T}$ and produces shared intermediate conditions that can be transferred to all the SFT layers in the SR branch. Since the SFT layers [44] modulate feature maps by applying affine transformation, they learn a mapping function that outputs a modulation parameter based on $\mathbf{T}$ . Specifically, $\mathbf{T}_t$ , with $t$ randomly changing in the pre-defined range, is fed into the condition branch during training, and this modulation layer allows the SR branch to optimize the changing objective by $t$ . As a result, $G_{\theta}$ learns all the objectives on the trajectory and generates SR results with spatially different objectives according to the map at inference time. $G_{\theta}$ is optimized on the training samples $\mathcal{Z} = (x,y)$ with the distribution $P_{\mathcal{Z}}$ , as follows:
+
+$$
+\theta^ {*} = \arg \min _ {\theta} \mathbb {E} _ {\mathcal {Z} \sim \mathcal {P} _ {\mathcal {Z}}} \left[ \mathcal {L} \left(\hat {y} _ {\mathbf {T} _ {t}}, y | t\right) \right], \tag {12}
+$$
+
+$$
+\mathcal {L} (t) = \lambda_ {\text {r e c}} (t) \cdot \mathcal {L} _ {\text {r e c}} + \lambda_ {\text {a d v}} (t) \cdot \mathcal {L} _ {\text {a d v}} + \sum_ {\text {p e r l}} \lambda_ {\text {p e r l}} (t) \cdot L _ {\text {p e r l}}. \tag {13}
+$$
+
+# 3.3. Optimal Objective Estimation (OOE)
+
+To estimate an optimal combination of objectives for each region, we train a predictive model, $C_{\psi}$ . This model produces an optimal objective map $\hat{\mathbf{T}}_B$ estimated for a given LR image, which is then delivered to the generative model in Eqn. 1. Since it is hard to find the ground truth map for $C_{\psi}$ training, we obtain its approximation $\mathbf{T}_S^*$ via a simple exhaustive searching to narrow down the range of the best possible values. Specifically, we generate a set of 21 SR results by changing $t$ from 0 to 1 with a step of 0.05, and the optimal objective maps are generated by selecting the $t$ with the lowest LPIPS among them for each pixel, as
+
+$$
+\mathbf {T} _ {S} ^ {*} (i, j) = \arg \min _ {t \in S} \mathbf {L P I P S} _ {t} (i, j), \tag {14}
+$$
+
+$$
+\mathbf {L P I P S} _ {t} = L P I P S \left(y, \hat {y} _ {\mathbf {T} _ {t}}\right), \tag {15}
+$$
+
+where $\mathbf{T}_t = \mathbf{1} \times t, t \in S = \{0.0, 0.05, 0.10, \dots, 1.0\}$ . Fig. 7 shows an example of the optimal objective selection (OOS) $\mathbf{T}_S^*$ . The SR result using $\mathbf{T}_S^*$ , SROOS, can be an upper-bound approximation for the performance of $G_{\theta}$ as
+
+$$
+\hat {y} _ {\mathbf {T} _ {S} ^ {*}} = G _ {\theta} \left(x | \mathbf {T} _ {S} ^ {*}\right). \tag {16}
+$$
+
+Although $\mathbf{T}_S^*$ is useful for training $C_{\psi}$ , this pixel-wise objective selection without considering the interference caused by the convolutions of $G_{\theta}$ is not accurate ground truth. Therefore, $C_{\psi}$ is optimized with three loss terms: pixel-wise objective map loss, pixel-wise reconstruction loss and perceptual loss, which measures the difference between the reconstructed and HR images, as follows:
+
+$$
+\psi^ {*} = \arg \min _ {\psi} \mathbb {E} _ {\mathcal {Z} _ {\mathbf {T}} \sim \mathcal {P} _ {\mathcal {Z} _ {\mathbf {T}}}} \mathcal {L}, \tag {17}
+$$
+
+$$
+\mathcal {L} = \lambda_ {\mathbf {T}} \cdot \mathcal {L} _ {\mathbf {T}} + \lambda_ {r e c} ^ {O O E} \cdot \mathcal {L} _ {r e c} + \lambda_ {R} \cdot \mathcal {L} _ {R}, \tag {18}
+$$
+
+$$
+\mathcal {L} _ {R} = \mathbb {E} \left[ L P I P S \left(y, \hat {y} _ {\hat {\mathbf {T}} _ {B}}\right) \right], \tag {19}
+$$
+
+where $\mathcal{L}_{\mathbf{T}}$ and $\mathcal{L}_{rec}$ is the L1 losses between $\mathbf{T}_S^*$ and $\hat{\mathbf{T}}_B$ and between $y$ and $\hat{y}_{\hat{\mathbf{T}}_B}$ , respectively. Meanwhile, $\mathcal{Z}_{\mathbf{T}} = (x,y,\mathbf{T}_S^*)$ is the training dataset, and $\lambda_{\mathbf{T}},\lambda_{rec}^{OOE}$ and $\lambda_R$ are the weights for each of the loss terms, respectively. During the $C_\psi$ model training, $C_\psi$ is combined with the already trained generative model, and the generator parameters are fixed. Therefore, losses for $C_\psi$ training, including LPIPS, are involved only in estimating locally-appropriate objective maps without changing the generator's parameters.
+
+The architecture of $C_{\psi}$ consists of two separate subnetwork: one is a feature extractor (F.E.) utilizing the VGG-19 [39] and the other is a predictor with the UNet architecture [37], as shown in Fig 2. For better performance, the feature extractor aims to get low to high-level features and delivers them to Unet, which makes the prediction. Since the structure of UNet has a wider receptive field, it is advantageous for predicting objectives in context.
+
+# 4. Experiments
+
+# 4.1. Experiment Setup
+
+Materials, Evaluation Metrics and Training Details. We use either the DIV2K [1] (800 images) or the DF2K [26] (3450 images) dataset to train our models. Our test datasets include BSD100 [32], General100 [9], Urban100 [17], Manga109 [33], and DIV2K validation set [1]. To evaluate the perceptual quality, we report LPIPS [52] and DISTS [6], which are full-reference metrics. DISTS is a perceptual metric that focuses on detail similarity. PSNR and SSIM [47] are also reported as fidelity-oriented metrics. The LR-PSNR metric is the PSNR between the LR input and downscaled SR images. The higher the LR-PSNR, the better the consistency between the SR results and LR images, where 45 dB or more is recommended for good LR consistency as addressed in NTIRE challenge [28]. Because consistency with the LR input images is important, we also report the LR-PSNR. All training parameters are set to be equal to those of ESRGAN [46], except for the
+
+Table 2. Comparison with state-of-the-art SR methods on benchmarks. The 1st and the 2nd best performances for each group are highlighted in red and blue, respectively. LR-PSNR values greater than 45dB are underlined.
+
+| Set | objec-tive | λper[λV12,λV22,λV34,λV44,λV54] | Normalized LperlLV12LV22LV34LV44LV54 | MetricPSNR|LPIPS |
| [0.0, 0.0, 0.0, 0.0, 0.0, 0.0] | [0.00, 0.00, 1.00, 1.00, 1.00] | [0.1960] |
| A | λ0 | [1.0, 0.0, 0.0, 0.0, 0.0] | 0.71 | 0.53 | 0.76 | 0.38 | 0.25 | 23.95 |
| λ1 | [1.0, 0.0, 0.0, 0.0, 0.0] | 0.72 | 0.26 | 0.35 | 0.22 | 0.15 | 23.84 |
| λ2 | [0.0, 0.0, 1.0, 0.0, 0.0] | 0.81 | 0.51 | 0.00 | 0.02 | 0.04 | 23.66 |
| λ3 | [0.0, 0.0, 0.0, 1.0, 0.0] | 0.92 | 0.78 | 0.51 | 0.11 | 0.05 | 23.28 |
| λ4 | [0.0, 0.0, 0.0, 0.0, 1.0] | 1.00 | 1.00 | 0.93 | 0.32 | 0.12 | 23.00 |
| B | λ1 | [1.0, 0.0, 0.0, 0.0, 0.0] | 0.71 | 0.53 | 0.76 | 0.38 | 0.25 | 23.95 |
| λ1-2 | [1/2, 1/2, 0.0, 0.0, 0.0] | 0.64 | 0.23 | 0.34 | 0.20 | 0.13 | 24.08 |
| λ1-3 | [1/3, 1/3, 1/3, 0.0, 0.0] | 0.78 | 0.42 | 0.10 | 0.04 | 0.03 | 23.81 |
| λ1-4 | [1/4, 1/4, 1/4, 1/4, 0.0] | 0.78 | 0.46 | 0.18 | 0.02 | 0.01 | 23.68 |
| ESRGAN-OOSA | [24.03, 0.0848] |
| ESRGAN-OOSB | [24.21, 0.0848] |
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+ "content": " randomly changing in the pre-defined range, is fed into the condition branch during training, and this modulation layer allows the SR branch to optimize the changing objective by "
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+ "content": "G_{\\theta}"
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+ "type": "text",
+ "content": " learns all the objectives on the trajectory and generates SR results with spatially different objectives according to the map at inference time. "
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+ "content": " estimated for a given LR image, which is then delivered to the generative model in Eqn. 1. Since it is hard to find the ground truth map for "
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+ "content": " via a simple exhaustive searching to narrow down the range of the best possible values. Specifically, we generate a set of 21 SR results by changing "
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+ "content": " from 0 to 1 with a step of 0.05, and the optimal objective maps are generated by selecting the "
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+ "content": " with the lowest LPIPS among them for each pixel, as"
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+ "content": "\\psi^ {*} = \\arg \\min _ {\\psi} \\mathbb {E} _ {\\mathcal {Z} _ {\\mathbf {T}} \\sim \\mathcal {P} _ {\\mathcal {Z} _ {\\mathbf {T}}}} \\mathcal {L}, \\tag {17}",
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+ "type": "text",
+ "content": " training, including LPIPS, are involved only in estimating locally-appropriate objective maps without changing the generator's parameters."
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| Summary | Backbone | QMUL-Shoe-V1 | QMUL-Shoe-V2 | QMUL-Chair-V1 | QMUL-Chair-V2 |
| Yu et al. (CVPR16 [78]) | Triplet Siamese | Sketch-a-Net | 52.17% | -- | 72.16% | -- |
| Song et al. (BMVC16 [66]) | Attribute learning | Sketch-a-Net | 50.43% | -- | 78.35% | -- |
| Song et al. (ICCV17 [67]) | Spatial attention | Sketch-a-Net | 61.74% | -- | 81.44% | -- |
| Li et al. (TIP17 [39]) | Multi-view alignment | GoogleNet‡ | 51.30% | -- | 79.38% | -- |
| Radenovic et al. (ECCV18 [57]) | Unsupervised shape matching | VGG-16‡ | 54.8% | -- | 85.6% | -- |
| Lin et al. (ACMMM19 [42]) | Retrieval by classification | DenseNet-169 | 63.48% | 40.02% | 95.88% | -- |
| Bhunia et al. § (CVPR20 [8]) | Early Retrieval with reward | InceptionV3 | -- | 30.8% | -- | 51.2% |
| Pang et al. (CVPR20 [51]) | Jigsaw pre-training | GoogleNet | 56.52% | 36.52% | 85.98% | -- |
| Zhang et al. (ECCV20 [84]) | Generative hashing | Sketch-a-Net | 35.7% | -- | 67.1% | -- |
| Sain et al. (BMVC20 [62]) | Hierarchical modelling | InceptionV3 | -- | 36.27% | -- | 62.45% |
| Bhunia et al. (CVPR21 [6]) | Help from unlabelled photos | InceptionV3 | -- | 39.1% | -- | 60.2% |
| Sain et al. (CVPR21 [63]) | Style-agnostic learning | InceptionV3 | -- | 36.47% | -- | 62.86% |
| Yu et al. (IJCV21 [79]) | Mid-level features | InceptionV3 | 66.1% | 42.3% | 91.8% | 69.1% |
| Bhunia et al. (CVPR22 [7]) | Noisy stroke removal | InceptionV3 | -- | 43.7% | -- | 64.8% |
| Human Trials [79] | -- | -- | 66.09% | 49.50% | 94.85% | 63.00% |
| Ours-Base (ImageNet) | LFG-SBIR - Eq. 1 | ResNet50 | 53.04% | 36.04% | 88.66% | 67.82% |
| Ours (ImageNet) | {LFG-SBIR, LNT} - Eq. 9 | ResNet50 | 67.83% | 42.04% | 94.85% | 71.70% |
| Ours-Base (Jigsaw) | LFG-SBIR - Eq. 1 | ResNet50 | 56.52% | 37.69% | 90.72% | 69.45% |
| Ours (Jigsaw) | {LFG-SBIR, LNT} - Eq. 9 | ResNet50 | 69.57% | 42.19% | 94.85% | 72.34% |
| Ours-Base (Barlow Twins) | LFG-SBIR - Eq. 1 | ResNet50 | 67.83% | 44.29% | 91.75% | 69.13% |
| Ours (Barlow Twins) | {LFG-SBIR, LNT} - Eq. 9 | ResNet50 | 72.17% | 47.90% | 95.88% | 73.95% |
| Ours-Base (CLIP) | LFG-SBIR - Eq. 1 | ViT-B/32 | 70.43% | 46.10% | 93.81% | 72.35% |
| Ours (CLIP) | {LFG-SBIR, LNT} - Eq. 9 | ViT-B/32 | 77.39% | 49.70% | 96.91% | 74.92% |
| Ours-Base (OBOW) | LFG-SBIR - Eq. 1 | ResNet50 | 68.70% | 45.20% | 92.78% | 71.06% |
| Ours (OBOW) | {LFG-SBIR, LNT} - Eq. 9 | ResNet50 | 76.52% | 50.75% | 98.97% | 75.56% |
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| Yu et al. (CVPR16 [78]) | Triplet Siamese | Sketch-a-Net | 52.17% | -- | 72.16% | -- |
| Song et al. (BMVC16 [66]) | Attribute learning | Sketch-a-Net | 50.43% | -- | 78.35% | -- |
| Song et al. (ICCV17 [67]) | Spatial attention | Sketch-a-Net | 61.74% | -- | 81.44% | -- |
| Li et al. (TIP17 [39]) | Multi-view alignment | GoogleNet‡ | 51.30% | -- | 79.38% | -- |
| Radenovic et al. (ECCV18 [57]) | Unsupervised shape matching | VGG-16‡ | 54.8% | -- | 85.6% | -- |
| Lin et al. (ACMMM19 [42]) | Retrieval by classification | DenseNet-169 | 63.48% | 40.02% | 95.88% | -- |
| Bhunia et al. § (CVPR20 [8]) | Early Retrieval with reward | InceptionV3 | -- | 30.8% | -- | 51.2% |
| Pang et al. (CVPR20 [51]) | Jigsaw pre-training | GoogleNet | 56.52% | 36.52% | 85.98% | -- |
| Zhang et al. (ECCV20 [84]) | Generative hashing | Sketch-a-Net | 35.7% | -- | 67.1% | -- |
| Sain et al. (BMVC20 [62]) | Hierarchical modelling | InceptionV3 | -- | 36.27% | -- | 62.45% |
| Bhunia et al. (CVPR21 [6]) | Help from unlabelled photos | InceptionV3 | -- | 39.1% | -- | 60.2% |
| Sain et al. (CVPR21 [63]) | Style-agnostic learning | InceptionV3 | -- | 36.47% | -- | 62.86% |
| Yu et al. (IJCV21 [79]) | Mid-level features | InceptionV3 | 66.1% | 42.3% | 91.8% | 69.1% |
| Bhunia et al. (CVPR22 [7]) | Noisy stroke removal | InceptionV3 | -- | 43.7% | -- | 64.8% |
| Human Trials [79] | -- | -- | 66.09% | 49.50% | 94.85% | 63.00% |
| Ours-Base (ImageNet) | LFG-SBIR - Eq. 1 | ResNet50 | 53.04% | 36.04% | 88.66% | 67.82% |
| Ours (ImageNet) | {LFG-SBIR, LNT} - Eq. 9 | ResNet50 | 67.83% | 42.04% | 94.85% | 71.70% |
| Ours-Base (Jigsaw) | LFG-SBIR - Eq. 1 | ResNet50 | 56.52% | 37.69% | 90.72% | 69.45% |
| Ours (Jigsaw) | {LFG-SBIR, LNT} - Eq. 9 | ResNet50 | 69.57% | 42.19% | 94.85% | 72.34% |
| Ours-Base (Barlow Twins) | LFG-SBIR - Eq. 1 | ResNet50 | 67.83% | 44.29% | 91.75% | 69.13% |
| Ours (Barlow Twins) | {LFG-SBIR, LNT} - Eq. 9 | ResNet50 | 72.17% | 47.90% | 95.88% | 73.95% |
| Ours-Base (CLIP) | LFG-SBIR - Eq. 1 | ViT-B/32 | 70.43% | 46.10% | 93.81% | 72.35% |
