deform_action = lgd.MatrixImageAffineAction(lie_grp, space)
else:
assert False
# Define what regularizer to use
regularizer = 'point'
if regularizer == 'image':
# Create set of all points in space
W = space.tangent_bundle
w = W.element(space.points().T)
# Create regularizing functional
regularizer = 0.1 * odl.solvers.L2NormSquared(W).translated(w)
# Create action
regularizer_action = lgd.ProductSpaceAction(deform_action, W.size)
elif regularizer == 'point':
W = odl.ProductSpace(odl.rn(space.ndim), 3)
w = W.element([[0, 0], [0, 1], [1, 0]])
# Create regularizing functional
regularizer = 0.01 * odl.solvers.L2NormSquared(W).translated(w)
# Create action
if lie_grp_type == 'affine' or lie_grp_type == 'rigid':
point_action = lgd.MatrixVectorAffineAction(lie_grp, W[0])
else:
point_action = lgd.MatrixVectorAction(lie_grp, W[0])
regularizer_action = lgd.ProductSpaceAction(point_action, W.size)
elif regularizer == 'determinant':
W = odl.rn(1)
grid = space.element(
lambda x: np.cos(x[0] * np.pi * 5)**20 + np.cos(x[1] * np.pi * 5)**20)
# Create regularizing functional
# regularizer = 3 * odl.solvers.KullbackLeibler(space, prior=w)
regularizer = 0.5 * (odl.solvers.L2NormSquared(space) *
weighting).translated(w)
# Create action
regularizer_action = lgd.JacobianDeterminantScalingAction(lie_grp, space)
# Initial guess
g = lie_grp.identity
# Combine action and functional into single object.
action = lgd.ProductSpaceAction(deform_action, regularizer_action,
geometric_deform_action)
x = action.domain.element([template, w, grid]).copy()
f = odl.solvers.SeparableSum(data_matching, regularizer,
odl.solvers.ZeroFunctional(space))
# Show some results, reuse the plot
template.show('template')
target.show('target')
# Create callback that displays the current iterate and prints the function
# value
callback = odl.solvers.CallbackShow('diffemorphic matching', step=20)
callback &= odl.solvers.CallbackPrint(f)
# Smoothing
filter_width = 0.5 # standard deviation of the Gaussian filter
v1 *= 1.5 / v1.norm() f1 = odl.solvers.L2NormSquared(r3).translated(v1) w1 = W.element([[1, 0, 0], [0, 1, 0], [0, 0, 1]]) f2 = 0.2 * odl.solvers.L2NormSquared(W).translated(w1) # SELECT GLn or SOn here # lie_grp = GLn(3) # lie_grp = lgd.SOn(3) # point_action = lgd.MatrixVectorAction(lie_grp, r3) lie_grp = lgd.AffineGroup(3) point_action = lgd.MatrixVectorAffineAction(lie_grp, r3) assalg = lie_grp.associated_algebra power_action = lgd.ProductSpaceAction(point_action, 3) # Combine action and functional into single object. action = lgd.ProductSpaceAction(point_action, power_action) x = action.domain.element([v0, w1]) f = odl.solvers.SeparableSum(f1, f2) # Initial guess g = lie_grp.identity # Create some plotting info fig = plt.figure() ax = fig.add_subplot(111, projection='3d') ax.set_xlim(-2, 2) ax.set_ylim(-2, 2) ax.set_zlim(-2, 2)