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import torch
import numpy as np
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 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 euclidean_losses(actual, target):
"""Calculate the average Euclidean loss for multi-point samples.
Each sample must contain `n` points, each with `d` dimensions. For example,
in the MPII human pose estimation task n=16 (16 joint locations) and
d=2 (locations are 2D).
Args:
actual (Tensor): Predictions (B x L x D)
target (Tensor): Ground truth target (B x L x D)
"""
assert actual.size() == target.size(), 'input tensors must have the same size'
# Calculate Euclidean distances between actual and target locations
diff = actual - target
dist_sq = diff.pow(2).sum(-1, keepdim=False)
dist = dist_sq.sqrt()
return dist
def pck(actual, expected, threshold=150):
dists = euclidean_losses(actual, expected)
return (dists < threshold).double().mean().item()
def auc(actual, expected):
# This range of thresholds mimics `mpii_compute_3d_pck.m`, which is provided as part of the
# MPI-INF-3DHP test data release.
thresholds = torch.linspace(0, 150, 31).tolist()
pck_values = torch.DoubleTensor(len(thresholds))
for i, threshold in enumerate(thresholds):
pck_values[i] = pck(actual, expected, threshold=threshold)
return pck_values.mean().item()
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