def test_mi_gradient_sparse():
# Test the gradient of mutual information
h = 1e-5
for ttype in factors:
transform = regtransforms[ttype]
dim = ttype[1]
if dim == 2:
nslices = 1
interp_method = vf.interpolate_scalar_2d
else:
nslices = 45
interp_method = vf.interpolate_scalar_3d
# Get data (pair of images related to each other by an known transform)
factor = factors[ttype]
static, moving, static_g2w, moving_g2w, smask, mmask, M = \
setup_random_transform(transform, factor, nslices, 5.0)
smask = None
mmask = None
# Sample static domain
k = 3
sigma = 0.25
seed = 1234
shape = np.array(static.shape, dtype=np.int32)
samples = sample_domain_regular(k, shape, static_g2w, sigma, seed)
samples = np.array(samples)
samples = np.hstack((samples, np.ones(samples.shape[0])[:, None]))
sp_to_static = np.linalg.inv(static_g2w)
samples_static_grid = (sp_to_static.dot(samples.T).T)[..., :dim]
intensities_static, inside = interp_method(static.astype(np.float32),
samples_static_grid)
intensities_static = np.array(intensities_static, dtype=np.float64)
# Prepare a MattesBase instance
# The computation of the metric is done in 3 steps:
# 1.Compute the joint distribution
# 2.Compute the gradient of the joint distribution
# 3.Compute the metric's value and gradient using results from 1 and 2
metric = MattesBase(32)
metric.setup(static, moving, smask, mmask)
# 1. Update the joint distribution
sp_to_moving = np.linalg.inv(moving_g2w)
samples_moving_grid = (sp_to_moving.dot(samples.T).T)[..., :dim]
intensities_moving, inside = interp_method(moving.astype(np.float32),
samples_moving_grid)
intensities_moving = np.array(intensities_moving, dtype=np.float64)
metric.update_pdfs_sparse(intensities_static, intensities_moving)
# 2. Update the joint distribution gradient (the derivative of each
# histogram cell w.r.t. the transform parameters). This requires
# to evaluate the gradient of the moving image at the sampling points
theta = transform.get_identity_parameters().copy()
spacing = np.ones(dim, dtype=np.float64)
shape = np.array(static.shape, dtype=np.int32)
mgrad, inside = vf.sparse_gradient(moving.astype(np.float32),
sp_to_moving,
spacing,
samples[..., :dim])
metric.update_gradient_sparse(theta, transform, intensities_static,
intensities_moving,
samples[..., :dim],
mgrad)
# 3. Update the metric (in this case, the Mutual Information) and its
# gradient, which is computed from the joint density and its gradient
metric.update_mi_metric(update_gradient=True)
# Now we can extract the value and gradient of the metric
# This is the gradient according to the implementation under test
val0 = metric.metric_val
actual = np.copy(metric.metric_grad)
# Compute the gradient using finite-diferences
n = transform.get_number_of_parameters()
expected = np.empty_like(actual)
for i in range(n):
dtheta = theta.copy()
dtheta[i] += h
M = transform.param_to_matrix(dtheta)
shape = np.array(static.shape, dtype=np.int32)
sp_to_moving = np.linalg.inv(moving_g2w).dot(M)
samples_moving_grid = (sp_to_moving.dot(samples.T).T)[..., :dim]
intensities_moving, inside =\
interp_method(moving.astype(np.float32), samples_moving_grid)
intensities_moving = np.array(intensities_moving, dtype=np.float64)
metric.update_pdfs_sparse(intensities_static, intensities_moving)
metric.update_mi_metric(update_gradient=False)
val1 = metric.metric_val
expected[i] = (val1 - val0) / h
dp = expected.dot(actual)
enorm = np.linalg.norm(expected)
anorm = np.linalg.norm(actual)
nprod = dp / (enorm * anorm)
assert(nprod > 0.9999)
def test_mi_gradient_sparse():
# Test the gradient of mutual information
h = 1e-5
for ttype in factors:
transform = regtransforms[ttype]
dim = ttype[1]
if dim == 2:
nslices = 1
interp_method = vf.interpolate_scalar_2d
else:
nslices = 45
interp_method = vf.interpolate_scalar_3d
# Get data (pair of images related to each other by an known transform)
factor = factors[ttype]
static, moving, static_g2w, moving_g2w, smask, mmask, M = \
