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import torch
import torch.nn as nn
import numpy as np
import torch.nn.functional as F
# Numpy-based errors
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 np.mean(np.linalg.norm(predicted - target, axis=len(target.shape)-1), axis=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), axis=1)
# PyTorch-based errors (for losses)
def loss_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 loss_2d_weighted(predicted, target, conf):
assert predicted.shape == target.shape
predicted_2d = predicted[:,:,:,:2]
target_2d = target[:,:,:,:2]
diff = (predicted_2d - target_2d) * conf
return torch.mean(torch.norm(diff, dim=-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 loss_mpjpe(scale * predicted, target)
def weighted_bonelen_loss(predict_3d_length, gt_3d_length):
loss_length = 0.001 * torch.pow(predict_3d_length - gt_3d_length, 2).mean()
return loss_length
def weighted_boneratio_loss(predict_3d_length, gt_3d_length):
loss_length = 0.1 * torch.pow((predict_3d_length - gt_3d_length)/gt_3d_length, 2).mean()
return loss_length
def get_limb_lens(x):
'''
Input: (N, T, 17, 3)
Output: (N, T, 16)
'''
limbs_id = [[0,1], [1,2], [2,3],
[0,4], [4,5], [5,6],
[0,7], [7,8], [8,9], [9,10],
[8,11], [11,12], [12,13],
[8,14], [14,15], [15,16]
]
limbs = x[:,:,limbs_id,:]
limbs = limbs[:,:,:,0,:]-limbs[:,:,:,1,:]
limb_lens = torch.norm(limbs, dim=-1)
return limb_lens
def loss_limb_var(x):
'''
Input: (N, T, 17, 3)
'''
if x.shape[1]<=1:
return torch.FloatTensor(1).fill_(0.)[0].to(x.device)
limb_lens = get_limb_lens(x)
limb_lens_var = torch.var(limb_lens, dim=1)
limb_loss_var = torch.mean(limb_lens_var)
return limb_loss_var
def loss_limb_gt(x, gt):
'''
Input: (N, T, 17, 3), (N, T, 17, 3)
'''
limb_lens_x = get_limb_lens(x)
limb_lens_gt = get_limb_lens(gt) # (N, T, 16)
return nn.L1Loss()(limb_lens_x, limb_lens_gt)
def loss_velocity(predicted, target):
"""
Mean per-joint velocity error (i.e. mean Euclidean distance of the 1st derivative)
"""
assert predicted.shape == target.shape
if predicted.shape[1]<=1:
return torch.FloatTensor(1).fill_(0.)[0].to(predicted.device)
velocity_predicted = predicted[:,1:] - predicted[:,:-1]
velocity_target = target[:,1:] - target[:,:-1]
return torch.mean(torch.norm(velocity_predicted - velocity_target, dim=-1))
def loss_joint(predicted, target):
assert predicted.shape == target.shape
return nn.L1Loss()(predicted, target)
def get_angles(x):
'''
Input: (N, T, 17, 3)
Output: (N, T, 16)
'''
limbs_id = [[0,1], [1,2], [2,3],
[0,4], [4,5], [5,6],
[0,7], [7,8], [8,9], [9,10],
[8,11], [11,12], [12,13],
[8,14], [14,15], [15,16]
]
angle_id = [[ 0, 3],
[ 0, 6],
[ 3, 6],
[ 0, 1],
[ 1, 2],
[ 3, 4],
[ 4, 5],
[ 6, 7],
[ 7, 10],
[ 7, 13],
[ 8, 13],
[10, 13],
[ 7, 8],
[ 8, 9],
[10, 11],
[11, 12],
[13, 14],
[14, 15] ]
eps = 1e-7
limbs = x[:,:,limbs_id,:]
limbs = limbs[:,:,:,0,:]-limbs[:,:,:,1,:]
angles = limbs[:,:,angle_id,:]
angle_cos = F.cosine_similarity(angles[:,:,:,0,:], angles[:,:,:,1,:], dim=-1)
return torch.acos(angle_cos.clamp(-1+eps, 1-eps))
def loss_angle(x, gt):
'''
Input: (N, T, 17, 3), (N, T, 17, 3)
'''
limb_angles_x = get_angles(x)
limb_angles_gt = get_angles(gt)
return nn.L1Loss()(limb_angles_x, limb_angles_gt)
def loss_angle_velocity(x, gt):
"""
Mean per-angle velocity error (i.e. mean Euclidean distance of the 1st derivative)
"""
assert x.shape == gt.shape
if x.shape[1]<=1:
return torch.FloatTensor(1).fill_(0.)[0].to(x.device)
x_a = get_angles(x)
gt_a = get_angles(gt)
x_av = x_a[:,1:] - x_a[:,:-1]
gt_av = gt_a[:,1:] - gt_a[:,:-1]
return nn.L1Loss()(x_av, gt_av)
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