face_geometry.py

# 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

        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(
    [
        0.000000,
        -3.406404,
        5.979507,
        0.499977,
        0.652534,
        0.000000,
        -1.126865,
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        0.500026,
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        -2.089024,
        6.058267,
        0.499974,
        0.602372,
        -0.463928,
        0.955357,
        6.633583,
        0.482113,
        0.471979,
        0.000000,
        -0.463170,
        7.586580,
        0.500151,
        0.527156,
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        2.473255,
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        0.499523,
        0.401062,
        -4.253081,
        2.577646,
        3.279702,
        0.289712,
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        4.019042,
        5.284764,
        0.499955,
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        0.000000,
        4.885979,
        5.385258,
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        8.261778,
        4.481535,
        0.500023,
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        -3.706811,
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        3.697603,
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    ]
)
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