setup_random_transform(transform, factor, nslices, 5.0)
smask = None
mmask = None
# Sample static domain
k = 3
sigma = 0.25
seed = 1234
shape = np.array(static.shape, dtype=np.int32)
samples = sample_domain_regular(k, shape, static_g2w, sigma, seed)
samples = np.array(samples)
samples = np.hstack((samples, np.ones(samples.shape[0])[:, None]))
sp_to_static = np.linalg.inv(static_g2w)
samples_static_grid = (sp_to_static.dot(samples.T).T)[..., :dim]
intensities_static, inside = interp_method(static.astype(np.float32),
samples_static_grid)
intensities_static = np.array(intensities_static, dtype=np.float64)
# Prepare a MattesBase instance
# The computation of the metric is done in 3 steps:
# 1.Compute the joint distribution
# 2.Compute the gradient of the joint distribution
# 3.Compute the metric's value and gradient using results from 1 and 2
metric = MattesBase(32)
metric.setup(static, moving, smask, mmask)
# 1. Update the joint distribution
sp_to_moving = np.linalg.inv(moving_g2w)
samples_moving_grid = (sp_to_moving.dot(samples.T).T)[..., :dim]
intensities_moving, inside = interp_method(moving.astype(np.float32),
samples_moving_grid)
intensities_moving = np.array(intensities_moving, dtype=np.float64)
metric.update_pdfs_sparse(intensities_static, intensities_moving)
# 2. Update the joint distribution gradient (the derivative of each
# histogram cell w.r.t. the transform parameters). This requires
# to evaluate the gradient of the moving image at the sampling points
theta = transform.get_identity_parameters().copy()
spacing = np.ones(dim, dtype=np.float64)
shape = np.array(static.shape, dtype=np.int32)
mgrad, inside = vf.sparse_gradient(moving.astype(np.float32),
sp_to_moving, spacing,
samples[..., :dim])
metric.update_gradient_sparse(theta, transform, intensities_static,
intensities_moving, samples[..., :dim],
mgrad)
# 3. Update the metric (in this case, the Mutual Information) and its
# gradient, which is computed from the joint density and its gradient
metric.update_mi_metric(update_gradient=True)
# Now we can extract the value and gradient of the metric
# This is the gradient according to the implementation under test
val0 = metric.metric_val
actual = np.copy(metric.metric_grad)
# Compute the gradient using finite-diferences
n = transform.get_number_of_parameters()
expected = np.empty_like(actual)
for i in range(n):
dtheta = theta.copy()
dtheta[i] += h
M = transform.param_to_matrix(dtheta)
shape = np.array(static.shape, dtype=np.int32)
sp_to_moving = np.linalg.inv(moving_g2w).dot(M)
samples_moving_grid = (sp_to_moving.dot(samples.T).T)[..., :dim]
intensities_moving, inside =\
interp_method(moving.astype(np.float32), samples_moving_grid)
intensities_moving = np.array(intensities_moving, dtype=np.float64)
metric.update_pdfs_sparse(intensities_static, intensities_moving)
metric.update_mi_metric(update_gradient=False)
val1 = metric.metric_val
expected[i] = (val1 - val0) / h
dp = expected.dot(actual)
enorm = np.linalg.norm(expected)
anorm = np.linalg.norm(actual)
nprod = dp / (enorm * anorm)
assert (nprod > 0.9999)
def test_mi_gradient_dense():
# Test the gradient of mutual information
h = 1e-5
for ttype in factors:
transform = regtransforms[ttype]
dim = ttype[1]
if dim == 2:
nslices = 1
warp_method = vf.warp_2d_affine
else:
nslices = 45
warp_method = vf.warp_3d_affine
# Get data (pair of images related to each other by an known transform)
factor = factors[ttype]
static, moving, static_g2w, moving_g2w, smask, mmask, M = \
setup_random_transform(transform, factor, nslices, 5.0)
smask = None
mmask = None
# Prepare a MattesBase instance
# The computation of the metric is done in 3 steps:
# 1.Compute the joint distribution
# 2.Compute the gradient of the joint distribution
# 3.Compute the metric's value and gradient using results from 1 and 2
metric = MattesBase(32)
metric.setup(static, moving, smask, mmask)
# 1. Update the joint distribution
metric.update_pdfs_dense(static.astype(np.float64),
moving.astype(np.float64))
