mmpose-0.29.0/mmpose/core/evaluation/mesh_eval.py

# ------------------------------------------------------------------------------
# Adapted from https://github.com/akanazawa/hmr
# Original licence: Copyright (c) 2018 akanazawa, under the MIT License.
# ------------------------------------------------------------------------------

import numpy as np


def compute_similarity_transform(source_points, target_points):
 """Computes a similarity transform (sR, t) that takes a set of 3D points
 source_points (N x 3) closest to a set of 3D points target_points, where R
 is an 3x3 rotation matrix, t 3x1 translation, s scale. And return the
 transformed 3D points source_points_hat (N x 3). i.e. solves the orthogonal
 Procrutes problem.

 Note:
 Points number: N

 Args:
 source_points (np.ndarray): Source point set with shape [N, 3].
 target_points (np.ndarray): Target point set with shape [N, 3].

 Returns:
 np.ndarray: Transformed source point set with shape [N, 3].
 """

 assert target_points.shape[0] == source_points.shape[0]
 assert target_points.shape[1] == 3 and source_points.shape[1] == 3

 source_points = source_points.T
 target_points = target_points.T

 # 1. Remove mean.
 mu1 = source_points.mean(axis=1, keepdims=True)
 mu2 = target_points.mean(axis=1, keepdims=True)
 X1 = source_points - mu1
 X2 = target_points - mu2

 # 2. Compute variance of X1 used for scale.
 var1 = np.sum(X1**2)

 # 3. The outer product of X1 and X2.
 K = X1.dot(X2.T)

 # 4. Solution that Maximizes trace(R'K) is R=U*V', where U, V are
 # singular vectors of K.
 U, _, Vh = np.linalg.svd(K)
 V = Vh.T
 # Construct Z that fixes the orientation of R to get det(R)=1.
 Z = np.eye(U.shape[0])
 Z[-1, -1] *= np.sign(np.linalg.det(U.dot(V.T)))
 # Construct R.
 R = V.dot(Z.dot(U.T))

 # 5. Recover scale.
 scale = np.trace(R.dot(K)) / var1

 # 6. Recover translation.
 t = mu2 - scale * (R.dot(mu1))

 # 7. Transform the source points:
 source_points_hat = scale * R.dot(source_points) + t

 source_points_hat = source_points_hat.T

 return source_points_hat