| Ours (CLIP) | {LFG-SBIR, LNT} - Eq. 9 | ViT-B/32 | 77.39% | 49.70% | 96.91% | 74.92% |
| Ours-Base (OBOW) | LFG-SBIR - Eq. 1 | ResNet50 | 68.70% | 45.20% | 92.78% | 71.06% |
| Ours (OBOW) | {LFG-SBIR, LNT} - Eq. 9 | ResNet50 | 76.52% | 50.75% | 98.97% | 75.56% |
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| Summary | Backbone | QMUL-Shoe-V1 | QMUL-Shoe-V2 | QMUL-Chair-V1 | QMUL-Chair-V2 |
| Yu et al. (CVPR16 [78]) | Triplet Siamese | Sketch-a-Net | 52.17% | -- | 72.16% | -- |
| Song et al. (BMVC16 [66]) | Attribute learning | Sketch-a-Net | 50.43% | -- | 78.35% | -- |
| Song et al. (ICCV17 [67]) | Spatial attention | Sketch-a-Net | 61.74% | -- | 81.44% | -- |
| Li et al. (TIP17 [39]) | Multi-view alignment | GoogleNet‡ | 51.30% | -- | 79.38% | -- |
| Radenovic et al. (ECCV18 [57]) | Unsupervised shape matching | VGG-16‡ | 54.8% | -- | 85.6% | -- |
| Lin et al. (ACMMM19 [42]) | Retrieval by classification | DenseNet-169 | 63.48% | 40.02% | 95.88% | -- |
| Bhunia et al. § (CVPR20 [8]) | Early Retrieval with reward | InceptionV3 | -- | 30.8% | -- | 51.2% |
| Pang et al. (CVPR20 [51]) | Jigsaw pre-training | GoogleNet | 56.52% | 36.52% | 85.98% | -- |
| Zhang et al. (ECCV20 [84]) | Generative hashing | Sketch-a-Net | 35.7% | -- | 67.1% | -- |
| Sain et al. (BMVC20 [62]) | Hierarchical modelling | InceptionV3 | -- | 36.27% | -- | 62.45% |
| Bhunia et al. (CVPR21 [6]) | Help from unlabelled photos | InceptionV3 | -- | 39.1% | -- | 60.2% |
| Sain et al. (CVPR21 [63]) | Style-agnostic learning | InceptionV3 | -- | 36.47% | -- | 62.86% |
| Yu et al. (IJCV21 [79]) | Mid-level features | InceptionV3 | 66.1% | 42.3% | 91.8% | 69.1% |
| Bhunia et al. (CVPR22 [7]) | Noisy stroke removal | InceptionV3 | -- | 43.7% | -- | 64.8% |
| Human Trials [79] | -- | -- | 66.09% | 49.50% | 94.85% | 63.00% |
| Ours-Base (ImageNet) | LFG-SBIR - Eq. 1 | ResNet50 | 53.04% | 36.04% | 88.66% | 67.82% |
| Ours (ImageNet) | {LFG-SBIR, LNT} - Eq. 9 | ResNet50 | 67.83% | 42.04% | 94.85% | 71.70% |
| Ours-Base (Jigsaw) | LFG-SBIR - Eq. 1 | ResNet50 | 56.52% | 37.69% | 90.72% | 69.45% |
| Ours (Jigsaw) | {LFG-SBIR, LNT} - Eq. 9 | ResNet50 | 69.57% | 42.19% | 94.85% | 72.34% |
| Ours-Base (Barlow Twins) | LFG-SBIR - Eq. 1 | ResNet50 | 67.83% | 44.29% | 91.75% | 69.13% |
| Ours (Barlow Twins) | {LFG-SBIR, LNT} - Eq. 9 | ResNet50 | 72.17% | 47.90% | 95.88% | 73.95% |
| Ours-Base (CLIP) | LFG-SBIR - Eq. 1 | ViT-B/32 | 70.43% | 46.10% | 93.81% | 72.35% |
| Ours (CLIP) | {LFG-SBIR, LNT} - Eq. 9 | ViT-B/32 | 77.39% | 49.70% | 96.91% | 74.92% |
| Ours-Base (OBOW) | LFG-SBIR - Eq. 1 | ResNet50 | 68.70% | 45.20% | 92.78% | 71.06% |
| Ours (OBOW) | {LFG-SBIR, LNT} - Eq. 9 | ResNet50 | 76.52% | 50.75% | 98.97% | 75.56% |
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| Summary | Backbone | QMUL-Shoe-V1 | QMUL-Shoe-V2 | QMUL-Chair-V1 | QMUL-Chair-V2 |
| Yu et al. (CVPR16 [78]) | Triplet Siamese | Sketch-a-Net | 52.17% | -- | 72.16% | -- |
| Song et al. (BMVC16 [66]) | Attribute learning | Sketch-a-Net | 50.43% | -- | 78.35% | -- |
| Song et al. (ICCV17 [67]) | Spatial attention | Sketch-a-Net | 61.74% | -- | 81.44% | -- |
| Li et al. (TIP17 [39]) | Multi-view alignment | GoogleNet‡ | 51.30% | -- | 79.38% | -- |
| Radenovic et al. (ECCV18 [57]) | Unsupervised shape matching | VGG-16‡ | 54.8% | -- | 85.6% | -- |
| Lin et al. (ACMMM19 [42]) | Retrieval by classification | DenseNet-169 | 63.48% | 40.02% | 95.88% | -- |
| Bhunia et al. § (CVPR20 [8]) | Early Retrieval with reward | InceptionV3 | -- | 30.8% | -- | 51.2% |
| Pang et al. (CVPR20 [51]) | Jigsaw pre-training | GoogleNet | 56.52% | 36.52% | 85.98% | -- |
| Zhang et al. (ECCV20 [84]) | Generative hashing | Sketch-a-Net | 35.7% | -- | 67.1% | -- |
| Sain et al. (BMVC20 [62]) | Hierarchical modelling | InceptionV3 | -- | 36.27% | -- | 62.45% |
| Bhunia et al. (CVPR21 [6]) | Help from unlabelled photos | InceptionV3 | -- | 39.1% | -- | 60.2% |
| Sain et al. (CVPR21 [63]) | Style-agnostic learning | InceptionV3 | -- | 36.47% | -- | 62.86% |
| Yu et al. (IJCV21 [79]) | Mid-level features | InceptionV3 | 66.1% | 42.3% | 91.8% | 69.1% |
| Bhunia et al. (CVPR22 [7]) | Noisy stroke removal | InceptionV3 | -- | 43.7% | -- | 64.8% |
| Human Trials [79] | -- | -- | 66.09% | 49.50% | 94.85% | 63.00% |
| Ours-Base (ImageNet) | LFG-SBIR - Eq. 1 | ResNet50 | 53.04% | 36.04% | 88.66% | 67.82% |
| Ours (ImageNet) | {LFG-SBIR, LNT} - Eq. 9 | ResNet50 | 67.83% | 42.04% | 94.85% | 71.70% |
| Ours-Base (Jigsaw) | LFG-SBIR - Eq. 1 | ResNet50 | 56.52% | 37.69% | 90.72% | 69.45% |
| Ours (Jigsaw) | {LFG-SBIR, LNT} - Eq. 9 | ResNet50 | 69.57% | 42.19% | 94.85% | 72.34% |
| Ours-Base (Barlow Twins) | LFG-SBIR - Eq. 1 | ResNet50 | 67.83% | 44.29% | 91.75% | 69.13% |
| Ours (Barlow Twins) | {LFG-SBIR, LNT} - Eq. 9 | ResNet50 | 72.17% | 47.90% | 95.88% | 73.95% |
| Ours-Base (CLIP) | LFG-SBIR - Eq. 1 | ViT-B/32 | 70.43% | 46.10% | 93.81% | 72.35% |
| Ours (CLIP) | {LFG-SBIR, LNT} - Eq. 9 | ViT-B/32 | 77.39% | 49.70% | 96.91% | 74.92% |
| Ours-Base (OBOW) | LFG-SBIR - Eq. 1 | ResNet50 | 68.70% | 45.20% | 92.78% | 71.06% |
| Ours (OBOW) | {LFG-SBIR, LNT} - Eq. 9 | ResNet50 | 76.52% | 50.75% | 98.97% | 75.56% |
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| SketchyGAN [16] | Categorical | Synth+Real | • Fully automatic edemap augmentation + input injection at multiple layers. |
| iSketch&Fill [30] | Categorical | Synthetic | • Edemap creation with Im2Pencil [54] and sketch-simplification [77] + ResNet [35] generator. |
| CoGS [33] | Categorical | Synth+Real | • Saliency with [40] for synthetic sketches + VQ-GAN [25] with VAE over codebook vectors. |
| ContextGAN [58] | Semi-FG | Synthetic | • Synthetic sketch generation with XDoG [87] and [43] + optimisation-based GAN inversion. |
| Two-Stage [57] | Semi-FG | Real | • Synthetic noisy-stroke for augmentation + two-stage sketch-to-edemap-to-photo generation. |
| SYO-GAN [86] | Semi-FG | Synthetic | • Pseudo sketch creation with PhotoSketch [52] + fine-tuning GAN model with a few pose-specific sketches. |
| SketchyCOCO [29] | Scene-level | Semi-real | • Synthetic scene sketch + generation of foreground object followed by contextual background. |
| Two-Stage [85] | Scene-level | Synthetic | • Edemaps generated with [66] + edemap standardisation followed by content-style disentanglement. |
| DeepFaceDraw [15] | Facial photo | Synthetic | • Photocopy filter and [77] for training data + region-wise embedding with 2-stage generation. |
| Controlled S2I [96] | Facial photo | Synthetic | • HED [92] for edemaps + dilation-based sketch refinement network for adapting edge-based models. |
| Proposed | Fine-grained | Real | • Unlabelled photos & sketch-photo pairs + autoregressive latent-mapper & pre-trained StyleGAN [46]. |
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+ "text": "outputs, StyleGAN [46, 47] introduced a non-linear mapping from input code vector $z \\in \\mathcal{Z}$ to intermediate latent code $w \\in \\mathcal{W}$ , which controlled the generation process. While traditional GAN is unable to generate conditional output, it can be augmented with additional information to conditionally control the data generation process [61]. However, existing conditional generative [55, 79] models are unable to inject fine-grained control, especially when conditioned with abstract free-hand sketches.",
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+ "text": "GAN Inversion: Exploring GANs has recently led to an interest in inverting a pre-trained GAN [4] for tasks like image manipulation [4]. Typical GAN training aims to learn the weights of generator and discriminator with appropriate loss objectives, to generate random new images $G(z)$ by sampling random noise vectors $z \\in \\mathcal{Z}$ [31]. Contrarily, during GAN inversion, given a reference image we try to find a noise vector $z^{*}$ in the generator latent space that can accurately reconstruct that image while its weights fixed [104]. While some methods [1,2,22,23] directly optimise the latent vector to minimise the reconstruction loss, a few works [4,32,69,82] train dedicated encoders to find the latent code corresponding to an input image. Among them, optimisation-based methods perform better in terms of reconstruction accuracy, while encoding-based methods work significantly faster. Other methods [5, 103], take a hybrid approach in order to attain \"the best of both worlds\" [88]. However, images from different domain (e.g., semantic label map, edgemap) are not invertible into the latent space of a photo pre-trained generator [6]. Consequently, end-to-end trainable methods [3,14,63,69] emerged which aims to map a given image (from a source domain) into the latent space of a pre-trained GAN trained with target domain images. These learned encoders are then used in tasks like, inversion [4], semantic editing [4], super-resolution [60], face frontalisation [69], inpainting [69].",
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+ "text": "3. Pilot Study: Problems and Analysis",
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+ "text": "Challenges: Sketches being highly abstract in nature, generating a photo from a sketch can have multiple possible outcomes [69]. Generating photorealistic images from sparse sketches incurs three major challenges – (i) Locality-bias assumes that any particular output (e.g., photo) pixel",
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+ "text": "position $I'(x, y)$ is perfectly aligned with the same pixel location $I(x, y)$ of the conditional input (e.g., sketch) [69]. However, a free-hand sketch being highly deformed does not necessarily follow the paired photo's intensity boundary [36]. (ii) Hallucinating the colour/texture in a realistic and contextually-meaningful manner, is difficult from sparse sketch input. (iii) Deciphering the fine-grained user intent is a major bottleneck as the same object can be sketched in diverse ways by different users [75].",
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+ "text": "Analysis: The popular encoder-decoder architecture [41] for converting an input sketch $S$ to output RGB photo $\\mathcal{R}$ via image-to-image translation [41] can be formulated as:",
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+ "text": "\n$$\nP (\\mathcal {R} | \\mathcal {S}) = \\underbrace {P (\\mathcal {Z} | \\mathcal {S})} _ {\\text {E n c o d e r}} \\underbrace {P (\\mathcal {R} | \\mathcal {Z})} _ {\\text {D e c o d e r}} \\tag {1}\n$$\n",
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+ "text": "where the encoder $P(\\mathcal{Z}|\\mathcal{S})$ embeds the sketch into a latent feature $\\mathcal{Z}$ , from which the decoder $P(\\mathcal{R}|\\mathcal{Z})$ generates the output photo. Existing works [18, 38, 105] have evolved through designing task-specific encoder/decoder frameworks. Despite achieving remarkable success in other image translation problems (e.g., image-restoration [67], colourisation [41]), adapting them off-the-shelf fails for our setup. Importantly, we realise that as the loss backpropagates from the decoder to encoder's end, while training [41] with sketch-photo pairs $(\\mathcal{S},\\mathcal{R})$ , it implicitly enforces the model to follow sketch as a pseudo edge-boundary [57]. Consequently, the model is hard-conditioned by the sketch to treat its strokes as the intensity boundary of the generated photo, thus resulting in a deformed output.",
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+ "text": "Instead of end-to-end encoder-decoder training, we adopt a two stage-approach (Fig. 2). In the first stage, we model $P(\\mathcal{R}|\\mathcal{Z})$ as an unsupervised GAN [31], which being trained from a large number of unlabeled photos of a particular class, is capable of generating realistic photos $G(z)$ , given a random vector $z \\sim \\mathcal{N}(0,1)$ [31]. As GAN models learn data distribution [68], we can loosely assume that any photo can be generated by sampling a specific $z^*$ from the GAN latent space [1]. Once the GAN model is trained, in the second stage, keeping the $G(\\cdot)$ fixed, we aim to learn $P(\\mathcal{Z}|\\mathcal{S})$ as a sketch mapper that would encode the input sketch $S$ into a latent code $\\mathcal{Z}$ corresponding to the paired photo $\\mathcal{R}$ in the pre-trained GAN latent space.",
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+ "text": "Advantages of decoupling the encoder-decoder training are twofold - (i) the GAN model [46, 47] pre-trained on real photos is bound to generate realistic photos devoid of unwanted deformation, (ii) while output quality and diversity of coupled encoder-decoder models were limited by the training sketch-photo pairs [41], our decoupled decoder being independent of such pairs, can model the large variation of a particular dataset using unlabelled photos [46, 47] only. Sketch-photo pairs are used to train the sketch mapper only.",
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+ "Figure 2. The sketch mapper aims to predict the corresponding latent code of associated photo in the manifold of pre-trained GAN."