# 2. Update the joint distribution gradient (the derivative of each
# histogram cell w.r.t. the transform parameters). This requires
# among other things, the spatial gradient of the moving image.
theta = transform.get_identity_parameters().copy()
grid_to_space = np.eye(dim + 1)
spacing = np.ones(dim, dtype=np.float64)
shape = np.array(static.shape, dtype=np.int32)
mgrad, inside = vf.gradient(moving.astype(np.float32), moving_g2w,
spacing, shape, grid_to_space)
metric.update_gradient_dense(theta, transform,
static.astype(np.float64),
moving.astype(np.float64),
grid_to_space, mgrad, smask, mmask)
# 3. Update the metric (in this case, the Mutual Information) and its
# gradient, which is computed from the joint density and its gradient
metric.update_mi_metric(update_gradient=True)
# Now we can extract the value and gradient of the metric
# This is the gradient according to the implementation under test
val0 = metric.metric_val
actual = np.copy(metric.metric_grad)
# Compute the gradient using finite-diferences
n = transform.get_number_of_parameters()
expected = np.empty_like(actual)
for i in range(n):
dtheta = theta.copy()
dtheta[i] += h
M = transform.param_to_matrix(dtheta)
shape = np.array(static.shape, dtype=np.int32)
warped = np.array(warp_method(moving.astype(np.float32), shape, M))
metric.update_pdfs_dense(static.astype(np.float64),
warped.astype(np.float64))
metric.update_mi_metric(update_gradient=False)
val1 = metric.metric_val
expected[i] = (val1 - val0) / h
dp = expected.dot(actual)
enorm = np.linalg.norm(expected)
anorm = np.linalg.norm(actual)
nprod = dp / (enorm * anorm)
assert(nprod >= 0.999)
def test_mi_gradient_dense():
# Test the gradient of mutual information
h = 1e-5
for ttype in factors:
transform = regtransforms[ttype]
dim = ttype[1]
if dim == 2:
nslices = 1
warp_method = vf.warp_2d_affine
else:
nslices = 45
warp_method = vf.warp_3d_affine
# Get data (pair of images related to each other by an known transform)
factor = factors[ttype]
static, moving, static_g2w, moving_g2w, smask, mmask, M = \
setup_random_transform(transform, factor, nslices, 5.0)
smask = None
mmask = None
# Prepare a MattesBase instance
# The computation of the metric is done in 3 steps:
# 1.Compute the joint distribution
# 2.Compute the gradient of the joint distribution
# 3.Compute the metric's value and gradient using results from 1 and 2
metric = MattesBase(32)
metric.setup(static, moving, smask, mmask)
# 1. Update the joint distribution
metric.update_pdfs_dense(static.astype(np.float64),
moving.astype(np.float64))
# 2. Update the joint distribution gradient (the derivative of each
# histogram cell w.r.t. the transform parameters). This requires
# among other things, the spatial gradient of the moving image.
theta = transform.get_identity_parameters().copy()
grid_to_space = np.eye(dim + 1)
spacing = np.ones(dim, dtype=np.float64)
shape = np.array(static.shape, dtype=np.int32)
mgrad, inside = vf.gradient(moving.astype(np.float32), moving_g2w,
spacing, shape, grid_to_space)
metric.update_gradient_dense(theta, transform,
static.astype(np.float64),
moving.astype(np.float64), grid_to_space,
mgrad, smask, mmask)
# 3. Update the metric (in this case, the Mutual Information) and its
# gradient, which is computed from the joint density and its gradient
metric.update_mi_metric(update_gradient=True)
# Now we can extract the value and gradient of the metric
# This is the gradient according to the implementation under test
val0 = metric.metric_val
actual = np.copy(metric.metric_grad)
# Compute the gradient using finite-diferences
n = transform.get_number_of_parameters()
expected = np.empty_like(actual)
for i in range(n):
dtheta = theta.copy()
dtheta[i] += h
M = transform.param_to_matrix(dtheta)
shape = np.array(static.shape, dtype=np.int32)
warped = np.array(warp_method(moving.astype(np.float32), shape, M))
metric.update_pdfs_dense(static.astype(np.float64),
warped.astype(np.float64))
metric.update_mi_metric(update_gradient=False)
val1 = metric.metric_val
expected[i] = (val1 - val0) / h
dp = expected.dot(actual)
enorm = np.linalg.norm(expected)
anorm = np.linalg.norm(actual)
nprod = dp / (enorm * anorm)
assert (nprod >= 0.999)
