102 lines
3.1 KiB
Python
102 lines
3.1 KiB
Python
import numpy as np
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def compute_similarity_transform(S1, S2):
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"""
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Computes a similarity transform (sR, t) that takes
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a set of 3D points S1 (3 x N) closest to a set of 3D points S2,
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where R is an 3x3 rotation matrix, t 3x1 translation, s scale.
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i.e. solves the orthogonal Procrutes problem.
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"""
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transposed = False
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if S1.shape[0] != 3 and S1.shape[0] != 2:
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S1 = S1.T
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S2 = S2.T
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transposed = True
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assert(S2.shape[1] == S1.shape[1])
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# 1. Remove mean.
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mu1 = S1.mean(axis=1, keepdims=True)
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mu2 = S2.mean(axis=1, keepdims=True)
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X1 = S1 - mu1
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X2 = S2 - mu2
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# 2. Compute variance of X1 used for scale.
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var1 = np.sum(X1**2)
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# 3. The outer product of X1 and X2.
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K = X1.dot(X2.T)
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# 4. Solution that Maximizes trace(R'K) is R=U*V', where U, V are
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# singular vectors of K.
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U, s, Vh = np.linalg.svd(K)
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V = Vh.T
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# Construct Z that fixes the orientation of R to get det(R)=1.
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Z = np.eye(U.shape[0])
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Z[-1, -1] *= np.sign(np.linalg.det(U.dot(V.T)))
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# Construct R.
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R = V.dot(Z.dot(U.T))
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# 5. Recover scale.
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scale = np.trace(R.dot(K)) / var1
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# 6. Recover translation.
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t = mu2 - scale*(R.dot(mu1))
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# 7. Error:
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S1_hat = scale*R.dot(S1) + t
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if transposed:
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S1_hat = S1_hat.T
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return S1_hat
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def reconstruction_error(S1, S2, reduction='mean'):
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"""Do Procrustes alignment and compute reconstruction error."""
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S1_hat = compute_similarity_transform(S1, S2)
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re = np.sqrt( ((S1_hat - S2)** 2).sum(axis=-1))
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if reduction == 'mean':
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re = re.mean()
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elif reduction == 'sum':
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re = re.sum()
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return re
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def align_by_pelvis(joints, names):
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l_id = names.index('LHip')
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r_id = names.index('RHip')
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pelvis = joints[[l_id, r_id], :].mean(axis=0, keepdims=True)
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return joints - pelvis
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def keypoints_error(gt, est, names, use_align=False, joint_level=True):
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assert gt.shape[-1] == 4
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assert est.shape[-1] == 4
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isValid = est[..., -1] > 0
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isValidGT = gt[..., -1] > 0
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isValid_common = isValid * isValidGT
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est = est[..., :-1]
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gt = gt[..., :-1]
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dist = {}
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dist['abs'] = np.sqrt(((gt - est)**2).sum(axis=-1)) * 1000
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dist['pck@50'] = dist['abs'] < 50
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# dist['pck@100'] = dist['abs'] < 100
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# dist['pck@150'] = dist['abs'] < 0.15
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if use_align:
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l_id = names.index('LHip')
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r_id = names.index('RHip')
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assert isValid[l_id] and isValid[r_id]
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assert isValidGT[l_id] and isValidGT[r_id]
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# root align
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gt, est = align_by_pelvis(gt, names), align_by_pelvis(est, names)
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# Absolute error (MPJPE)
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dist['ra'] = np.sqrt(((est - gt) ** 2).sum(axis=-1)) * 1000
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# Reconstuction_error
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est_hat = compute_similarity_transform(est, gt)
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dist['pa'] = np.sqrt(((est_hat - gt) ** 2).sum(axis=-1)) * 1000
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result = {}
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for key in ['abs', 'ra', 'pa', 'pck@50', 'pck@100']:
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if key not in dist:
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continue
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result[key+'_mean'] = dist[key].mean()
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if joint_level:
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for i, name in enumerate(names):
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result[key+'_'+name] = dist[key][i]
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return result |