def test_recover_Gk_no_noise():
# Generate some synthetic data.
n_frames = 30
n_basis = 2
n_points = 15
gt_model = model.generate_synthetic_model(n_frames, n_basis, n_points)
# Factor the matrix.
from rigid import factor_matrix
W = gt_model.W.copy()
W -= W.mean(axis=-1)[:, np.newaxis]
M_hat, B_hat = factor_matrix(W, J=n_basis * 3)
# Try to find a G_k
G_k = shape.find_G_k(M_hat)
# Get the k'th column triple of M_k
M_k = np.dot(M_hat, G_k)
M_kx = M_k[0::2]
M_ky = M_k[1::2]
# Ensure they are orthogonal.
npt.assert_allclose((M_kx * M_ky).sum(), 0, atol=1e-3)
# And that the length of x and y are equal.
npt.assert_allclose((M_kx * M_kx).sum() - (M_ky * M_ky).sum(),
0,
atol=1e-3)
def factor(W, n_basis=2, use_method_1=False):
"""Factor's W using
Dai, Y., Li, H. and He, M. "A Simple Prior-free Method for Non-Rigid
Structure-from-Motion Factorization". CVPR, 2012
Note that we use the letter M in place of PI from this paper.
"""
n_frames = W.shape[0] / 2
# Estimate 2D translation.
T = W.mean(axis=-1)
Ts = np.zeros((n_frames, 3))
Ts[:, :2] = T.reshape(n_frames, 2)
# Center observation matrix
W_cent = W.copy() - T[:, np.newaxis]
# Factor
M_hat, B_hat = rigid.factor_matrix(W_cent, n_basis * 3)
# Recover G_k
G_k = find_G_k(M_hat)
# Recover M_k
M_k = np.dot(M_hat, G_k)
# Recover R
Rs = Rs_from_M_k(M_k)
if use_method_1:
# Recover S
S = S_from_Rs_method_1(W_cent, Rs)
# Build the scene.
scene = Scene(S=S, Rs=Rs, Ts=Ts)
else:
# Recover S_sharp
S_sharp = S_sharp_from_Rs(W_cent, Rs)
# Factor to C and B matrices.
C, B = factor_S_sharp_to_C_and_B(S_sharp, n_basis)
# Build linear model.
scene = model.BasisShapeModel(Rs,
Bs=B.reshape(n_basis, 3, B.shape[1]),
C=C,
Ts=Ts)
return scene
def factor(W, n_basis=2, use_method_1 = False):
"""Factor's W using
Dai, Y., Li, H. and He, M. "A Simple Prior-free Method for Non-Rigid
Structure-from-Motion Factorization". CVPR, 2012
Note that we use the letter M in place of PI from this paper.
"""
n_frames = W.shape[0]/2
# Estimate 2D translation.
T = W.mean(axis=-1)
Ts = np.zeros((n_frames,3))
Ts[:,:2] = T.reshape(n_frames,2)
# Center observation matrix
W_cent = W.copy() - T[:,np.newaxis]
# Factor
M_hat, B_hat = rigid.factor_matrix(W_cent, n_basis*3)
# Recover G_k
G_k = find_G_k(M_hat)
# Recover M_k
M_k = np.dot(M_hat, G_k)
# Recover R
Rs = Rs_from_M_k(M_k)
if use_method_1:
# Recover S
S = S_from_Rs_method_1(W_cent, Rs)
# Build the scene.
scene = Scene(S = S, Rs = Rs, Ts = Ts)
else:
# Recover S_sharp
S_sharp = S_sharp_from_Rs(W_cent, Rs)
# Factor to C and B matrices.
C, B = factor_S_sharp_to_C_and_B(S_sharp, n_basis)
# Build linear model.
scene = model.BasisShapeModel(Rs, Bs = B.reshape(n_basis, 3, B.shape[1]), C=C, Ts=Ts)
return scene
