def forward_alpha(self, v_t, x):
"""
helper function for step (4): Calculation of forward flows
@param v_t: the velocity field
@param x: coordinates
@return:
"""
alpha = np.zeros(v_t.shape)
for i in range(5):
alpha = sampler.sample(v_t, x - 0.5 * alpha)
return alpha
def pull_back(self, I1, Phi1):
"""
implements step (6): pull back image I1 along flow Phi1
@param I1: image
@param Phi1: flow
@return: sequence of back-pulled images J1
"""
J1 = np.zeros((self.T, ) + I1.shape)
for t in range(self.T - 1, -1, -1):
J1[t] = sampler.sample(I1, Phi1[t])
return J1
def push_forward(self, I0, Phi0):
"""
implements step (5): push forward image I0 along flow Phi0
@param I0: image
@param Phi0: flow
@return: sequence of forward pushed images J0
"""
J0 = np.zeros((self.T, ) + I0.shape)
for t in range(0, self.T):
J0[t] = sampler.sample(I0, Phi0[t])
return J0
def integrate_forward_flow(self, v):
"""
implements step (4): Calculation of forward flows
@return:
"""
# make identity grid
x = grid.coordinate_grid((self.H, self.W))
# create flow
Phi0 = np.zeros((self.T, self.H, self.W, 2))
# Phi0_0 is the identity mapping
Phi0[0] = x
for t in range(0, self.T - 1):
alpha = self.forward_alpha(v[t], x)
Phi0[t + 1] = sampler.sample(Phi0[t], x - alpha)
return Phi0
def integrate_backward_flow(self, v):
"""
implements step (3): Calculation of backward flows
@return:
"""
# make identity grid
x = grid.coordinate_grid((self.H, self.W))
# create flow
Phi1 = np.zeros((self.T, self.H, self.W, 2))
# Phi1_1 is the identity mapping
Phi1[self.T - 1] = x
for t in range(self.T - 2, -1, -1):
alpha = self.backwards_alpha(v[t], x)
Phi1[t] = sampler.sample(Phi1[t + 1], x + alpha)
return Phi1