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# Many parts taken from the cpp implementation from github.com/google/mediapipe
#
# Copyright 2020 The MediaPipe Authors.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
import numpy as np
class Singleton(type):
_instances = {}
def __call__(cls, *args, **kwargs):
if cls not in cls._instances:
cls._instances[cls] = super(Singleton, cls).__call__(*args, **kwargs)
return cls._instances[cls]
class Debugger(metaclass=Singleton):
def set_debug(self, debug):
self.debug = debug
def toggle(self):
self.debug = not self.debug
def get_debug(self):
return self.debug
DEBUG = Debugger()
DEBUG.set_debug(False)
class PCF:
def __init__(
self,
near=1,
far=10000,
frame_height=1920,
frame_width=1080,
fy=1074.520446598223,
):
self.near = near
self.far = far
self.frame_height = frame_height
self.frame_width = frame_width
self.fy = fy
fov_y = 2 * np.arctan(frame_height / (2 * fy))
# kDegreesToRadians = np.pi / 180.0 # never used
height_at_near = 2 * near * np.tan(0.5 * fov_y)
width_at_near = frame_width * height_at_near / frame_height
# print(height_at_near)
self.fov_y = fov_y
self.left = -0.5 * width_at_near
self.right = 0.5 * width_at_near
self.bottom = -0.5 * height_at_near
self.top = 0.5 * height_at_near
canonical_metric_landmarks = np.array(
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0.624563,
0.924192,
6.954154,
-2.439843,
-0.131163,
0.885770,
0.615029,
1.098819,
-4.458788,
5.120727,
0.551338,
0.695278,
1.181124,
-4.579996,
5.189564,
0.551980,
0.704632,
1.255818,
-4.787901,
5.237051,
0.552888,
0.715808,
1.325085,
-5.106507,
5.205010,
0.555168,
0.730794,
1.546388,
-5.819392,
4.757893,
0.569944,
0.767035,
1.953754,
-4.183892,
4.431713,
0.593203,
0.685676,
2.117802,
-4.137093,
4.555096,
0.599262,
0.681069,
2.285339,
-4.051196,
4.582438,
0.607600,
0.677703,
2.850160,
-3.665720,
4.484994,
0.631938,
0.663500,
5.278538,
-2.238942,
2.861224,
0.752033,
0.601315,
0.946709,
1.907628,
5.196779,
0.547226,
0.420395,
1.314173,
3.104912,
4.231404,
0.563544,
0.359828,
1.780000,
2.860000,
3.881555,
0.583841,
0.368714,
1.845110,
-4.098880,
4.247264,
0.586614,
0.692366,
5.436187,
-4.030482,
2.109852,
0.771915,
0.683578,
0.766444,
3.182131,
4.861453,
0.531597,
0.352483,
1.938616,
-6.614410,
4.521085,
0.588371,
0.804441,
0.516573,
1.583572,
6.148363,
0.520797,
0.442565,
1.246815,
0.230297,
5.681036,
0.567985,
0.493479,
0.997827,
-6.930921,
4.979576,
0.543283,
0.819255,
3.288807,
-5.382514,
3.795752,
0.655317,
0.745515,
2.311631,
-1.566237,
4.590085,
0.621009,
0.574018,
2.680250,
-6.111567,
4.096152,
0.625560,
0.780312,
3.832928,
-1.537326,
4.137731,
0.680198,
0.570719,
2.961860,
-2.274215,
4.440943,
0.642764,
0.604338,
4.386901,
-2.683286,
3.643886,
0.704663,
0.621530,
1.217295,
-7.834465,
4.969286,
0.552012,
0.862592,
1.542374,
-0.136843,
5.201008,
0.589072,
0.508637,
3.878377,
-6.041764,
3.311079,
0.685945,
0.775357,
3.084037,
-6.809842,
3.814195,
0.645735,
0.812640,
3.747321,
-4.503545,
3.726453,
0.675343,
0.703978,
6.094129,
-3.205991,
1.473482,
0.810858,
0.646305,
4.588995,
-4.728726,
2.983221,
0.720122,
