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# Copyright (c) 2018-present, Facebook, Inc.
# All rights reserved.
#
# This source code is licensed under the license found in the
# LICENSE file in the root directory of this source tree.
#
import numpy as np
import torch
def mpjpe(predicted, target):
"""
Mean per-joint position error (i.e. mean Euclidean distance),
often referred to as "Protocol #1" in many papers.
"""
assert predicted.shape == target.shape
return torch.mean(torch.norm(predicted - target, dim=len(target.shape) - 1))
def weighted_mpjpe(predicted, target, w):
"""
Weighted mean per-joint position error (i.e. mean Euclidean distance)
"""
assert predicted.shape == target.shape
assert w.shape[0] == predicted.shape[0]
return torch.mean(w * torch.norm(predicted - target, dim=len(target.shape) - 1))
def p_mpjpe(predicted, target):
"""
Pose error: MPJPE after rigid alignment (scale, rotation, and translation),
often referred to as "Protocol #2" in many papers.
"""
assert predicted.shape == target.shape
muX = np.mean(target, axis=1, keepdims=True)
muY = np.mean(predicted, axis=1, keepdims=True)
X0 = target - muX
Y0 = predicted - muY
normX = np.sqrt(np.sum(X0 ** 2, axis=(1, 2), keepdims=True))
normY = np.sqrt(np.sum(Y0 ** 2, axis=(1, 2), keepdims=True))
X0 /= normX
Y0 /= normY
H = np.matmul(X0.transpose(0, 2, 1), Y0)
U, s, Vt = np.linalg.svd(H)
V = Vt.transpose(0, 2, 1)
R = np.matmul(V, U.transpose(0, 2, 1))
# Avoid improper rotations (reflections), i.e. rotations with det(R) = -1
sign_detR = np.sign(np.expand_dims(np.linalg.det(R), axis=1))
V[:, :, -1] *= sign_detR
s[:, -1] *= sign_detR.flatten()
R = np.matmul(V, U.transpose(0, 2, 1)) # Rotation
tr = np.expand_dims(np.sum(s, axis=1, keepdims=True), axis=2)
a = tr * normX / normY # Scale
t = muX - a * np.matmul(muY, R) # Translation
# Perform rigid transformation on the input
predicted_aligned = a * np.matmul(predicted, R) + t
# Return MPJPE
return np.mean(np.linalg.norm(predicted_aligned - target, axis=len(target.shape) - 1))
def n_mpjpe(predicted, target):
"""
Normalized MPJPE (scale only), adapted from:
https://github.com/hrhodin/UnsupervisedGeometryAwareRepresentationLearning/blob/master/losses/poses.py
"""
assert predicted.shape == target.shape
norm_predicted = torch.mean(torch.sum(predicted ** 2, dim=3, keepdim=True), dim=2, keepdim=True)
norm_target = torch.mean(torch.sum(target * predicted, dim=3, keepdim=True), dim=2, keepdim=True)
scale = norm_target / norm_predicted
return mpjpe(scale * predicted, target)
def mean_velocity_error(predicted, target):
"""
Mean per-joint velocity error (i.e. mean Euclidean distance of the 1st derivative)
"""
assert predicted.shape == target.shape
velocity_predicted = np.diff(predicted, axis=0)
velocity_target = np.diff(target, axis=0)
return np.mean(np.linalg.norm(velocity_predicted - velocity_target, axis=len(target.shape) - 1))
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