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"""
Functions for compuing Procrustes alignment and reconstruction error
Parts of the code are adapted from https://github.com/akanazawa/hmr
"""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import numpy as np
def compute_similarity_transform(S1, S2):
"""Computes a similarity transform (sR, t) that takes
a set of 3D points S1 (3 x N) closest to a set of 3D points S2,
where R is an 3x3 rotation matrix, t 3x1 translation, s scale.
i.e. solves the orthogonal Procrutes problem.
"""
transposed = False
if S1.shape[0] != 3 and S1.shape[0] != 2:
S1 = S1.T
S2 = S2.T
transposed = True
assert(S2.shape[1] == S1.shape[1])
# 1. Remove mean.
mu1 = S1.mean(axis=1, keepdims=True)
mu2 = S2.mean(axis=1, keepdims=True)
X1 = S1 - mu1
X2 = S2 - 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, s, 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. Error:
S1_hat = scale*R.dot(S1) + t
if transposed:
S1_hat = S1_hat.T
return S1_hat
def compute_similarity_transform_batch(S1, S2):
"""Batched version of compute_similarity_transform."""
S1_hat = np.zeros_like(S1)
for i in range(S1.shape[0]):
S1_hat[i] = compute_similarity_transform(S1[i], S2[i])
return S1_hat
def reconstruction_error(S1, S2, reduction='mean'):
"""Do Procrustes alignment and compute reconstruction error."""
S1_hat = compute_similarity_transform_batch(S1, S2)
re = np.sqrt( ((S1_hat - S2)** 2).sum(axis=-1)).mean(axis=-1)
if reduction == 'mean':
re = re.mean()
elif reduction == 'sum':
re = re.sum()
return re
def reconstruction_error_v2(S1, S2, J24_TO_J14, reduction='mean'):
"""Do Procrustes alignment and compute reconstruction error."""
S1_hat = compute_similarity_transform_batch(S1, S2)
S1_hat = S1_hat[:,J24_TO_J14,:]
S2 = S2[:,J24_TO_J14,:]
re = np.sqrt( ((S1_hat - S2)** 2).sum(axis=-1)).mean(axis=-1)
if reduction == 'mean':
re = re.mean()
elif reduction == 'sum':
re = re.sum()
return re
def get_alignMesh(S1, S2, reduction='mean'):
"""Do Procrustes alignment and compute reconstruction error."""
S1_hat = compute_similarity_transform_batch(S1, S2)
re = np.sqrt( ((S1_hat - S2)** 2).sum(axis=-1)).mean(axis=-1)
if reduction == 'mean':
re = re.mean()
elif reduction == 'sum':
re = re.sum()
return re, S1_hat, S2
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