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+ "text": "4. Background: StyleGAN",
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+ "text": "In a GAN [31] framework, a generator $G(\\cdot)$ aims to generate an image $G(z)$ from a noise vector $z \\in \\mathcal{Z}$ of size $\\mathbb{R}^d$ sampled from a Gaussian distribution [31], while a discriminator $D(\\cdot)$ tries to distinguish between a real and a generated fake image [31]. The training progresses through a two-player minimax game, thus gradually improving each other over the value function $V(D,G)$ as [31]:",
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+ "text": "\n$$\n\\begin{array}{l} \\min _ {G} \\max _ {D} V (D, G) = \\mathbb {E} _ {x \\sim p _ {\\text {d a t a}} (x)} [ \\log D (x) ] \\tag {2} \\\\ + \\mathbb {E} _ {z \\sim p _ {z} (z)} [ \\log (1 - D (G (z))) ] \\\\ \\end{array}\n$$\n",
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+ "text": "Instead of passing a random noise vector $z \\in \\mathcal{Z}$ directly as the network input [68], StyleGAN [46, 47] eliminates the idea of input layer and always starts from a learned constant tensor of size $\\mathbb{R}^{4 \\times 4 \\times d}$ . The generator network $\\mathcal{G}(\\cdot)$ consists of a number of progressive resolution blocks, each having the sequence $\\mathrm{conv}3 \\times 3 \\to \\mathrm{AdaIN} \\to \\mathrm{conv}3 \\times 3 \\to \\mathrm{AdaIN}$ [46, 47]. StyleGAN employs a non-linear mapping network $f: \\mathcal{Z} \\to \\mathcal{W}$ (an 8-layer MLP) to transform $z$ into an intermediate latent vector $w \\in \\mathcal{W}$ of size $\\mathbb{R}^d$ [46, 47]. The same latent vector $w$ , upon repeatedly passing through a common affine transformation layer $A$ at each level of the generator network, generates the style $y = (y_s, y_b) = A(w)$ for that level. Adaptive instance normalisation (AdaIN) [46, 47] is then controlled by $y$ via modulating the feature-map $x_f$ as $\\mathrm{AdaIN}(x_f, y) = y_s \\frac{x_f - \\mu(x_f)}{\\sigma(x_f)} + y_b$ after each $\\mathrm{conv}3 \\times 3$ block of $\\mathcal{G}(\\cdot)$ [46, 47]. Moreover, stochasticity is injected by adding one-channel uncorrelated Gaussian noise image (per-channel scaled with a learned scaling factor $B$ ) to each layer of the network before every AdaIN operation [46, 47].",
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+ "text": "However, due to the limited representability and disentanglement of a single latent vector $w \\in \\mathcal{W}$ [1], we embed the input in the extended $\\mathcal{W}^+$ latent space [1] consisting of different latent vectors $w^+ \\in \\mathcal{W}^+$ of size $\\mathbb{R}^{k \\times d}$ , one for each level of the generator network $\\mathcal{G}(\\cdot)$ . For an output of",
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+ "text": "resolution $M \\times M$ , $k = 2\\log_2(M) - 2$ [47]. In this work, we set $M = 256$ , making $k = 14$ .",
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+ "text": "5. Sketch-to-Photo Generation Model",
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+ "text": "Overview: We aim to devise a sketch-to-photo generation model utilising the rich latent space of a pre-trained StyleGAN [47] trained on a particular class to achieve fine-grained generation. Once the StyleGAN [47] is trained, we fix its weights and train a sketch mapper $\\mathcal{E}_s$ that projects an input sketch $(s)$ into a latent code $w_{s}^{+} = \\mathcal{E}_{s}(s)\\in \\mathbb{R}^{14\\times d}$ lying in the manifold of pre-trained StyleGAN. In other words, given a sketch input we aim to pick the corresponding latent which when passed through the frozen generator $\\mathcal{G}(\\cdot)$ would generate an output $(\\hat{r})$ most similar to the ground-truth paired photo $(r)$ . In particular, we have three salient design components: (i) an autoregressive sketch mapper (ii) fine-grained discriminative loss besides usual reconstruction objective, and (iii) a photo-to-photo mapper $\\mathcal{E}_r$ working as a teacher [27] to improve the learning of $\\mathcal{E}_s$ .",
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+ "text": "5.1. Model Architecture",
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+ "text": "Baseline Sketch Mapper: Inspired by GAN inversion literature [88], we design our baseline sketch mapper using a ResNet50 [35] backbone extracting feature map $f_{s} = \\mathcal{F}_{s}(s) \\in \\mathbb{R}^{h_{f} \\times w_{f} \\times d}$ . In order to generate the latent code of size $\\mathbb{R}^{14 \\times d}$ , we use 14 individual (not shared) latent embedding networks (successive stride-two conv-layers with LeakyReLU [93]), each of them takes $f_{s}$ as input to predict a $d$ -dimensional latent vector. Concatenating them results in the $\\mathbb{R}^{14 \\times d}$ latent code [69]. Finally, this latent code upon passing through the pre-trained generator $\\mathcal{G}(\\cdot)$ generates the output photo $\\hat{r}$ . Trained with weighted summation of pixel loss $(l_{2})$ and perceptual [102] loss, baseline sketch mapper eventually learns to map an input sketch to its corresponding photo in the latent space of a pre-trained StyleGAN [47].",
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+ "text": "However, it has a few limitations: Firstly, this baseline ignores the varying levels of sketch abstraction [95]. Ideally, for highly abstract/partial sketches, the output space should be large with many plausible RGB photos [12], whereas, for a detailed sketch, it should reflect the fine-grained details. Secondly, reconstruction loss [69] alone, fails to decipher the fine-grained semantic intent of the user.",
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+ "text": "Autoregressive Latent Mapper: Instead of predicting the latent code $w_{s}^{+} = \\{w_{1}^{+},\\dots ,w_{k}^{+}\\}$ in one shot, we aim to model it in an autoregressive setting keeping a sequential dependency among them. Given an input sketch (s), the autoregressive sketch mapper $\\mathcal{E}_s$ modelling the distribution $P(w_s^+ |s)$ can be mathematically expressed as:",
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+ "text": "\n$$\nP \\left(w _ {s} ^ {+} \\mid s\\right) = P \\left(w _ {1} ^ {+}, \\dots , w _ {k} ^ {+} \\mid s\\right) = \\prod_ {i = 1} ^ {k} P \\left(w _ {i} ^ {+} \\mid w _ {< k} ^ {+}, s\\right) \\tag {3}\n$$\n",
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+ "text": "where the value of the $i^{th}$ predicted latent vector $w_{i}^{+}$ depends on all preceding latents. The motivations behind autoregressive modelling are: (i) the disentangled latent space",
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+ "text": "of a StyleGAN depicts semantic feature hierarchy [94], where the latent code $w_{1}^{+}$ to $w_{14}^{+}$ controls coarse to fine-level features. (ii) a highly abstract/partial sketch should ideally influence the first few latent vectors governing the major semantic structure, while the later vectors could be sampled randomly from a Gaussian distribution to account for the uncertainty involving such sparse sketches. Whereas, a highly detailed sketch should influence more latent vectors to faithfully reproduce the user's intent. (iii) we aim to synergise the disentangled property of StyleGAN's latent space and the varying levels of sketch abstraction such that the user has the provision to decide how far should the generated output be conditioned on the input sketch and to what extent can it be hallucinated. This is decided by the number of steps of unrolling in the autoregressive process and additionally keeping the later latent codes as random vectors to facilitate multi-modal generation [69].",
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+ "text": "Given the extracted feature map $f_{s} = \\mathcal{F}_{s}(s)$ , the global average pooled holistic visual feature vector $v_{h}$ is transformed via a fully-connected (FC) layer to initialise the first hidden state of sequential decoder $f_{seq}(\\cdot, \\cdot)$ as $h_0 = \\tanh(W_h \\otimes v_h + b_h)$ , with $W_{h}, b_{h}$ being trainable parameters. At every $j^{th}$ time step, we apply a shared FC-layer on the hidden state $h_j$ to obtain the $j^{th}$ latent code as $w_{k}^{+} = W_{o} \\otimes h_{j} + b_{o}$ . The current hidden state is updated by $h_k = f_{seq}(h_{k-1}; \\eta(f_s, w_{k-1}^+)$ ), where the previous hidden state of sequential decoder $h_{k-1}$ holds the knowledge about previously predicted latent codes, and $\\eta$ models the influence of the formerly predicted latent code on the next prediction along with extracting the relevant information from the feature map $f_{s}$ . In order to model the interaction between $w_{k}^{+}$ and $f_{s}$ , we use a simple Hadamard product $\\hat{f}_s = f_s \\odot w_{k-1}^+ \\in \\mathbb{R}^{h_f \\times w_f \\times d}$ which upon passing through successive two-strided convolutional layers followed by LeakyReLU produces a $d$ -dimensional output of $\\eta$ . $f_{seq}(\\cdot, \\cdot)$ can be modelled using any sequential network (e.g., LSTM [37], RNN [59], GRU [17]) or self-attention based transformer [83] network. However, here we use GRU [17], as it was empirically found to be easily optimisable and cheaper while producing compelling results. We wrap this entire process inside the sketch mapper $\\mathcal{E}_s$ .",
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+ "text": "To allow multi-modal generation, we always predict a maximum 10 out of the 14 unique latent vectors and sample the rest 4 from Gaussian distribution to inject output variation [69]. Moreover, to enforce our model in learning to generate from partial sketches, we introduce a smart augmentation strategy, where, we partially render the sketch from $30 - 100\\%$ at an interval of $10\\%$ . While feeding the $\\{30\\%, 40\\%, \\dots, 100\\}$ sketches, we enforce the mapper to predict only the first $m = \\{3, 4, \\dots, 10\\}$ corresponding latent vectors. In every case, we pass random vectors sampled from Gaussian distribution in place of the remaining $(14 - m)$ unpredicted vectors. This strategy ensures that",
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+ "Figure 3. $\\mathcal{E}_s$ learns to map a sketch to the latent code of its paired photo in a pre-trained StyleGAN manifold, trained with a mix of reconstruction, fine-grained discriminative, and distillation losses. our model eventually learns to generate plausible photos at varying levels of completion, thus allowing the user to control the extent of abstraction as per his/her choice."