0.714667,
6.583231,
-3.941269,
0.070268,
0.866152,
0.682705,
3.492580,
-3.195820,
4.130198,
0.663187,
0.644597,
1.255543,
0.802341,
5.307551,
0.570082,
0.466326,
1.126122,
-0.933602,
6.538785,
0.544562,
0.548376,
1.443109,
-1.142774,
5.905127,
0.562759,
0.558785,
0.923043,
-0.529042,
7.003423,
0.531987,
0.530140,
1.755386,
3.529117,
4.327696,
0.585271,
0.335177,
2.632589,
3.713828,
4.364629,
0.622953,
0.322779,
3.388062,
3.721976,
4.309028,
0.655896,
0.320163,
4.075766,
3.675413,
4.076063,
0.687132,
0.322346,
4.622910,
3.474691,
3.646321,
0.716482,
0.333201,
5.171755,
2.535753,
2.670867,
0.758757,
0.382787,
7.297331,
0.763172,
-0.048769,
0.897013,
0.468769,
4.706828,
1.651000,
3.109532,
0.732392,
0.424547,
4.071712,
1.476821,
3.476944,
0.702114,
0.433163,
3.269817,
1.470659,
3.731945,
0.666525,
0.433866,
2.527572,
1.617311,
3.865444,
0.633505,
0.426088,
1.970894,
1.858505,
3.961782,
0.603876,
0.416587,
1.579543,
2.097941,
4.084996,
0.579658,
0.409945,
7.664182,
0.673132,
-2.435867,
0.992440,
0.480777,
1.397041,
-1.340139,
5.630378,
0.567192,
0.569420,
0.884838,
0.658740,
6.233232,
0.541366,
0.478899,
0.767097,
-0.968035,
7.077932,
0.526564,
0.546118,
0.460213,
-1.334106,
6.787447,
0.523913,
0.563830,
0.748618,
-1.067994,
6.798303,
0.531529,
0.555057,
1.236408,
-1.585568,
5.480490,
0.566036,
0.582329,
0.387306,
-1.409990,
6.957705,
0.516311,
0.563054,
0.319925,
-1.607931,
6.508676,
0.517472,
0.577877,
1.639633,
2.556298,
3.863736,
0.573595,
0.389807,
1.255645,
2.467144,
4.203800,
0.560698,
0.395332,
1.031362,
2.382663,
4.615849,
0.549756,
0.399751,
4.253081,
2.772296,
3.315305,
0.710288,
0.368253,
4.530000,
2.910000,
3.339685,
0.723330,
0.363373,
]
)
canonical_metric_landmarks = np.reshape(
canonical_metric_landmarks, (canonical_metric_landmarks.shape[0] // 5, 5)
).T
canonical_metric_landmarks = canonical_metric_landmarks[:3, :]
procrustes_landmark_basis = [
(4, 0.070909939706326),
(6, 0.032100144773722),
(10, 0.008446550928056),
(33, 0.058724168688059),
(54, 0.007667080033571),
(67, 0.009078059345484),
(117, 0.009791937656701),
(119, 0.014565368182957),
(121, 0.018591361120343),
(127, 0.005197994410992),
(129, 0.120625205338001),
(132, 0.005560018587857),
(133, 0.05328618362546),
(136, 0.066890455782413),
(143, 0.014816547743976),
(147, 0.014262833632529),
(198, 0.025462191551924),
(205, 0.047252278774977),
(263, 0.058724168688059),
(284, 0.007667080033571),
(297, 0.009078059345484),
(346, 0.009791937656701),
(348, 0.014565368182957),
(350, 0.018591361120343),
(356, 0.005197994410992),
(358, 0.120625205338001),
(361, 0.005560018587857),
(362, 0.05328618362546),
(365, 0.066890455782413),
(372, 0.014816547743976),
(376, 0.014262833632529),
(420, 0.025462191551924),
(425, 0.047252278774977),
]
landmark_weights = np.zeros((canonical_metric_landmarks.shape[1],))
for idx, weight in procrustes_landmark_basis:
landmark_weights[idx] = weight
def log(name, f):
if DEBUG.get_debug():
print(f"{name} logged:", f)
print()
def cpp_compare(name, np_matrix):
if DEBUG.get_debug():
# reorder cpp matrix as memory alignment is not correct
cpp_matrix = np.load(f"{name}_cpp.npy")
