def local_cost(self, J, I):
Ai = sliding_matmul(I, self.matrix)
Aj = sliding_matmul(J, self.matrix)
II = np.einsum("...i,...i->...", Ai, Ai)
JJ = np.einsum("...i,...i->...", Aj, Aj)
IJ = np.einsum("...i,...i->...", Ai, Aj)
IIJJ = II * JJ
cost = -(IJ ** 2) / IIJJ
cost[np.where((II < 1e-5) + (JJ < 1e-5))] = 0
return cost
def local_cost(self, J, I):
Ai = sliding_matmul(I, self.matrix)
Aj = sliding_matmul(J, self.matrix)
II = np.einsum('...i,...i->...', Ai, Ai)
JJ = np.einsum('...i,...i->...', Aj, Aj)
IJ = np.einsum('...i,...i->...', Ai, Aj)
IIJJ = II * JJ
cost = -(IJ**2) / IIJJ
cost[np.where((II < 1e-5) + (JJ < 1e-5))] = 0
return cost
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