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+ "text": "5.2. Training Procedure",
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+ "text": "Reconstruction Loss: Given an input sketch-photo pair $\\{s, r\\}$ and the generated output photo $\\hat{r} = \\mathcal{G}(\\mathcal{E}_s(s))$ , we compute pixel level $l_2$ reconstruction loss as:",
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+ "text": "\n$$\n\\mathcal {L} _ {\\mathrm {r e c}} (r, \\hat {r}) = | | r - \\hat {r} | | _ {2} \\tag {4}\n$$\n",
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+ "text": "Besides pixel-wise similarity, we also learn perceptual similarities via LPIPS [102] loss, which has been found [32] to retain photorealism. With $\\phi(\\cdot)$ as the pre-trained perceptual feature encoder [102], LPIPS loss becomes:",
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+ "text": "\n$$\n\\mathcal {L} _ {\\mathrm {L P I P S}} (\\boldsymbol {r}, \\hat {\\boldsymbol {r}}) = | | \\phi (\\boldsymbol {r}) - \\phi (\\hat {\\boldsymbol {r}}) | | _ {2} \\tag {5}\n$$\n",
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+ "text": "Fine-Grained Discriminative Loss: While reconstruction loss aims to align the pixel values between generated and ground-truth photo, the discriminative sketchphoto (paired) association compared to other photos needs to be modelled further to reflect the fine-grained user intent of input sketch in the output space. Triplet with cosine-distance based pre-trained fine-grained SBIR [19] model $\\mathcal{F}_g(\\cdot)$ places a sketch nearer to its paired photo compared to others in a joint-embedding space. Therefore, we compute a discriminative fine-grained loss that measures the cosine similarity between $s$ and $\\hat{r}$ as:",
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+ "text": "\n$$\n\\mathcal {L} _ {\\text {d i s c}} (s, \\hat {r}) = 1 - \\frac {\\mathcal {F} _ {g} (s) \\cdot \\mathcal {F} _ {g} (\\hat {r})}{| | \\mathcal {F} _ {g} (s) | | | | \\mathcal {F} _ {g} (\\hat {r}) | |} \\tag {6}\n$$\n",
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+ "text": "Photo-to-Photo Mapper as Teacher: Photo-to-photo mapping being an easier task than sketch-to-photo underpins our motivation towards introducing a photo-to-photo mapper $\\mathcal{E}_r(\\cdot)$ as a teacher [27] to additionally guide the learning of our sketch-mapper $\\mathcal{E}_s(\\cdot)$ , thus handling the subjective nature of sketches and its resultant large sketchphoto domain gap. Architecturally, $\\mathcal{E}_r(\\cdot)$ is identical to our baseline $\\mathcal{E}_s(\\cdot)$ with the aim of reconstructing the input photo $(r)$ at the output $(\\hat{r})$ : $\\mathcal{G}(\\mathcal{E}_r(r)) \\approx \\hat{r}$ . Once trained, latent vectors predicted by $\\mathcal{E}_r$ (weights frozen) acts as a groundtruth additionally supervising $\\mathcal{E}_s$ via a distillation loss as:",
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+ "text": "\n$$\n\\mathcal {L} _ {\\mathrm {K D}} (s, r) = \\left| \\left| \\mathcal {E} _ {s} (s) - \\mathcal {E} _ {r} (r) \\right| \\right| _ {2} \\tag {7}\n$$\n",
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+ "text": "We impose $\\mathcal{L}_{\\mathrm{KD}}$ only on the predicted latents (max 10) not on the random ones. Our overall training objective is $\\mathcal{L}_{\\mathrm{total}} = \\lambda_1\\mathcal{L}_{\\mathrm{rec}} + \\lambda_2\\mathcal{L}_{\\mathrm{LPIPS}} + \\lambda_3\\mathcal{L}_{\\mathrm{disc}} + \\lambda_4\\mathcal{L}_{\\mathrm{KD}}$ .",
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+ "text": "6. Experiments",
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+ "text": "Dataset: UT Zappos50K [98] and pix2pix Handbag [41] datasets are used to pre-train the StyleGAN generator in shoe and handbag classes respectively. While for chair class, we collected over 10,000 photos from websites like IKEA, ARGOS, etc. We used QMUL-ShoeV2 [12, 80], QMUL-ChairV2 [12, 80], and Handbag [81] datasets containing sketch-photo pairs to train the sketch mapper. Out of 6730/1800/568 sketches and 2000/400/568 photos from ShoeV2/ChairV2/Handbag datasets, 6051/1275/400 sketches and 1800/300/400 photos are used for training respectively, keeping the rest for testing. Notably, StyleGAN pre-training does not involve any sketch-photo pairs.",
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+ "text": "Implementation Details: Adam [49] optimiser is used to pre-train a category specific StyleGAN [47] with feature embedding size of $d = 512$ for $8M$ iterations at learning rate of $10^{-3}$ and batch size 8. Based on empirical observations, we disable path-length regularisation [47] and reduce $R1$ regularisation's weight to 2 for superior quality and diversity. We use a combination of Rectified Adam [56] and Lookahead [101] method as an optimiser to train the sketch-to-photo mapper for $5M$ iterations at a constant learning rate of $10^{-5}$ and a batch size of 4. $\\lambda_1, \\lambda_2, \\lambda_3$ , and $\\lambda_4$ are set to 1, 0.8, 0.5, and 0.6 respectively.",
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+ "text": "Evaluation: We use four metrics - (i) Fréchet Inception Distance (FID) [46]: uses pre-trained InceptionV3's activation distribution statistics to estimate distance between synthetic and real data where a lower value indicates better generation quality. (ii) Learned Perceptual Image Patch Similarity (LPIPS) [102]: is a weighted $l_{2}$ distance between two ImageNet-pretrained AlexNet [50]-extracted deep features of ground-truth and generated images. A higher LPIPS value denotes better diversity. (iii) Mean Opinion Score (MOS): for human study, each of the 30 human workers was asked to draw 50 sketches in our system, and rate every generated photo (both ours and competitor's) on a scale of 1 to 5 [39] (bad→excellent) based on their opinion of how closely it matched their photorealistic imagination of the associated sketch. For each method, we compute the final MOS value by taking the mean $(\\mu)$ and variance $(\\sigma)$ of all 1500 of its MOS responses. (iv) Fine-Grained Metric (FGM): to judge the fine-grainedness of sketch mapping, we propose a new metric, which uses features from a pretrained FG-SBIR model [100] to compute cosine similarity between input sketch and generated photo. A higher FGM value denotes better fine-grained association between them.",
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+ "text": "Competitors: We compare our proposed framework with various state-of-the-art (SOTA) methods and two self-designed baselines. Among those, pix2pix [41] uses a conditional generative model for sketch-to-photo translation. MUNIT [38] aims to produce diverse outputs given one input sketch. It tries to decompose an image into a content and",
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+ "text": "a style code followed by learning those codes simultaneously. CycleGAN [105] utilises cycle-consistency loss with a GAN model for bidirectional image-to-image translation. U-GAT-IT [48] uses an attention module for image translation while focusing on the domain-discriminative parts. Moreover, employing a pre-trained StyleGAN [47] we compare with the baseline B-Sketch Mapper which is equivalent to the baseline sketch mapper described in Sec. 5.1. Following optimisation-based GAN inversion [1], we design B-Sketch Optimiser where we iteratively optimise the latent code using input sketch as a ground-truth with perceptual loss [102]. For a fair comparison, we trained all competing methods in a supervised manner with sketch-photo pairs from ShoeV2, ChairV2, and Handbag datasets.",
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+ "text": "6.1. Performance Analysis & Discussion",
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+ "text": "Result Analysis: The proposed method consistently surpasses (Table 2) other state-of-the-arts in terms of quality (FID), and diversity (LPIPS). Pix2pix [41] with its naive conditional image-to-image translation formulation is outperformed by CycleGAN [105] (by $-14.26$ FID on ShoeV2), as the latter is reinforced with a cycle consistency loss in an adversarial training paradigm in addition to the bidirectional guidance. U-GAT-IT [48] with its attention-based formulation, surpasses others proving the efficacy of attention-module in image translation tasks. Although MU-NIT [38] and pSp [69] supports multi-modal generation, our method, excels both in terms of output diversity (0.489 LPIPS on ShoeV2). Naive Baselines of B-Sketch Mapper and B-Sketch Optimiser with their simplistic design fall short of surpassing the proposed framework. Our method achieves the highest (Table 2) degree of fine-grained association (0.88 FGM on ShoeV2), thanks to its novel fine-grained discriminative loss. When compared to our framework, there exists a noticeable deformity in the photos generated by its competitors (Fig. 4). Photos generated by pix2pix [41], MUNIT [38] and CycleGAN [105] suffer from deformity and lack of photorealism. Although U-GAT-IT [48] and pSp [69] outputs are somewhat realistic, they are mostly unfaithful to the input sketch. As observed from Fig. 4, the photos generated by SOTA methods almost invariably fail to capture the semantic intent of the user, yielding deformed images. Contrarily, given the visually pleasing (Fig. 4), and richer generation quality, our method vastly outperforms most SOTA and baselines in terms of MOS value (Table 2). Furthermore, our method can replicate the appearance of a given photo onto the generated one (Fig. 4) by predicting coarse and mid-level latent codes from the input sketch and taking the fine-level codes of the reference photo predicted by our photo-to-photo mapper.",
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+ "text": "In summary, with the help of smooth [6] latent space of StyleGAN [46, 47] along with auto-regressive sketch mapper and the fine-grained discriminative loss, our approach almost always ensures photorealistic translations with ac",
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+ "img_path": "images/dc0ee4b31e3c44409421c7bec8de51b69245aa7d1bd019246ebf031b2730e00c.jpg",
+ "image_caption": [
+ "Figure 4. Qualitative comparison with various state-of-the-art competitors on ShoeV2 dataset. Ours-ref (column 3) results depict that our method can faithfully replicate the appearance of a given reference photo (shown in the top-right inset)."
+ ],
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+ "img_path": "images/b4a5fc509b59213a0ff2bb9377df9fc3bfc533c3251ffa085bc471d543f17a95.jpg",
+ "table_caption": [
+ "Table 2. Benchmarks on ChairV2, ShoeV2, and Handbag datasets."
+ ],
+ "table_footnote": [],
+ "table_body": "| Paper | Category | Type of Sketch | Data Preparation + Salient Design Component |
| SketchyGAN [16] | Categorical | Synth+Real | • Fully automatic edemap augmentation + input injection at multiple layers. |
| iSketch&Fill [30] | Categorical | Synthetic | • Edemap creation with Im2Pencil [54] and sketch-simplification [77] + ResNet [35] generator. |
| CoGS [33] | Categorical | Synth+Real | • Saliency with [40] for synthetic sketches + VQ-GAN [25] with VAE over codebook vectors. |
| ContextGAN [58] | Semi-FG | Synthetic | • Synthetic sketch generation with XDoG [87] and [43] + optimisation-based GAN inversion. |
| Two-Stage [57] | Semi-FG | Real | • Synthetic noisy-stroke for augmentation + two-stage sketch-to-edemap-to-photo generation. |
| SYO-GAN [86] | Semi-FG | Synthetic | • Pseudo sketch creation with PhotoSketch [52] + fine-tuning GAN model with a few pose-specific sketches. |
| SketchyCOCO [29] | Scene-level | Semi-real | • Synthetic scene sketch + generation of foreground object followed by contextual background. |
| Two-Stage [85] | Scene-level | Synthetic | • Edemaps generated with [66] + edemap standardisation followed by content-style disentanglement. |
| DeepFaceDraw [15] | Facial photo | Synthetic | • Photocopy filter and [77] for training data + region-wise embedding with 2-stage generation. |
| Controlled S2I [96] | Facial photo | Synthetic | • HED [92] for edemaps + dilation-based sketch refinement network for adapting edge-based models. |
| Proposed | Fine-grained | Real | • Unlabelled photos & sketch-photo pairs + autoregressive latent-mapper & pre-trained StyleGAN [46]. |
"
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+ "type": "text",
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+ "content": "outputs, StyleGAN [46, 47] introduced a non-linear mapping from input code vector \\( z \\in \\mathcal{Z} \\) to intermediate latent code \\( w \\in \\mathcal{W} \\), which controlled the generation process. While traditional GAN is unable to generate conditional output, it can be augmented with additional information to conditionally control the data generation process [61]. However, existing conditional generative [55, 79] models are unable to inject fine-grained control, especially when conditioned with abstract free-hand sketches."
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+ "type": "text",
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+ "content": "GAN Inversion: Exploring GANs has recently led to an interest in inverting a pre-trained GAN [4] for tasks like image manipulation [4]. Typical GAN training aims to learn the weights of generator and discriminator with appropriate loss objectives, to generate random new images \\(G(z)\\) by sampling random noise vectors \\(z \\in \\mathcal{Z}\\) [31]. Contrarily, during GAN inversion, given a reference image we try to find a noise vector \\(z^{*}\\) in the generator latent space that can accurately reconstruct that image while its weights fixed [104]. While some methods [1,2,22,23] directly optimise the latent vector to minimise the reconstruction loss, a few works [4,32,69,82] train dedicated encoders to find the latent code corresponding to an input image. Among them, optimisation-based methods perform better in terms of reconstruction accuracy, while encoding-based methods work significantly faster. Other methods [5, 103], take a hybrid approach in order to attain \"the best of both worlds\" [88]. However, images from different domain (e.g., semantic label map, edgemap) are not invertible into the latent space of a photo pre-trained generator [6]. Consequently, end-to-end trainable methods [3,14,63,69] emerged which aims to map a given image (from a source domain) into the latent space of a pre-trained GAN trained with target domain images. These learned encoders are then used in tasks like, inversion [4], semantic editing [4], super-resolution [60], face frontalisation [69], inpainting [69]."
+ },
+ {
+ "type": "title",
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+ "content": "3. Pilot Study: Problems and Analysis"
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+ "content": "Challenges: Sketches being highly abstract in nature, generating a photo from a sketch can have multiple possible outcomes [69]. Generating photorealistic images from sparse sketches incurs three major challenges – (i) Locality-bias assumes that any particular output (e.g., photo) pixel"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "position \\( I'(x, y) \\) is perfectly aligned with the same pixel location \\( I(x, y) \\) of the conditional input (e.g., sketch) [69]. However, a free-hand sketch being highly deformed does not necessarily follow the paired photo's intensity boundary [36]. (ii) Hallucinating the colour/texture in a realistic and contextually-meaningful manner, is difficult from sparse sketch input. (iii) Deciphering the fine-grained user intent is a major bottleneck as the same object can be sketched in diverse ways by different users [75]."
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+ "content": "Analysis: The popular encoder-decoder architecture [41] for converting an input sketch \\(S\\) to output RGB photo \\(\\mathcal{R}\\) via image-to-image translation [41] can be formulated as:"
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+ "content": "\\[\nP (\\mathcal {R} | \\mathcal {S}) = \\underbrace {P (\\mathcal {Z} | \\mathcal {S})} _ {\\text {E n c o d e r}} \\underbrace {P (\\mathcal {R} | \\mathcal {Z})} _ {\\text {D e c o d e r}} \\tag {1}\n\\]"
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "where the encoder \\( P(\\mathcal{Z}|\\mathcal{S}) \\) embeds the sketch into a latent feature \\( \\mathcal{Z} \\), from which the decoder \\( P(\\mathcal{R}|\\mathcal{Z}) \\) generates the output photo. Existing works [18, 38, 105] have evolved through designing task-specific encoder/decoder frameworks. Despite achieving remarkable success in other image translation problems (e.g., image-restoration [67], colourisation [41]), adapting them off-the-shelf fails for our setup. Importantly, we realise that as the loss backpropagates from the decoder to encoder's end, while training [41] with sketch-photo pairs \\( (\\mathcal{S},\\mathcal{R}) \\), it implicitly enforces the model to follow sketch as a pseudo edge-boundary [57]. Consequently, the model is hard-conditioned by the sketch to treat its strokes as the intensity boundary of the generated photo, thus resulting in a deformed output."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Instead of end-to-end encoder-decoder training, we adopt a two stage-approach (Fig. 2). In the first stage, we model \\( P(\\mathcal{R}|\\mathcal{Z}) \\) as an unsupervised GAN [31], which being trained from a large number of unlabeled photos of a particular class, is capable of generating realistic photos \\( G(z) \\), given a random vector \\( z \\sim \\mathcal{N}(0,1) \\) [31]. As GAN models learn data distribution [68], we can loosely assume that any photo can be generated by sampling a specific \\( z^* \\) from the GAN latent space [1]. Once the GAN model is trained, in the second stage, keeping the \\( G(\\cdot) \\) fixed, we aim to learn \\( P(\\mathcal{Z}|\\mathcal{S}) \\) as a sketch mapper that would encode the input sketch \\( S \\) into a latent code \\( \\mathcal{Z} \\) corresponding to the paired photo \\( \\mathcal{R} \\) in the pre-trained GAN latent space."
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+ [
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+ "content": "Advantages of decoupling the encoder-decoder training are twofold - (i) the GAN model [46, 47] pre-trained on real photos is bound to generate realistic photos devoid of unwanted deformation, (ii) while output quality and diversity of coupled encoder-decoder models were limited by the training sketch-photo pairs [41], our decoupled decoder being independent of such pairs, can model the large variation of a particular dataset using unlabelled photos [46, 47] only. Sketch-photo pairs are used to train the sketch mapper only."
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+ "angle": 0,
+ "content": "Figure 2. The sketch mapper aims to predict the corresponding latent code of associated photo in the manifold of pre-trained GAN."
