def jacobian_matrix(grid):
"""
Jacobian matrix at all points
Parameters
----------
grid : ndarray
Input grid.
eg. if 3 dimensional ((dimension, len(x), len(y), len(z)))
Returns
-------
J : ndarray
Jacobian matrix.
eg. 3d case (dimension, dimension, len(x), len(y), len(z))
"""
dimension = grid.ndim - 1
if dimension == 2:
return np.array([gradient(grid[0]), gradient(grid[1])])
elif dimension == 3:
return np.array(
[gradient(grid[0]), gradient(grid[1]), gradient(grid[2])])
def get_derivative_template(reg, epsilon, params_der, window, T, n_jobs):
# get I composed with phi
# print moving_imgs.data[-1].shape, template_img.shape
moving = copy.deepcopy(reg.moving)
warp_fixed = np.copy(
moving.apply_transform(
Deformation(grid=reg.deformation.forward_mappings[-1]),
order=3).data)
# plt.imshow(warp_fixed.data)
# plt.title('in dJ')
# plt.show()
dl_dv = -2. / reg.similarity.variance * gradient(
warp_fixed) * reg.deformation.forward_dets[-1]
# (t=1, ndim, img_shape)-for v and (img_shape,)- for template img J
dl_dJ_dv = double_dev_J_v(dl_dv)
params_grad = {
'reg': copy.deepcopy(reg),
'epsilon': epsilon,
'deformation': copy.deepcopy(reg.old_deformation)
}
loss = loss_func(reg=copy.deepcopy(reg),
deformation=copy.deepcopy(reg.deformation))
dv_dJ = sparse_dot_product_forward(vector=np.copy(
reg.resulting_vector_fields[-1].vector_fields),
ndim=len(reg.fixed.shape),
loss=loss,
T=T,
mat_shape=reg.fixed.shape,
window=window,
params_grad=params_grad,
param_der=params_der,
n_jobs=n_jobs).dot(dl_dJ_dv)
# del dl_dv, dl_dJ_dv
# gc.collect()
return [-dv_dJ]
def derivative(self, J, I):
Im = gaussian_filter(I, self.sigma, mode="constant")
Jm = gaussian_filter(J, self.sigma, mode="constant")
Ibar = I - Im
Jbar = J - Jm
II = gaussian_filter(I * I, self.sigma, mode="constant") - Im * Im
JJ = gaussian_filter(J * J, self.sigma, mode="constant") - Jm * Jm
IJ = gaussian_filter(I * J, self.sigma, mode="constant") - Im * Jm
denom = II * JJ
IJoverIIJJ = IJ / denom
IJoverII = IJ / II
IJoverIIJJ[np.where(denom < 1e-3)] = 0
IJoverII[np.where(II < 1e-3)] = 0
return (2 * gradient(Ibar) * IJoverIIJJ
* (Jbar - Ibar * IJoverII) / self.variance)
def derivative(self, J, I):
Im = gaussian_filter(I, self.sigma, mode="constant")
Jm = gaussian_filter(J, self.sigma, mode="constant")
Ibar = I - Im
Jbar = J - Jm
II = gaussian_filter(I * I, self.sigma, mode="constant") - Im * Im
JJ = gaussian_filter(J * J, self.sigma, mode="constant") - Jm * Jm
IJ = gaussian_filter(I * J, self.sigma, mode="constant") - Im * Jm
denom = II * JJ
IJoverIIJJ = IJ / denom
IJoverII = IJ / II
IJoverIIJJ[np.where(denom < 1e-3)] = 0
IJoverII[np.where(II < 1e-3)] = 0
return (2 * gradient(Ibar) * IJoverIIJJ * (Jbar - Ibar * IJoverII) /
self.variance)
def derivative(self, J, I):
"""
derivative of cost function of mahalanobis normalized cross correlation
Parameters
----------
J : ndarray
Input deformed fixed image.
eg. 3 dimensional case (len(x), len(y), len(z))
I : ndarray
Input deformed moving image.
matrix : ndarray
metric matrix
Returns
-------
momentum : ndarray
Unsmoothed vector field
"""
assert (I.dtype == np.float)
assert (J.dtype == np.float)
Ai = sliding_matmul(I, self.matrix)
Aj = sliding_matmul(J, self.matrix)
Ibar = np.copy(Ai[..., self.index]).astype(np.float)
Jbar = np.copy(Aj[..., self.index]).astype(np.float)
II = np.einsum('...i,...i->...', Ai, Ai)
JJ = np.einsum('...i,...i->...', Aj, Aj)
IJ = np.einsum('...i,...i->...', Ai, Aj)
IIJJ = II * JJ
IJoverIIJJ = IJ / IIJJ
IJoverII = IJ / II
IJoverIIJJ[np.where(IIJJ < 1e-3)] = 0
IJoverII[np.where(II < 1e-3)] = 0
return (2 * gradient(Ibar) * IJoverIIJJ * (Jbar - Ibar * IJoverII) /
self.variance)
def derivative(self, J, I):
"""
derivative of cost function of mahalanobis normalized cross correlation
Parameters
----------
J : ndarray
Input deformed fixed image.
eg. 3 dimensional case (len(x), len(y), len(z))
I : ndarray
Input deformed moving image.
matrix : ndarray
metric matrix
Returns
-------
momentum : ndarray
Unsmoothed vector field
"""
assert I.dtype == np.float
assert J.dtype == np.float
Ai = sliding_matmul(I, self.matrix)
Aj = sliding_matmul(J, self.matrix)
Ibar = np.copy(Ai[..., self.index]).astype(np.float)
Jbar = np.copy(Aj[..., self.index]).astype(np.float)
II = np.einsum("...i,...i->...", Ai, Ai)
JJ = np.einsum("...i,...i->...", Aj, Aj)
IJ = np.einsum("...i,...i->...", Ai, Aj)
IIJJ = II * JJ
IJoverIIJJ = IJ / IIJJ
IJoverII = IJ / II
IJoverIIJJ[np.where(IIJJ < 1e-3)] = 0
IJoverII[np.where(II < 1e-3)] = 0
return 2 * gradient(Ibar) * IJoverIIJJ * (Jbar - Ibar * IJoverII) / self.variance
def derivative(self, J, I):
"""
derivative of cost function of zero means normalized cross correlation
Parameters
----------
J : ndarray
Input deformed fixed images.
eg. 3 dimensional case (len(x), len(y), len(z))
I : ndarray
Input deformed moving images.
Returns
-------
momentum : ndarray
momentum field.
eg. 3d case (dimension, len(x), len(y), len(z))
"""
Im = uniform_filter(I, self.window_length)
Jm = uniform_filter(J, self.window_length)
Ibar = I - Im
Jbar = J - Jm
II = uniform_filter(I * I, self.window_length) - Im * Im
JJ = uniform_filter(J * J, self.window_length) - Jm * Jm
IJ = uniform_filter(I * J, self.window_length) - Im * Jm
denom = II * JJ
IJoverIIJJ = IJ / denom
IJoverII = IJ / II
IJoverIIJJ[np.where(denom < 1e-3)] = 0
IJoverII[np.where(II < 1e-3)] = 0
return (2 * gradient(Ibar) * IJoverIIJJ
* (Jbar - Ibar * IJoverII) / self.variance)
def derivative(self, fixed, moving):
return 2 * gradient(moving) * (fixed - moving) / self.variance