rows, cols = cpp_matrix.shape
cpp_matrix = np.split(np.reshape(cpp_matrix, -1), cols)
cpp_matrix = np.stack(cpp_matrix, 1)
print(f"{name}:", np.sum(np.abs(cpp_matrix - np_matrix[:rows, :cols]) ** 2))
print()
def get_metric_landmarks(screen_landmarks, pcf):
screen_landmarks = project_xy(screen_landmarks, pcf)
depth_offset = np.mean(screen_landmarks[2, :])
intermediate_landmarks = screen_landmarks.copy()
intermediate_landmarks = change_handedness(intermediate_landmarks)
first_iteration_scale = estimate_scale(intermediate_landmarks)
intermediate_landmarks = screen_landmarks.copy()
intermediate_landmarks = move_and_rescale_z(
pcf, depth_offset, first_iteration_scale, intermediate_landmarks
)
intermediate_landmarks = unproject_xy(pcf, intermediate_landmarks)
intermediate_landmarks = change_handedness(intermediate_landmarks)
second_iteration_scale = estimate_scale(intermediate_landmarks)
metric_landmarks = screen_landmarks.copy()
total_scale = first_iteration_scale * second_iteration_scale
metric_landmarks = move_and_rescale_z(
pcf, depth_offset, total_scale, metric_landmarks
)
metric_landmarks = unproject_xy(pcf, metric_landmarks)
metric_landmarks = change_handedness(metric_landmarks)
pose_transform_mat = solve_weighted_orthogonal_problem(
canonical_metric_landmarks, metric_landmarks, landmark_weights
)
cpp_compare("pose_transform_mat", pose_transform_mat)
inv_pose_transform_mat = np.linalg.inv(pose_transform_mat)
inv_pose_rotation = inv_pose_transform_mat[:3, :3]
inv_pose_translation = inv_pose_transform_mat[:3, 3]
metric_landmarks = (
inv_pose_rotation @ metric_landmarks + inv_pose_translation[:, None]
)
return metric_landmarks, pose_transform_mat
def project_xy(landmarks, pcf):
x_scale = pcf.right - pcf.left
y_scale = pcf.top - pcf.bottom
x_translation = pcf.left
y_translation = pcf.bottom
landmarks[1, :] = 1.0 - landmarks[1, :]
landmarks = landmarks * np.array([[x_scale, y_scale, x_scale]]).T
landmarks = landmarks + np.array([[x_translation, y_translation, 0]]).T
return landmarks
def change_handedness(landmarks):
landmarks[2, :] *= -1.0
return landmarks
def move_and_rescale_z(pcf, depth_offset, scale, landmarks):
landmarks[2, :] = (landmarks[2, :] - depth_offset + pcf.near) / scale
return landmarks
def unproject_xy(pcf, landmarks):
landmarks[0, :] = landmarks[0, :] * landmarks[2, :] / pcf.near
landmarks[1, :] = landmarks[1, :] * landmarks[2, :] / pcf.near
return landmarks
def estimate_scale(landmarks):
transform_mat = solve_weighted_orthogonal_problem(
canonical_metric_landmarks, landmarks, landmark_weights
)
return np.linalg.norm(transform_mat[:, 0])
def extract_square_root(point_weights):
return np.sqrt(point_weights)
def solve_weighted_orthogonal_problem(source_points, target_points, point_weights):
sqrt_weights = extract_square_root(point_weights)
transform_mat = internal_solve_weighted_orthogonal_problem(
source_points, target_points, sqrt_weights
)
return transform_mat
def internal_solve_weighted_orthogonal_problem(sources, targets, sqrt_weights):
cpp_compare("sources", sources)
cpp_compare("targets", targets)