+ },
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+ "content": "4. Background: StyleGAN"
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+ "bbox": [
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+ "angle": 0,
+ "content": "In a GAN [31] framework, a generator \\(G(\\cdot)\\) aims to generate an image \\(G(z)\\) from a noise vector \\(z \\in \\mathcal{Z}\\) of size \\(\\mathbb{R}^d\\) sampled from a Gaussian distribution [31], while a discriminator \\(D(\\cdot)\\) tries to distinguish between a real and a generated fake image [31]. The training progresses through a two-player minimax game, thus gradually improving each other over the value function \\(V(D,G)\\) as [31]:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
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+ "angle": 0,
+ "content": "\\[\n\\begin{array}{l} \\min _ {G} \\max _ {D} V (D, G) = \\mathbb {E} _ {x \\sim p _ {\\text {d a t a}} (x)} [ \\log D (x) ] \\tag {2} \\\\ + \\mathbb {E} _ {z \\sim p _ {z} (z)} [ \\log (1 - D (G (z))) ] \\\\ \\end{array}\n\\]"
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Instead of passing a random noise vector \\( z \\in \\mathcal{Z} \\) directly as the network input [68], StyleGAN [46, 47] eliminates the idea of input layer and always starts from a learned constant tensor of size \\( \\mathbb{R}^{4 \\times 4 \\times d} \\). The generator network \\( \\mathcal{G}(\\cdot) \\) consists of a number of progressive resolution blocks, each having the sequence \\( \\mathrm{conv}3 \\times 3 \\to \\mathrm{AdaIN} \\to \\mathrm{conv}3 \\times 3 \\to \\mathrm{AdaIN} \\) [46, 47]. StyleGAN employs a non-linear mapping network \\( f: \\mathcal{Z} \\to \\mathcal{W} \\) (an 8-layer MLP) to transform \\( z \\) into an intermediate latent vector \\( w \\in \\mathcal{W} \\) of size \\( \\mathbb{R}^d \\) [46, 47]. The same latent vector \\( w \\), upon repeatedly passing through a common affine transformation layer \\( A \\) at each level of the generator network, generates the style \\( y = (y_s, y_b) = A(w) \\) for that level. Adaptive instance normalisation (AdaIN) [46, 47] is then controlled by \\( y \\) via modulating the feature-map \\( x_f \\) as \\( \\mathrm{AdaIN}(x_f, y) = y_s \\frac{x_f - \\mu(x_f)}{\\sigma(x_f)} + y_b \\) after each \\( \\mathrm{conv}3 \\times 3 \\) block of \\( \\mathcal{G}(\\cdot) \\) [46, 47]. Moreover, stochasticity is injected by adding one-channel uncorrelated Gaussian noise image (per-channel scaled with a learned scaling factor \\( B \\)) to each layer of the network before every AdaIN operation [46, 47]."
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "However, due to the limited representability and disentanglement of a single latent vector \\( w \\in \\mathcal{W} \\) [1], we embed the input in the extended \\( \\mathcal{W}^+ \\) latent space [1] consisting of different latent vectors \\( w^+ \\in \\mathcal{W}^+ \\) of size \\( \\mathbb{R}^{k \\times d} \\), one for each level of the generator network \\( \\mathcal{G}(\\cdot) \\). For an output of"
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "resolution \\( M \\times M \\), \\( k = 2\\log_2(M) - 2 \\) [47]. In this work, we set \\( M = 256 \\), making \\( k = 14 \\)."
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+ "content": "5. Sketch-to-Photo Generation Model"
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+ "content": "Overview: We aim to devise a sketch-to-photo generation model utilising the rich latent space of a pre-trained StyleGAN [47] trained on a particular class to achieve fine-grained generation. Once the StyleGAN [47] is trained, we fix its weights and train a sketch mapper \\(\\mathcal{E}_s\\) that projects an input sketch \\((s)\\) into a latent code \\(w_{s}^{+} = \\mathcal{E}_{s}(s)\\in \\mathbb{R}^{14\\times d}\\) lying in the manifold of pre-trained StyleGAN. In other words, given a sketch input we aim to pick the corresponding latent which when passed through the frozen generator \\(\\mathcal{G}(\\cdot)\\) would generate an output \\((\\hat{r})\\) most similar to the ground-truth paired photo \\((r)\\). In particular, we have three salient design components: (i) an autoregressive sketch mapper (ii) fine-grained discriminative loss besides usual reconstruction objective, and (iii) a photo-to-photo mapper \\(\\mathcal{E}_r\\) working as a teacher [27] to improve the learning of \\(\\mathcal{E}_s\\)."
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+ "content": "5.1. Model Architecture"
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+ "content": "Baseline Sketch Mapper: Inspired by GAN inversion literature [88], we design our baseline sketch mapper using a ResNet50 [35] backbone extracting feature map \\( f_{s} = \\mathcal{F}_{s}(s) \\in \\mathbb{R}^{h_{f} \\times w_{f} \\times d} \\). In order to generate the latent code of size \\( \\mathbb{R}^{14 \\times d} \\), we use 14 individual (not shared) latent embedding networks (successive stride-two conv-layers with LeakyReLU [93]), each of them takes \\( f_{s} \\) as input to predict a \\( d \\)-dimensional latent vector. Concatenating them results in the \\( \\mathbb{R}^{14 \\times d} \\) latent code [69]. Finally, this latent code upon passing through the pre-trained generator \\( \\mathcal{G}(\\cdot) \\) generates the output photo \\( \\hat{r} \\). Trained with weighted summation of pixel loss \\( (l_{2}) \\) and perceptual [102] loss, baseline sketch mapper eventually learns to map an input sketch to its corresponding photo in the latent space of a pre-trained StyleGAN [47]."
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+ "content": "However, it has a few limitations: Firstly, this baseline ignores the varying levels of sketch abstraction [95]. Ideally, for highly abstract/partial sketches, the output space should be large with many plausible RGB photos [12], whereas, for a detailed sketch, it should reflect the fine-grained details. Secondly, reconstruction loss [69] alone, fails to decipher the fine-grained semantic intent of the user."
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+ "content": "Autoregressive Latent Mapper: Instead of predicting the latent code \\( w_{s}^{+} = \\{w_{1}^{+},\\dots ,w_{k}^{+}\\} \\) in one shot, we aim to model it in an autoregressive setting keeping a sequential dependency among them. Given an input sketch (s), the autoregressive sketch mapper \\( \\mathcal{E}_s \\) modelling the distribution \\( P(w_s^+ |s) \\) can be mathematically expressed as:"
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+ "content": "\\[\nP \\left(w _ {s} ^ {+} \\mid s\\right) = P \\left(w _ {1} ^ {+}, \\dots , w _ {k} ^ {+} \\mid s\\right) = \\prod_ {i = 1} ^ {k} P \\left(w _ {i} ^ {+} \\mid w _ {< k} ^ {+}, s\\right) \\tag {3}\n\\]"
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+ "angle": 0,
+ "content": "where the value of the \\(i^{th}\\) predicted latent vector \\(w_{i}^{+}\\) depends on all preceding latents. The motivations behind autoregressive modelling are: (i) the disentangled latent space"
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+ "content": "of a StyleGAN depicts semantic feature hierarchy [94], where the latent code \\( w_{1}^{+} \\) to \\( w_{14}^{+} \\) controls coarse to fine-level features. (ii) a highly abstract/partial sketch should ideally influence the first few latent vectors governing the major semantic structure, while the later vectors could be sampled randomly from a Gaussian distribution to account for the uncertainty involving such sparse sketches. Whereas, a highly detailed sketch should influence more latent vectors to faithfully reproduce the user's intent. (iii) we aim to synergise the disentangled property of StyleGAN's latent space and the varying levels of sketch abstraction such that the user has the provision to decide how far should the generated output be conditioned on the input sketch and to what extent can it be hallucinated. This is decided by the number of steps of unrolling in the autoregressive process and additionally keeping the later latent codes as random vectors to facilitate multi-modal generation [69]."
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+ "content": "Given the extracted feature map \\( f_{s} = \\mathcal{F}_{s}(s) \\), the global average pooled holistic visual feature vector \\( v_{h} \\) is transformed via a fully-connected (FC) layer to initialise the first hidden state of sequential decoder \\( f_{seq}(\\cdot, \\cdot) \\) as \\( h_0 = \\tanh(W_h \\otimes v_h + b_h) \\), with \\( W_{h}, b_{h} \\) being trainable parameters. At every \\( j^{th} \\) time step, we apply a shared FC-layer on the hidden state \\( h_j \\) to obtain the \\( j^{th} \\) latent code as \\( w_{k}^{+} = W_{o} \\otimes h_{j} + b_{o} \\). The current hidden state is updated by \\( h_k = f_{seq}(h_{k-1}; \\eta(f_s, w_{k-1}^+) \\)), where the previous hidden state of sequential decoder \\( h_{k-1} \\) holds the knowledge about previously predicted latent codes, and \\( \\eta \\) models the influence of the formerly predicted latent code on the next prediction along with extracting the relevant information from the feature map \\( f_{s} \\). In order to model the interaction between \\( w_{k}^{+} \\) and \\( f_{s} \\), we use a simple Hadamard product \\( \\hat{f}_s = f_s \\odot w_{k-1}^+ \\in \\mathbb{R}^{h_f \\times w_f \\times d} \\) which upon passing through successive two-strided convolutional layers followed by LeakyReLU produces a \\( d \\)-dimensional output of \\( \\eta \\). \\( f_{seq}(\\cdot, \\cdot) \\) can be modelled using any sequential network (e.g., LSTM [37], RNN [59], GRU [17]) or self-attention based transformer [83] network. However, here we use GRU [17], as it was empirically found to be easily optimisable and cheaper while producing compelling results. We wrap this entire process inside the sketch mapper \\( \\mathcal{E}_s \\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.076,
+ 0.72,
+ 0.473,
+ 0.904
+ ],
+ "angle": 0,
+ "content": "To allow multi-modal generation, we always predict a maximum 10 out of the 14 unique latent vectors and sample the rest 4 from Gaussian distribution to inject output variation [69]. Moreover, to enforce our model in learning to generate from partial sketches, we introduce a smart augmentation strategy, where, we partially render the sketch from \\(30 - 100\\%\\) at an interval of \\(10\\%\\). While feeding the \\(\\{30\\%, 40\\%, \\dots, 100\\}\\) sketches, we enforce the mapper to predict only the first \\(m = \\{3, 4, \\dots, 10\\}\\) corresponding latent vectors. In every case, we pass random vectors sampled from Gaussian distribution in place of the remaining \\((14 - m)\\) unpredicted vectors. This strategy ensures that"
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.503,
+ 0.089,
+ 0.891,
+ 0.224
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.498,
+ 0.224,
+ 0.894,
+ 0.316
+ ],
+ "angle": 0,
+ "content": "Figure 3. \\(\\mathcal{E}_s\\) learns to map a sketch to the latent code of its paired photo in a pre-trained StyleGAN manifold, trained with a mix of reconstruction, fine-grained discriminative, and distillation losses. our model eventually learns to generate plausible photos at varying levels of completion, thus allowing the user to control the extent of abstraction as per his/her choice."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.5,
+ 0.32,
+ 0.688,
+ 0.336
+ ],
+ "angle": 0,
+ "content": "5.2. Training Procedure"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.5,
+ 0.337,
+ 0.892,
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+ ],
+ "angle": 0,
+ "content": "Reconstruction Loss: Given an input sketch-photo pair \\(\\{s, r\\}\\) and the generated output photo \\(\\hat{r} = \\mathcal{G}(\\mathcal{E}_s(s))\\), we compute pixel level \\(l_2\\) reconstruction loss as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.622,
+ 0.382,
+ 0.891,
+ 0.399
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {\\mathrm {r e c}} (r, \\hat {r}) = | | r - \\hat {r} | | _ {2} \\tag {4}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.498,
+ 0.4,
+ 0.892,
+ 0.461
+ ],
+ "angle": 0,
+ "content": "Besides pixel-wise similarity, we also learn perceptual similarities via LPIPS [102] loss, which has been found [32] to retain photorealism. With \\(\\phi(\\cdot)\\) as the pre-trained perceptual feature encoder [102], LPIPS loss becomes:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.591,
+ 0.464,
+ 0.891,
+ 0.481
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {\\mathrm {L P I P S}} (\\boldsymbol {r}, \\hat {\\boldsymbol {r}}) = | | \\phi (\\boldsymbol {r}) - \\phi (\\hat {\\boldsymbol {r}}) | | _ {2} \\tag {5}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.498,
+ 0.482,
+ 0.892,
+ 0.646
+ ],
+ "angle": 0,
+ "content": "Fine-Grained Discriminative Loss: While reconstruction loss aims to align the pixel values between generated and ground-truth photo, the discriminative sketchphoto (paired) association compared to other photos needs to be modelled further to reflect the fine-grained user intent of input sketch in the output space. Triplet with cosine-distance based pre-trained fine-grained SBIR [19] model \\(\\mathcal{F}_g(\\cdot)\\) places a sketch nearer to its paired photo compared to others in a joint-embedding space. Therefore, we compute a discriminative fine-grained loss that measures the cosine similarity between \\(s\\) and \\(\\hat{r}\\) as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.571,
+ 0.643,
+ 0.891,
+ 0.677
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {\\text {d i s c}} (s, \\hat {r}) = 1 - \\frac {\\mathcal {F} _ {g} (s) \\cdot \\mathcal {F} _ {g} (\\hat {r})}{| | \\mathcal {F} _ {g} (s) | | | | \\mathcal {F} _ {g} (\\hat {r}) | |} \\tag {6}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.498,
+ 0.677,
+ 0.892,
+ 0.842
+ ],
+ "angle": 0,
+ "content": "Photo-to-Photo Mapper as Teacher: Photo-to-photo mapping being an easier task than sketch-to-photo underpins our motivation towards introducing a photo-to-photo mapper \\(\\mathcal{E}_r(\\cdot)\\) as a teacher [27] to additionally guide the learning of our sketch-mapper \\(\\mathcal{E}_s(\\cdot)\\), thus handling the subjective nature of sketches and its resultant large sketchphoto domain gap. Architecturally, \\(\\mathcal{E}_r(\\cdot)\\) is identical to our baseline \\(\\mathcal{E}_s(\\cdot)\\) with the aim of reconstructing the input photo \\((r)\\) at the output \\((\\hat{r})\\): \\(\\mathcal{G}(\\mathcal{E}_r(r)) \\approx \\hat{r}\\). Once trained, latent vectors predicted by \\(\\mathcal{E}_r\\) (weights frozen) acts as a groundtruth additionally supervising \\(\\mathcal{E}_s\\) via a distillation loss as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.591,
+ 0.843,
+ 0.891,
+ 0.86
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {\\mathrm {K D}} (s, r) = \\left| \\left| \\mathcal {E} _ {s} (s) - \\mathcal {E} _ {r} (r) \\right| \\right| _ {2} \\tag {7}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.498,
+ 0.861,
+ 0.892,
+ 0.907
+ ],
+ "angle": 0,
+ "content": "We impose \\(\\mathcal{L}_{\\mathrm{KD}}\\) only on the predicted latents (max 10) not on the random ones. Our overall training objective is \\(\\mathcal{L}_{\\mathrm{total}} = \\lambda_1\\mathcal{L}_{\\mathrm{rec}} + \\lambda_2\\mathcal{L}_{\\mathrm{LPIPS}} + \\lambda_3\\mathcal{L}_{\\mathrm{disc}} + \\lambda_4\\mathcal{L}_{\\mathrm{KD}}\\)."
