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""" | ||
Utils for evaluation. | ||
""" | ||
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from __future__ import absolute_import | ||
from __future__ import division | ||
from __future__ import print_function | ||
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import numpy as np | ||
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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]) | ||
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# 1. Remove mean. | ||
mu1 = S1.mean(axis=1, keepdims=True) | ||
mu2 = S2.mean(axis=1, keepdims=True) | ||
X1 = S1 - mu1 | ||
X2 = S2 - mu2 | ||
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# 2. Compute variance of X1 used for scale. | ||
var1 = np.sum(X1**2) | ||
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# 3. The outer product of X1 and X2. | ||
K = X1.dot(X2.T) | ||
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# 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)) | ||
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# 5. Recover scale. | ||
scale = np.trace(R.dot(K)) / var1 | ||
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# 6. Recover translation. | ||
t = mu2 - scale*(R.dot(mu1)) | ||
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# 7. Error: | ||
S1_hat = scale*R.dot(S1) + t | ||
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if transposed: | ||
S1_hat = S1_hat.T | ||
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return S1_hat | ||
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def align_by_pelvis(joints, get_pelvis=False): | ||
""" | ||
Assumes joints is 14 x 3 in LSP order. | ||
Then hips are: [3, 2] | ||
Takes mid point of these points, then subtracts it. | ||
""" | ||
left_id = 3 | ||
right_id = 2 | ||
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pelvis = (joints[left_id, :] + joints[right_id, :]) / 2. | ||
if get_pelvis: | ||
return joints - np.expand_dims(pelvis, axis=0), pelvis | ||
else: | ||
return joints - np.expand_dims(pelvis, axis=0) | ||
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def compute_errors(gt3ds, preds): | ||
""" | ||
Gets MPJPE after pelvis alignment + MPJPE after Procrustes. | ||
Evaluates on the 14 common joints. | ||
Inputs: | ||
- gt3ds: N x 14 x 3 | ||
- preds: N x 14 x 3 | ||
""" | ||
errors, errors_pa = [], [] | ||
for i, (gt3d, pred) in enumerate(zip(gt3ds, preds)): | ||
gt3d = gt3d.reshape(-1, 3) | ||
# Root align. | ||
gt3d = align_by_pelvis(gt3d) | ||
pred3d = align_by_pelvis(pred) | ||
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joint_error = np.sqrt(np.sum((gt3d - pred3d)**2, axis=1)) | ||
errors.append(np.mean(joint_error)) | ||
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# Get PA error. | ||
pred3d_sym = compute_similarity_transform(pred3d, gt3d) | ||
pa_error = np.sqrt(np.sum((gt3d - pred3d_sym)**2, axis=1)) | ||
errors_pa.append(np.mean(pa_error)) | ||
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return errors, errors_pa |
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