# tranposed(A_w).
weighted_sources = sources * sqrt_weights[None, :]
# tranposed(B_w).
weighted_targets = targets * sqrt_weights[None, :]
cpp_compare("weighted_sources", weighted_sources)
cpp_compare("weighted_targets", weighted_targets)
# w = tranposed(j_w) j_w.
total_weight = np.sum(sqrt_weights * sqrt_weights)
log("total_weight", total_weight)
# Let C = (j_w tranposed(j_w)) / (tranposed(j_w) j_w).
# Note that C = tranposed(C), hence (I - C) = tranposed(I - C).
#
# tranposed(A_w) C = tranposed(A_w) j_w tranposed(j_w) / w =
# (tranposed(A_w) j_w) tranposed(j_w) / w = c_w tranposed(j_w),
#
# where c_w = tranposed(A_w) j_w / w is a k x 1 vector calculated here:
twice_weighted_sources = weighted_sources * sqrt_weights[None, :]
source_center_of_mass = np.sum(twice_weighted_sources, axis=1) / total_weight
log("source_center_of_mass", source_center_of_mass)
# tranposed((I - C) A_w) = tranposed(A_w) (I - C) =
# tranposed(A_w) - tranposed(A_w) C = tranposed(A_w) - c_w tranposed(j_w).
centered_weighted_sources = weighted_sources - np.matmul(
source_center_of_mass[:, None], sqrt_weights[None, :]
)
cpp_compare("centered_weighted_sources", centered_weighted_sources)
design_matrix = np.matmul(weighted_targets, centered_weighted_sources.T)
cpp_compare("design_matrix", design_matrix)
log("design_matrix_norm", np.linalg.norm(design_matrix))
rotation = compute_optimal_rotation(design_matrix)
scale = compute_optimal_scale(
centered_weighted_sources, weighted_sources, weighted_targets, rotation
)
log("scale", scale)
rotation_and_scale = scale * rotation
pointwise_diffs = weighted_targets - np.matmul(rotation_and_scale, weighted_sources)
cpp_compare("pointwise_diffs", pointwise_diffs)
weighted_pointwise_diffs = pointwise_diffs * sqrt_weights[None, :]
cpp_compare("weighted_pointwise_diffs", weighted_pointwise_diffs)
translation = np.sum(weighted_pointwise_diffs, axis=1) / total_weight
log("translation", translation)
transform_mat = combine_transform_matrix(rotation_and_scale, translation)
cpp_compare("transform_mat", transform_mat)
return transform_mat
def compute_optimal_rotation(design_matrix):
if np.linalg.norm(design_matrix) < 1e-9:
print("Design matrix norm is too small!")
u, _, vh = np.linalg.svd(design_matrix, full_matrices=True)
postrotation = u
prerotation = vh
if np.linalg.det(postrotation) * np.linalg.det(prerotation) < 0:
postrotation[:, 2] = -1 * postrotation[:, 2]
cpp_compare("postrotation", postrotation)
cpp_compare("prerotation", prerotation)
rotation = np.matmul(postrotation, prerotation)
cpp_compare("rotation", rotation)
return rotation
def compute_optimal_scale(
centered_weighted_sources, weighted_sources, weighted_targets, rotation
):
rotated_centered_weighted_sources = np.matmul(rotation, centered_weighted_sources)
numerator = np.sum(rotated_centered_weighted_sources * weighted_targets)
denominator = np.sum(centered_weighted_sources * weighted_sources)
if denominator < 1e-9:
print("Scale expression denominator is too small!")
if numerator / denominator < 1e-9:
print("Scale is too small!")
return numerator / denominator
def combine_transform_matrix(r_and_s, t):
result = np.eye(4)
result[:3, :3] = r_and_s
result[:3, 3] = t
return result