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.483,
+ 0.945,
+ 0.516,
+ 0.957
+ ],
+ "angle": 0,
+ "content": "6854"
+ }
+ ],
+ [
+ {
+ "type": "title",
+ "bbox": [
+ 0.077,
+ 0.091,
+ 0.21,
+ 0.108
+ ],
+ "angle": 0,
+ "content": "6. Experiments"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.076,
+ 0.112,
+ 0.47,
+ 0.295
+ ],
+ "angle": 0,
+ "content": "Dataset: UT Zappos50K [98] and pix2pix Handbag [41] datasets are used to pre-train the StyleGAN generator in shoe and handbag classes respectively. While for chair class, we collected over 10,000 photos from websites like IKEA, ARGOS, etc. We used QMUL-ShoeV2 [12, 80], QMUL-ChairV2 [12, 80], and Handbag [81] datasets containing sketch-photo pairs to train the sketch mapper. Out of 6730/1800/568 sketches and 2000/400/568 photos from ShoeV2/ChairV2/Handbag datasets, 6051/1275/400 sketches and 1800/300/400 photos are used for training respectively, keeping the rest for testing. Notably, StyleGAN pre-training does not involve any sketch-photo pairs."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.076,
+ 0.3,
+ 0.471,
+ 0.466
+ ],
+ "angle": 0,
+ "content": "Implementation Details: Adam [49] optimiser is used to pre-train a category specific StyleGAN [47] with feature embedding size of \\( d = 512 \\) for \\( 8M \\) iterations at learning rate of \\( 10^{-3} \\) and batch size 8. Based on empirical observations, we disable path-length regularisation [47] and reduce \\( R1 \\) regularisation's weight to 2 for superior quality and diversity. We use a combination of Rectified Adam [56] and Lookahead [101] method as an optimiser to train the sketch-to-photo mapper for \\( 5M \\) iterations at a constant learning rate of \\( 10^{-5} \\) and a batch size of 4. \\( \\lambda_1, \\lambda_2, \\lambda_3 \\), and \\( \\lambda_4 \\) are set to 1, 0.8, 0.5, and 0.6 respectively."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.076,
+ 0.472,
+ 0.47,
+ 0.805
+ ],
+ "angle": 0,
+ "content": "Evaluation: We use four metrics - (i) Fréchet Inception Distance (FID) [46]: uses pre-trained InceptionV3's activation distribution statistics to estimate distance between synthetic and real data where a lower value indicates better generation quality. (ii) Learned Perceptual Image Patch Similarity (LPIPS) [102]: is a weighted \\( l_{2} \\) distance between two ImageNet-pretrained AlexNet [50]-extracted deep features of ground-truth and generated images. A higher LPIPS value denotes better diversity. (iii) Mean Opinion Score (MOS): for human study, each of the 30 human workers was asked to draw 50 sketches in our system, and rate every generated photo (both ours and competitor's) on a scale of 1 to 5 [39] (bad→excellent) based on their opinion of how closely it matched their photorealistic imagination of the associated sketch. For each method, we compute the final MOS value by taking the mean \\( (\\mu) \\) and variance \\( (\\sigma) \\) of all 1500 of its MOS responses. (iv) Fine-Grained Metric (FGM): to judge the fine-grainedness of sketch mapping, we propose a new metric, which uses features from a pretrained FG-SBIR model [100] to compute cosine similarity between input sketch and generated photo. A higher FGM value denotes better fine-grained association between them."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.076,
+ 0.81,
+ 0.47,
+ 0.902
+ ],
+ "angle": 0,
+ "content": "Competitors: We compare our proposed framework with various state-of-the-art (SOTA) methods and two self-designed baselines. Among those, pix2pix [41] uses a conditional generative model for sketch-to-photo translation. MUNIT [38] aims to produce diverse outputs given one input sketch. It tries to decompose an image into a content and"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.498,
+ 0.092,
+ 0.892,
+ 0.304
+ ],
+ "angle": 0,
+ "content": "a style code followed by learning those codes simultaneously. CycleGAN [105] utilises cycle-consistency loss with a GAN model for bidirectional image-to-image translation. U-GAT-IT [48] uses an attention module for image translation while focusing on the domain-discriminative parts. Moreover, employing a pre-trained StyleGAN [47] we compare with the baseline B-Sketch Mapper which is equivalent to the baseline sketch mapper described in Sec. 5.1. Following optimisation-based GAN inversion [1], we design B-Sketch Optimiser where we iteratively optimise the latent code using input sketch as a ground-truth with perceptual loss [102]. For a fair comparison, we trained all competing methods in a supervised manner with sketch-photo pairs from ShoeV2, ChairV2, and Handbag datasets."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.499,
+ 0.31,
+ 0.81,
+ 0.325
+ ],
+ "angle": 0,
+ "content": "6.1. Performance Analysis & Discussion"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.498,
+ 0.327,
+ 0.893,
+ 0.841
+ ],
+ "angle": 0,
+ "content": "Result Analysis: The proposed method consistently surpasses (Table 2) other state-of-the-arts in terms of quality (FID), and diversity (LPIPS). Pix2pix [41] with its naive conditional image-to-image translation formulation is outperformed by CycleGAN [105] (by \\(-14.26\\) FID on ShoeV2), as the latter is reinforced with a cycle consistency loss in an adversarial training paradigm in addition to the bidirectional guidance. U-GAT-IT [48] with its attention-based formulation, surpasses others proving the efficacy of attention-module in image translation tasks. Although MU-NIT [38] and pSp [69] supports multi-modal generation, our method, excels both in terms of output diversity (0.489 LPIPS on ShoeV2). Naive Baselines of B-Sketch Mapper and B-Sketch Optimiser with their simplistic design fall short of surpassing the proposed framework. Our method achieves the highest (Table 2) degree of fine-grained association (0.88 FGM on ShoeV2), thanks to its novel fine-grained discriminative loss. When compared to our framework, there exists a noticeable deformity in the photos generated by its competitors (Fig. 4). Photos generated by pix2pix [41], MUNIT [38] and CycleGAN [105] suffer from deformity and lack of photorealism. Although U-GAT-IT [48] and pSp [69] outputs are somewhat realistic, they are mostly unfaithful to the input sketch. As observed from Fig. 4, the photos generated by SOTA methods almost invariably fail to capture the semantic intent of the user, yielding deformed images. Contrarily, given the visually pleasing (Fig. 4), and richer generation quality, our method vastly outperforms most SOTA and baselines in terms of MOS value (Table 2). Furthermore, our method can replicate the appearance of a given photo onto the generated one (Fig. 4) by predicting coarse and mid-level latent codes from the input sketch and taking the fine-level codes of the reference photo predicted by our photo-to-photo mapper."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.498,
+ 0.841,
+ 0.894,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "In summary, with the help of smooth [6] latent space of StyleGAN [46, 47] along with auto-regressive sketch mapper and the fine-grained discriminative loss, our approach almost always ensures photorealistic translations with ac"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.483,
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+ ],
+ "angle": 0,
+ "content": "6855"
+ }
+ ],
+ [
+ {
+ "type": "image",
+ "bbox": [
+ 0.102,
+ 0.089,
+ 0.868,
+ 0.352
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.076,
+ 0.353,
+ 0.894,
+ 0.381
+ ],
+ "angle": 0,
+ "content": "Figure 4. Qualitative comparison with various state-of-the-art competitors on ShoeV2 dataset. Ours-ref (column 3) results depict that our method can faithfully replicate the appearance of a given reference photo (shown in the top-right inset)."
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.287,
+ 0.388,
+ 0.682,
+ 0.402
+ ],
+ "angle": 0,
+ "content": "Table 2. Benchmarks on ChairV2, ShoeV2, and Handbag datasets."
+ },
+ {
+ "type": "table",
+ "bbox": [
+ 0.085,
+ 0.403,
+ 0.884,
+ 0.535
+ ],
+ "angle": 0,
+ "content": "| Paper | Category | Type of Sketch | Data Preparation + Salient Design Component |
| SketchyGAN [16] | Categorical | Synth+Real | • Fully automatic edemap augmentation + input injection at multiple layers. |
| iSketch&Fill [30] | Categorical | Synthetic | • Edemap creation with Im2Pencil [54] and sketch-simplification [77] + ResNet [35] generator. |
| CoGS [33] | Categorical | Synth+Real | • Saliency with [40] for synthetic sketches + VQ-GAN [25] with VAE over codebook vectors. |
| ContextGAN [58] | Semi-FG | Synthetic | • Synthetic sketch generation with XDoG [87] and [43] + optimisation-based GAN inversion. |
| Two-Stage [57] | Semi-FG | Real | • Synthetic noisy-stroke for augmentation + two-stage sketch-to-edemap-to-photo generation. |
| SYO-GAN [86] | Semi-FG | Synthetic | • Pseudo sketch creation with PhotoSketch [52] + fine-tuning GAN model with a few pose-specific sketches. |
| SketchyCOCO [29] | Scene-level | Semi-real | • Synthetic scene sketch + generation of foreground object followed by contextual background. |
| Two-Stage [85] | Scene-level | Synthetic | • Edemaps generated with [66] + edemap standardisation followed by content-style disentanglement. |
| DeepFaceDraw [15] | Facial photo | Synthetic | • Photocopy filter and [77] for training data + region-wise embedding with 2-stage generation. |
| Controlled S2I [96] | Facial photo | Synthetic | • HED [92] for edemaps + dilation-based sketch refinement network for adapting edge-based models. |
| Proposed | Fine-grained | Real | • Unlabelled photos & sketch-photo pairs + autoregressive latent-mapper & pre-trained StyleGAN [46]. |
+
+outputs, StyleGAN [46, 47] introduced a non-linear mapping from input code vector $z \in \mathcal{Z}$ to intermediate latent code $w \in \mathcal{W}$ , which controlled the generation process. While traditional GAN is unable to generate conditional output, it can be augmented with additional information to conditionally control the data generation process [61]. However, existing conditional generative [55, 79] models are unable to inject fine-grained control, especially when conditioned with abstract free-hand sketches.
+
+GAN Inversion: Exploring GANs has recently led to an interest in inverting a pre-trained GAN [4] for tasks like image manipulation [4]. Typical GAN training aims to learn the weights of generator and discriminator with appropriate loss objectives, to generate random new images $G(z)$ by sampling random noise vectors $z \in \mathcal{Z}$ [31]. Contrarily, during GAN inversion, given a reference image we try to find a noise vector $z^{*}$ in the generator latent space that can accurately reconstruct that image while its weights fixed [104]. While some methods [1,2,22,23] directly optimise the latent vector to minimise the reconstruction loss, a few works [4,32,69,82] train dedicated encoders to find the latent code corresponding to an input image. Among them, optimisation-based methods perform better in terms of reconstruction accuracy, while encoding-based methods work significantly faster. Other methods [5, 103], take a hybrid approach in order to attain "the best of both worlds" [88]. However, images from different domain (e.g., semantic label map, edgemap) are not invertible into the latent space of a photo pre-trained generator [6]. Consequently, end-to-end trainable methods [3,14,63,69] emerged which aims to map a given image (from a source domain) into the latent space of a pre-trained GAN trained with target domain images. These learned encoders are then used in tasks like, inversion [4], semantic editing [4], super-resolution [60], face frontalisation [69], inpainting [69].
+
+# 3. Pilot Study: Problems and Analysis
+
+Challenges: Sketches being highly abstract in nature, generating a photo from a sketch can have multiple possible outcomes [69]. Generating photorealistic images from sparse sketches incurs three major challenges – (i) Locality-bias assumes that any particular output (e.g., photo) pixel
+
+position $I'(x, y)$ is perfectly aligned with the same pixel location $I(x, y)$ of the conditional input (e.g., sketch) [69]. However, a free-hand sketch being highly deformed does not necessarily follow the paired photo's intensity boundary [36]. (ii) Hallucinating the colour/texture in a realistic and contextually-meaningful manner, is difficult from sparse sketch input. (iii) Deciphering the fine-grained user intent is a major bottleneck as the same object can be sketched in diverse ways by different users [75].
+
+Analysis: The popular encoder-decoder architecture [41] for converting an input sketch $S$ to output RGB photo $\mathcal{R}$ via image-to-image translation [41] can be formulated as:
+
+$$
+P (\mathcal {R} | \mathcal {S}) = \underbrace {P (\mathcal {Z} | \mathcal {S})} _ {\text {E n c o d e r}} \underbrace {P (\mathcal {R} | \mathcal {Z})} _ {\text {D e c o d e r}} \tag {1}
+$$
+
+where the encoder $P(\mathcal{Z}|\mathcal{S})$ embeds the sketch into a latent feature $\mathcal{Z}$ , from which the decoder $P(\mathcal{R}|\mathcal{Z})$ generates the output photo. Existing works [18, 38, 105] have evolved through designing task-specific encoder/decoder frameworks. Despite achieving remarkable success in other image translation problems (e.g., image-restoration [67], colourisation [41]), adapting them off-the-shelf fails for our setup. Importantly, we realise that as the loss backpropagates from the decoder to encoder's end, while training [41] with sketch-photo pairs $(\mathcal{S},\mathcal{R})$ , it implicitly enforces the model to follow sketch as a pseudo edge-boundary [57]. Consequently, the model is hard-conditioned by the sketch to treat its strokes as the intensity boundary of the generated photo, thus resulting in a deformed output.
+
+Instead of end-to-end encoder-decoder training, we adopt a two stage-approach (Fig. 2). In the first stage, we model $P(\mathcal{R}|\mathcal{Z})$ as an unsupervised GAN [31], which being trained from a large number of unlabeled photos of a particular class, is capable of generating realistic photos $G(z)$ , given a random vector $z \sim \mathcal{N}(0,1)$ [31]. As GAN models learn data distribution [68], we can loosely assume that any photo can be generated by sampling a specific $z^*$ from the GAN latent space [1]. Once the GAN model is trained, in the second stage, keeping the $G(\cdot)$ fixed, we aim to learn $P(\mathcal{Z}|\mathcal{S})$ as a sketch mapper that would encode the input sketch $S$ into a latent code $\mathcal{Z}$ corresponding to the paired photo $\mathcal{R}$ in the pre-trained GAN latent space.
+
+Advantages of decoupling the encoder-decoder training are twofold - (i) the GAN model [46, 47] pre-trained on real photos is bound to generate realistic photos devoid of unwanted deformation, (ii) while output quality and diversity of coupled encoder-decoder models were limited by the training sketch-photo pairs [41], our decoupled decoder being independent of such pairs, can model the large variation of a particular dataset using unlabelled photos [46, 47] only. Sketch-photo pairs are used to train the sketch mapper only.
+
+
+Figure 2. The sketch mapper aims to predict the corresponding latent code of associated photo in the manifold of pre-trained GAN.
+
+# 4. Background: StyleGAN
+
+In a GAN [31] framework, a generator $G(\cdot)$ aims to generate an image $G(z)$ from a noise vector $z \in \mathcal{Z}$ of size $\mathbb{R}^d$ sampled from a Gaussian distribution [31], while a discriminator $D(\cdot)$ tries to distinguish between a real and a generated fake image [31]. The training progresses through a two-player minimax game, thus gradually improving each other over the value function $V(D,G)$ as [31]:
+
+$$
+\begin{array}{l} \min _ {G} \max _ {D} V (D, G) = \mathbb {E} _ {x \sim p _ {\text {d a t a}} (x)} [ \log D (x) ] \tag {2} \\ + \mathbb {E} _ {z \sim p _ {z} (z)} [ \log (1 - D (G (z))) ] \\ \end{array}
+$$
+
+Instead of passing a random noise vector $z \in \mathcal{Z}$ directly as the network input [68], StyleGAN [46, 47] eliminates the idea of input layer and always starts from a learned constant tensor of size $\mathbb{R}^{4 \times 4 \times d}$ . The generator network $\mathcal{G}(\cdot)$ consists of a number of progressive resolution blocks, each having the sequence $\mathrm{conv}3 \times 3 \to \mathrm{AdaIN} \to \mathrm{conv}3 \times 3 \to \mathrm{AdaIN}$ [46, 47]. StyleGAN employs a non-linear mapping network $f: \mathcal{Z} \to \mathcal{W}$ (an 8-layer MLP) to transform $z$ into an intermediate latent vector $w \in \mathcal{W}$ of size $\mathbb{R}^d$ [46, 47]. The same latent vector $w$ , upon repeatedly passing through a common affine transformation layer $A$ at each level of the generator network, generates the style $y = (y_s, y_b) = A(w)$ for that level. Adaptive instance normalisation (AdaIN) [46, 47] is then controlled by $y$ via modulating the feature-map $x_f$ as $\mathrm{AdaIN}(x_f, y) = y_s \frac{x_f - \mu(x_f)}{\sigma(x_f)} + y_b$ after each $\mathrm{conv}3 \times 3$ block of $\mathcal{G}(\cdot)$ [46, 47]. Moreover, stochasticity is injected by adding one-channel uncorrelated Gaussian noise image (per-channel scaled with a learned scaling factor $B$ ) to each layer of the network before every AdaIN operation [46, 47].
+
+However, due to the limited representability and disentanglement of a single latent vector $w \in \mathcal{W}$ [1], we embed the input in the extended $\mathcal{W}^+$ latent space [1] consisting of different latent vectors $w^+ \in \mathcal{W}^+$ of size $\mathbb{R}^{k \times d}$ , one for each level of the generator network $\mathcal{G}(\cdot)$ . For an output of
+
+resolution $M \times M$ , $k = 2\log_2(M) - 2$ [47]. In this work, we set $M = 256$ , making $k = 14$ .
+
+# 5. Sketch-to-Photo Generation Model
+
+Overview: We aim to devise a sketch-to-photo generation model utilising the rich latent space of a pre-trained StyleGAN [47] trained on a particular class to achieve fine-grained generation. Once the StyleGAN [47] is trained, we fix its weights and train a sketch mapper $\mathcal{E}_s$ that projects an input sketch $(s)$ into a latent code $w_{s}^{+} = \mathcal{E}_{s}(s)\in \mathbb{R}^{14\times d}$ lying in the manifold of pre-trained StyleGAN. In other words, given a sketch input we aim to pick the corresponding latent which when passed through the frozen generator $\mathcal{G}(\cdot)$ would generate an output $(\hat{r})$ most similar to the ground-truth paired photo $(r)$ . In particular, we have three salient design components: (i) an autoregressive sketch mapper (ii) fine-grained discriminative loss besides usual reconstruction objective, and (iii) a photo-to-photo mapper $\mathcal{E}_r$ working as a teacher [27] to improve the learning of $\mathcal{E}_s$ .
+
+# 5.1. Model Architecture
+
+Baseline Sketch Mapper: Inspired by GAN inversion literature [88], we design our baseline sketch mapper using a ResNet50 [35] backbone extracting feature map $f_{s} = \mathcal{F}_{s}(s) \in \mathbb{R}^{h_{f} \times w_{f} \times d}$ . In order to generate the latent code of size $\mathbb{R}^{14 \times d}$ , we use 14 individual (not shared) latent embedding networks (successive stride-two conv-layers with LeakyReLU [93]), each of them takes $f_{s}$ as input to predict a $d$ -dimensional latent vector. Concatenating them results in the $\mathbb{R}^{14 \times d}$ latent code [69]. Finally, this latent code upon passing through the pre-trained generator $\mathcal{G}(\cdot)$ generates the output photo $\hat{r}$ . Trained with weighted summation of pixel loss $(l_{2})$ and perceptual [102] loss, baseline sketch mapper eventually learns to map an input sketch to its corresponding photo in the latent space of a pre-trained StyleGAN [47].
+
+However, it has a few limitations: Firstly, this baseline ignores the varying levels of sketch abstraction [95]. Ideally, for highly abstract/partial sketches, the output space should be large with many plausible RGB photos [12], whereas, for a detailed sketch, it should reflect the fine-grained details. Secondly, reconstruction loss [69] alone, fails to decipher the fine-grained semantic intent of the user.
+
+Autoregressive Latent Mapper: Instead of predicting the latent code $w_{s}^{+} = \{w_{1}^{+},\dots ,w_{k}^{+}\}$ in one shot, we aim to model it in an autoregressive setting keeping a sequential dependency among them. Given an input sketch (s), the autoregressive sketch mapper $\mathcal{E}_s$ modelling the distribution $P(w_s^+ |s)$ can be mathematically expressed as:
+
+$$
+P \left(w _ {s} ^ {+} \mid s\right) = P \left(w _ {1} ^ {+}, \dots , w _ {k} ^ {+} \mid s\right) = \prod_ {i = 1} ^ {k} P \left(w _ {i} ^ {+} \mid w _ {< k} ^ {+}, s\right) \tag {3}
+$$
+
+where the value of the $i^{th}$ predicted latent vector $w_{i}^{+}$ depends on all preceding latents. The motivations behind autoregressive modelling are: (i) the disentangled latent space
+
+of a StyleGAN depicts semantic feature hierarchy [94], where the latent code $w_{1}^{+}$ to $w_{14}^{+}$ controls coarse to fine-level features. (ii) a highly abstract/partial sketch should ideally influence the first few latent vectors governing the major semantic structure, while the later vectors could be sampled randomly from a Gaussian distribution to account for the uncertainty involving such sparse sketches. Whereas, a highly detailed sketch should influence more latent vectors to faithfully reproduce the user's intent. (iii) we aim to synergise the disentangled property of StyleGAN's latent space and the varying levels of sketch abstraction such that the user has the provision to decide how far should the generated output be conditioned on the input sketch and to what extent can it be hallucinated. This is decided by the number of steps of unrolling in the autoregressive process and additionally keeping the later latent codes as random vectors to facilitate multi-modal generation [69].
+
+Given the extracted feature map $f_{s} = \mathcal{F}_{s}(s)$ , the global average pooled holistic visual feature vector $v_{h}$ is transformed via a fully-connected (FC) layer to initialise the first hidden state of sequential decoder $f_{seq}(\cdot, \cdot)$ as $h_0 = \tanh(W_h \otimes v_h + b_h)$ , with $W_{h}, b_{h}$ being trainable parameters. At every $j^{th}$ time step, we apply a shared FC-layer on the hidden state $h_j$ to obtain the $j^{th}$ latent code as $w_{k}^{+} = W_{o} \otimes h_{j} + b_{o}$ . The current hidden state is updated by $h_k = f_{seq}(h_{k-1}; \eta(f_s, w_{k-1}^+)$ ), where the previous hidden state of sequential decoder $h_{k-1}$ holds the knowledge about previously predicted latent codes, and $\eta$ models the influence of the formerly predicted latent code on the next prediction along with extracting the relevant information from the feature map $f_{s}$ . In order to model the interaction between $w_{k}^{+}$ and $f_{s}$ , we use a simple Hadamard product $\hat{f}_s = f_s \odot w_{k-1}^+ \in \mathbb{R}^{h_f \times w_f \times d}$ which upon passing through successive two-strided convolutional layers followed by LeakyReLU produces a $d$ -dimensional output of $\eta$ . $f_{seq}(\cdot, \cdot)$ can be modelled using any sequential network (e.g., LSTM [37], RNN [59], GRU [17]) or self-attention based transformer [83] network. However, here we use GRU [17], as it was empirically found to be easily optimisable and cheaper while producing compelling results. We wrap this entire process inside the sketch mapper $\mathcal{E}_s$ .
+
+To allow multi-modal generation, we always predict a maximum 10 out of the 14 unique latent vectors and sample the rest 4 from Gaussian distribution to inject output variation [69]. Moreover, to enforce our model in learning to generate from partial sketches, we introduce a smart augmentation strategy, where, we partially render the sketch from $30 - 100\%$ at an interval of $10\%$ . While feeding the $\{30\%, 40\%, \dots, 100\}$ sketches, we enforce the mapper to predict only the first $m = \{3, 4, \dots, 10\}$ corresponding latent vectors. In every case, we pass random vectors sampled from Gaussian distribution in place of the remaining $(14 - m)$ unpredicted vectors. This strategy ensures that
+
+
+Figure 3. $\mathcal{E}_s$ learns to map a sketch to the latent code of its paired photo in a pre-trained StyleGAN manifold, trained with a mix of reconstruction, fine-grained discriminative, and distillation losses. our model eventually learns to generate plausible photos at varying levels of completion, thus allowing the user to control the extent of abstraction as per his/her choice.
+
+# 5.2. Training Procedure
+
+Reconstruction Loss: Given an input sketch-photo pair $\{s, r\}$ and the generated output photo $\hat{r} = \mathcal{G}(\mathcal{E}_s(s))$ , we compute pixel level $l_2$ reconstruction loss as:
+
+$$
+\mathcal {L} _ {\mathrm {r e c}} (r, \hat {r}) = | | r - \hat {r} | | _ {2} \tag {4}
+$$
+
+Besides pixel-wise similarity, we also learn perceptual similarities via LPIPS [102] loss, which has been found [32] to retain photorealism. With $\phi(\cdot)$ as the pre-trained perceptual feature encoder [102], LPIPS loss becomes:
+
+$$
+\mathcal {L} _ {\mathrm {L P I P S}} (\boldsymbol {r}, \hat {\boldsymbol {r}}) = | | \phi (\boldsymbol {r}) - \phi (\hat {\boldsymbol {r}}) | | _ {2} \tag {5}
+$$
+
+Fine-Grained Discriminative Loss: While reconstruction loss aims to align the pixel values between generated and ground-truth photo, the discriminative sketchphoto (paired) association compared to other photos needs to be modelled further to reflect the fine-grained user intent of input sketch in the output space. Triplet with cosine-distance based pre-trained fine-grained SBIR [19] model $\mathcal{F}_g(\cdot)$ places a sketch nearer to its paired photo compared to others in a joint-embedding space. Therefore, we compute a discriminative fine-grained loss that measures the cosine similarity between $s$ and $\hat{r}$ as:
+
+$$
+\mathcal {L} _ {\text {d i s c}} (s, \hat {r}) = 1 - \frac {\mathcal {F} _ {g} (s) \cdot \mathcal {F} _ {g} (\hat {r})}{| | \mathcal {F} _ {g} (s) | | | | \mathcal {F} _ {g} (\hat {r}) | |} \tag {6}
+$$
+
+Photo-to-Photo Mapper as Teacher: Photo-to-photo mapping being an easier task than sketch-to-photo underpins our motivation towards introducing a photo-to-photo mapper $\mathcal{E}_r(\cdot)$ as a teacher [27] to additionally guide the learning of our sketch-mapper $\mathcal{E}_s(\cdot)$ , thus handling the subjective nature of sketches and its resultant large sketchphoto domain gap. Architecturally, $\mathcal{E}_r(\cdot)$ is identical to our baseline $\mathcal{E}_s(\cdot)$ with the aim of reconstructing the input photo $(r)$ at the output $(\hat{r})$ : $\mathcal{G}(\mathcal{E}_r(r)) \approx \hat{r}$ . Once trained, latent vectors predicted by $\mathcal{E}_r$ (weights frozen) acts as a groundtruth additionally supervising $\mathcal{E}_s$ via a distillation loss as:
+
+$$
+\mathcal {L} _ {\mathrm {K D}} (s, r) = \left| \left| \mathcal {E} _ {s} (s) - \mathcal {E} _ {r} (r) \right| \right| _ {2} \tag {7}
+$$
+
+We impose $\mathcal{L}_{\mathrm{KD}}$ only on the predicted latents (max 10) not on the random ones. Our overall training objective is $\mathcal{L}_{\mathrm{total}} = \lambda_1\mathcal{L}_{\mathrm{rec}} + \lambda_2\mathcal{L}_{\mathrm{LPIPS}} + \lambda_3\mathcal{L}_{\mathrm{disc}} + \lambda_4\mathcal{L}_{\mathrm{KD}}$ .
+
+# 6. Experiments
+
+Dataset: UT Zappos50K [98] and pix2pix Handbag [41] datasets are used to pre-train the StyleGAN generator in shoe and handbag classes respectively. While for chair class, we collected over 10,000 photos from websites like IKEA, ARGOS, etc. We used QMUL-ShoeV2 [12, 80], QMUL-ChairV2 [12, 80], and Handbag [81] datasets containing sketch-photo pairs to train the sketch mapper. Out of 6730/1800/568 sketches and 2000/400/568 photos from ShoeV2/ChairV2/Handbag datasets, 6051/1275/400 sketches and 1800/300/400 photos are used for training respectively, keeping the rest for testing. Notably, StyleGAN pre-training does not involve any sketch-photo pairs.
+
+Implementation Details: Adam [49] optimiser is used to pre-train a category specific StyleGAN [47] with feature embedding size of $d = 512$ for $8M$ iterations at learning rate of $10^{-3}$ and batch size 8. Based on empirical observations, we disable path-length regularisation [47] and reduce $R1$ regularisation's weight to 2 for superior quality and diversity. We use a combination of Rectified Adam [56] and Lookahead [101] method as an optimiser to train the sketch-to-photo mapper for $5M$ iterations at a constant learning rate of $10^{-5}$ and a batch size of 4. $\lambda_1, \lambda_2, \lambda_3$ , and $\lambda_4$ are set to 1, 0.8, 0.5, and 0.6 respectively.
+
+Evaluation: We use four metrics - (i) Fréchet Inception Distance (FID) [46]: uses pre-trained InceptionV3's activation distribution statistics to estimate distance between synthetic and real data where a lower value indicates better generation quality. (ii) Learned Perceptual Image Patch Similarity (LPIPS) [102]: is a weighted $l_{2}$ distance between two ImageNet-pretrained AlexNet [50]-extracted deep features of ground-truth and generated images. A higher LPIPS value denotes better diversity. (iii) Mean Opinion Score (MOS): for human study, each of the 30 human workers was asked to draw 50 sketches in our system, and rate every generated photo (both ours and competitor's) on a scale of 1 to 5 [39] (bad→excellent) based on their opinion of how closely it matched their photorealistic imagination of the associated sketch. For each method, we compute the final MOS value by taking the mean $(\mu)$ and variance $(\sigma)$ of all 1500 of its MOS responses. (iv) Fine-Grained Metric (FGM): to judge the fine-grainedness of sketch mapping, we propose a new metric, which uses features from a pretrained FG-SBIR model [100] to compute cosine similarity between input sketch and generated photo. A higher FGM value denotes better fine-grained association between them.
+
+Competitors: We compare our proposed framework with various state-of-the-art (SOTA) methods and two self-designed baselines. Among those, pix2pix [41] uses a conditional generative model for sketch-to-photo translation. MUNIT [38] aims to produce diverse outputs given one input sketch. It tries to decompose an image into a content and
+
+a style code followed by learning those codes simultaneously. CycleGAN [105] utilises cycle-consistency loss with a GAN model for bidirectional image-to-image translation. U-GAT-IT [48] uses an attention module for image translation while focusing on the domain-discriminative parts. Moreover, employing a pre-trained StyleGAN [47] we compare with the baseline B-Sketch Mapper which is equivalent to the baseline sketch mapper described in Sec. 5.1. Following optimisation-based GAN inversion [1], we design B-Sketch Optimiser where we iteratively optimise the latent code using input sketch as a ground-truth with perceptual loss [102]. For a fair comparison, we trained all competing methods in a supervised manner with sketch-photo pairs from ShoeV2, ChairV2, and Handbag datasets.
+
+# 6.1. Performance Analysis & Discussion
+
+Result Analysis: The proposed method consistently surpasses (Table 2) other state-of-the-arts in terms of quality (FID), and diversity (LPIPS). Pix2pix [41] with its naive conditional image-to-image translation formulation is outperformed by CycleGAN [105] (by $-14.26$ FID on ShoeV2), as the latter is reinforced with a cycle consistency loss in an adversarial training paradigm in addition to the bidirectional guidance. U-GAT-IT [48] with its attention-based formulation, surpasses others proving the efficacy of attention-module in image translation tasks. Although MU-NIT [38] and pSp [69] supports multi-modal generation, our method, excels both in terms of output diversity (0.489 LPIPS on ShoeV2). Naive Baselines of B-Sketch Mapper and B-Sketch Optimiser with their simplistic design fall short of surpassing the proposed framework. Our method achieves the highest (Table 2) degree of fine-grained association (0.88 FGM on ShoeV2), thanks to its novel fine-grained discriminative loss. When compared to our framework, there exists a noticeable deformity in the photos generated by its competitors (Fig. 4). Photos generated by pix2pix [41], MUNIT [38] and CycleGAN [105] suffer from deformity and lack of photorealism. Although U-GAT-IT [48] and pSp [69] outputs are somewhat realistic, they are mostly unfaithful to the input sketch. As observed from Fig. 4, the photos generated by SOTA methods almost invariably fail to capture the semantic intent of the user, yielding deformed images. Contrarily, given the visually pleasing (Fig. 4), and richer generation quality, our method vastly outperforms most SOTA and baselines in terms of MOS value (Table 2). Furthermore, our method can replicate the appearance of a given photo onto the generated one (Fig. 4) by predicting coarse and mid-level latent codes from the input sketch and taking the fine-level codes of the reference photo predicted by our photo-to-photo mapper.
+
+In summary, with the help of smooth [6] latent space of StyleGAN [46, 47] along with auto-regressive sketch mapper and the fine-grained discriminative loss, our approach almost always ensures photorealistic translations with ac
+
+
+Figure 4. Qualitative comparison with various state-of-the-art competitors on ShoeV2 dataset. Ours-ref (column 3) results depict that our method can faithfully replicate the appearance of a given reference photo (shown in the top-right inset).
+
+Table 2. Benchmarks on ChairV2, ShoeV2, and Handbag datasets.
+
+| Paper | Category | Type of Sketch | Data Preparation + Salient Design Component |
| SketchyGAN [16] | Categorical | Synth+Real | • Fully automatic edemap augmentation + input injection at multiple layers. |
| iSketch&Fill [30] | Categorical | Synthetic | • Edemap creation with Im2Pencil [54] and sketch-simplification [77] + ResNet [35] generator. |
| CoGS [33] | Categorical | Synth+Real | • Saliency with [40] for synthetic sketches + VQ-GAN [25] with VAE over codebook vectors. |
| ContextGAN [58] | Semi-FG | Synthetic | • Synthetic sketch generation with XDoG [87] and [43] + optimisation-based GAN inversion. |
| Two-Stage [57] | Semi-FG | Real | • Synthetic noisy-stroke for augmentation + two-stage sketch-to-edemap-to-photo generation. |
| SYO-GAN [86] | Semi-FG | Synthetic | • Pseudo sketch creation with PhotoSketch [52] + fine-tuning GAN model with a few pose-specific sketches. |
| SketchyCOCO [29] | Scene-level | Semi-real | • Synthetic scene sketch + generation of foreground object followed by contextual background. |
| Two-Stage [85] | Scene-level | Synthetic | • Edemaps generated with [66] + edemap standardisation followed by content-style disentanglement. |
| DeepFaceDraw [15] | Facial photo | Synthetic | • Photocopy filter and [77] for training data + region-wise embedding with 2-stage generation. |
| Controlled S2I [96] | Facial photo | Synthetic | • HED [92] for edemaps + dilation-based sketch refinement network for adapting edge-based models. |
| Proposed | Fine-grained | Real | • Unlabelled photos & sketch-photo pairs + autoregressive latent-mapper & pre-trained StyleGAN [46]. |
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+ "content": "5. Sketch-to-Photo Generation Model"
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+ "content": "Overview: We aim to devise a sketch-to-photo generation model utilising the rich latent space of a pre-trained StyleGAN [47] trained on a particular class to achieve fine-grained generation. Once the StyleGAN [47] is trained, we fix its weights and train a sketch mapper "
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+ "content": " lying in the manifold of pre-trained StyleGAN. In other words, given a sketch input we aim to pick the corresponding latent which when passed through the frozen generator "
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+ "content": " would generate an output "
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+ "content": ". In particular, we have three salient design components: (i) an autoregressive sketch mapper (ii) fine-grained discriminative loss besides usual reconstruction objective, and (iii) a photo-to-photo mapper "
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+ "content": " and perceptual [102] loss, baseline sketch mapper eventually learns to map an input sketch to its corresponding photo in the latent space of a pre-trained StyleGAN [47]."
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+ "content": "However, it has a few limitations: Firstly, this baseline ignores the varying levels of sketch abstraction [95]. Ideally, for highly abstract/partial sketches, the output space should be large with many plausible RGB photos [12], whereas, for a detailed sketch, it should reflect the fine-grained details. Secondly, reconstruction loss [69] alone, fails to decipher the fine-grained semantic intent of the user."
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| MinkowskiNet42†[9] | 10cm | 37.9 | Voxel | 60.5 |
| PointConv* | 10cm | 5.4 | Point | 62.6 |
| Fast Point Transformer [54] | 10cm | 37.9 | Voxel | 65.9 |
| PointConvFormer(ours) | 10cm | 5.5 | Point | 71.4 |
| PointConvFormer(ours) + mix3D | 10cm | 5.5 | Point | 72.6 |
| PointConvFormer-Lite (ours) | 10cm | 1.6 | Point | 70.6 |
| MinkowskiNet42†[9] | 5cm | 37.9 | Voxel | 66.7 |
| Fast Point Transformer [54] | 5cm | 37.9 | Voxel | 70.0 |
| PointConv* | 5cm | 5.4 | Point | 68.5 |
| PointConvFormer(ours) | 5cm | 5.5 | Point | 74.0 |
| PointConvFormer (ours) + mix3D | 5cm | 5.5 | Point | 74.3 |
| PointConvFormer-Lite (ours) | 5cm | 1.9 | Point | 73.3 |
| MinkowskiNet42†[9] | 2cm | 37.9 | Voxel | 71.9 |
| Fast Point Transformer [54] | 2cm | 37.9 | Voxel | 72.1 |
| PointConv* | 2cm | 5.4 | Point | 70.3 |
| PointConvFormer(ours) | 2cm | 9.4 | Point | 74.5 |
| PointConvFormer (ours) + mix3D | 2cm | 5.8 | Point | 74.4 |
| PointConvFormer-Lite (ours) | 2cm | 3.8 | Point | 73.3 |
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| MinkowskiNet42†[9] | 10cm | 37.9 | Voxel | 60.5 |
| PointConv* | 10cm | 5.4 | Point | 62.6 |
| Fast Point Transformer [54] | 10cm | 37.9 | Voxel | 65.9 |
| PointConvFormer(ours) | 10cm | 5.5 | Point | 71.4 |
| PointConvFormer(ours) + mix3D | 10cm | 5.5 | Point | 72.6 |
| PointConvFormer-Lite (ours) | 10cm | 1.6 | Point | 70.6 |
| MinkowskiNet42†[9] | 5cm | 37.9 | Voxel | 66.7 |
| Fast Point Transformer [54] | 5cm | 37.9 | Voxel | 70.0 |
| PointConv* | 5cm | 5.4 | Point | 68.5 |
| PointConvFormer(ours) | 5cm | 5.5 | Point | 74.0 |
| PointConvFormer (ours) + mix3D | 5cm | 5.5 | Point | 74.3 |
| PointConvFormer-Lite (ours) | 5cm | 1.9 | Point | 73.3 |
| MinkowskiNet42†[9] | 2cm | 37.9 | Voxel | 71.9 |
| Fast Point Transformer [54] | 2cm | 37.9 | Voxel | 72.1 |
| PointConv* | 2cm | 5.4 | Point | 70.3 |
| PointConvFormer(ours) | 2cm | 9.4 | Point | 74.5 |
| PointConvFormer (ours) + mix3D | 2cm | 5.8 | Point | 74.4 |
| PointConvFormer-Lite (ours) | 2cm | 3.8 | Point | 73.3 |
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| MinkowskiNet42†[9] | 10cm | 37.9 | Voxel | 60.5 |
| PointConv* | 10cm | 5.4 | Point | 62.6 |
| Fast Point Transformer [54] | 10cm | 37.9 | Voxel | 65.9 |
| PointConvFormer(ours) | 10cm | 5.5 | Point | 71.4 |
| PointConvFormer(ours) + mix3D | 10cm | 5.5 | Point | 72.6 |
| PointConvFormer-Lite (ours) | 10cm | 1.6 | Point | 70.6 |
| MinkowskiNet42†[9] | 5cm | 37.9 | Voxel | 66.7 |
| Fast Point Transformer [54] | 5cm | 37.9 | Voxel | 70.0 |
| PointConv* | 5cm | 5.4 | Point | 68.5 |
| PointConvFormer(ours) | 5cm | 5.5 | Point | 74.0 |
| PointConvFormer (ours) + mix3D | 5cm | 5.5 | Point | 74.3 |
| PointConvFormer-Lite (ours) | 5cm | 1.9 | Point | 73.3 |
| MinkowskiNet42†[9] | 2cm | 37.9 | Voxel | 71.9 |
| Fast Point Transformer [54] | 2cm | 37.9 | Voxel | 72.1 |
| PointConv* | 2cm | 5.4 | Point | 70.3 |
| PointConvFormer(ours) | 2cm | 9.4 | Point | 74.5 |
| PointConvFormer (ours) + mix3D | 2cm | 5.8 | Point | 74.4 |
| PointConvFormer-Lite (ours) | 2cm | 3.8 | Point | 73.3 |
+
+coordinates are given without any color information. It is a challenging dataset because the scanning density is uneven as faraway points are more sparse in LIDAR scans.
+
+Table 3 reports the results on the semanticKitti dataset. Because this work mainly focuses on the basic building block, PointConvFormer, which is applicable to any kind of 3D point cloud data, of deep neural network, we did not compare with work [7,98] whose main novelties work mostly on LiDAR datasets due to the additional assumption that there are no occlusions from the bird-eye view. From the table, one can see that our PointConvFormer outperforms both point-based methods and point+voxel fusion methods. Especially, our method obtains better results comparing with SPVNAS [68], which utilizes the network architecture search (NAS) techniques and fuses both point and voxel branches. We did not utilize any NAS in our system which would only further improve our performance.
+
+# 4.3. Scene Flow Estimation from Point Clouds
+
+Scene flow is the 3D displacement vector between each surface in two consecutive frames. As a fundamental tool for low-level understanding of the world, scene flow can be used in many 3D applications. Traditionally, scene flow was estimated directly from RGB data [28, 51, 72]. However, with the recent development of 3D sensors such as LiDAR and 3D deep learning techniques, there is increasing interest on directly estimating scene flow from 3D point clouds [21, 44, 56, 78, 82]. In this work, we adopt PointConvFormer into the PointPWC-Net [82], which utilizes a coarse-to-fine framework for scene flow estimation, by replacing the PointConv in the feature pyramid layers with the
+
+
+Figure 4. ScanNet result visualization. We visualize the ScanNet prediction results from our PointConvFormer, PointConv* [81] and Point Transformer [96]. The red ellipses indicate the improvements of our PointConvFormer over other approaches. Points with ignore labels are filtered for a better visualization. (Best viewed in color)
+
+Table 2. Semantic segmentation results on ScanNet dataset. We compare both the ScanNet [11] validation set and test set. Numbers for baselines are taken from the literature. The numbers for test set are from the official ScanNet benchmark.
+
+| Methods | Voxel/grid size | # Params(M) | Input | mIoU(%) |
| MinkowskiNet42†[9] | 10cm | 37.9 | Voxel | 60.5 |
| PointConv* | 10cm | 5.4 | Point | 62.6 |
| Fast Point Transformer [54] | 10cm | 37.9 | Voxel | 65.9 |
| PointConvFormer(ours) | 10cm | 5.5 | Point | 71.4 |
| PointConvFormer(ours) + mix3D | 10cm | 5.5 | Point | 72.6 |
| PointConvFormer-Lite (ours) | 10cm | 1.6 | Point | 70.6 |
| MinkowskiNet42†[9] | 5cm | 37.9 | Voxel | 66.7 |
| Fast Point Transformer [54] | 5cm | 37.9 | Voxel | 70.0 |
| PointConv* | 5cm | 5.4 | Point | 68.5 |
| PointConvFormer(ours) | 5cm | 5.5 | Point | 74.0 |
| PointConvFormer (ours) + mix3D | 5cm | 5.5 | Point | 74.3 |
| PointConvFormer-Lite (ours) | 5cm | 1.9 | Point | 73.3 |
| MinkowskiNet42†[9] | 2cm | 37.9 | Voxel | 71.9 |
| Fast Point Transformer [54] | 2cm | 37.9 | Voxel | 72.1 |
| PointConv* | 2cm | 5.4 | Point | 70.3 |
| PointConvFormer(ours) | 2cm | 9.4 | Point | 74.5 |
| PointConvFormer (ours) + mix3D | 2cm | 5.8 | Point | 74.4 |
| PointConvFormer-Lite (ours) | 2cm | 3.8 | Point | 73.3 |
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