def test_sample_domain_regular():
# Test 2D sampling
shape = np.array((10, 10), dtype=np.int32)
affine = np.eye(3)
invalid_affine = np.eye(2)
sigma = 0
dim = len(shape)
n = shape[0] * shape[1]
k = 2
# Verify exception is raised with invalid affine
assert_raises(ValueError, sample_domain_regular, k, shape,
invalid_affine, sigma)
samples = sample_domain_regular(k, shape, affine, sigma)
isamples = np.array(samples, dtype=np.int32)
indices = (isamples[:, 0] * shape[1] + isamples[:, 1])
# Verify correct number of points sampled
assert_array_equal(samples.shape, [n // k, dim])
# Verify all sampled points are different
assert_equal(len(set(indices)), len(indices))
# Verify the sampling was regular at rate k
assert_equal((indices % k).sum(), 0)
# Test 3D sampling
shape = np.array((5, 10, 10), dtype=np.int32)
affine = np.eye(4)
invalid_affine = np.eye(3)
sigma = 0
dim = len(shape)
n = shape[0] * shape[1] * shape[2]
k = 10
# Verify exception is raised with invalid affine
assert_raises(ValueError, sample_domain_regular, k, shape,
invalid_affine, sigma)
samples = sample_domain_regular(k, shape, affine, sigma)
isamples = np.array(samples, dtype=np.int32)
indices = (isamples[:, 0] * shape[1] * shape[2] +
isamples[:, 1] * shape[2] +
isamples[:, 2])
# Verify correct number of points sampled
assert_array_equal(samples.shape, [n // k, dim])
# Verify all sampled points are different
assert_equal(len(set(indices)), len(indices))
# Verify the sampling was regular at rate k
assert_equal((indices % k).sum(), 0)
def test_sample_domain_regular():
# Test 2D sampling
shape = np.array((10, 10), dtype=np.int32)
affine = np.eye(3)
invalid_affine = np.eye(2)
sigma = 0
dim = len(shape)
n = shape[0] * shape[1]
k = 2
# Verify exception is raised with invalid affine
assert_raises(ValueError, sample_domain_regular, k, shape, invalid_affine,
sigma)
samples = sample_domain_regular(k, shape, affine, sigma)
isamples = np.array(samples, dtype=np.int32)
indices = (isamples[:, 0] * shape[1] + isamples[:, 1])
# Verify correct number of points sampled
assert_array_equal(samples.shape, [n // k, dim])
# Verify all sampled points are different
assert_equal(len(set(indices)), len(indices))
# Verify the sampling was regular at rate k
assert_equal((indices % k).sum(), 0)
# Test 3D sampling
shape = np.array((5, 10, 10), dtype=np.int32)
affine = np.eye(4)
invalid_affine = np.eye(3)
sigma = 0
dim = len(shape)
n = shape[0] * shape[1] * shape[2]
k = 10
# Verify exception is raised with invalid affine
assert_raises(ValueError, sample_domain_regular, k, shape, invalid_affine,
sigma)
samples = sample_domain_regular(k, shape, affine, sigma)
isamples = np.array(samples, dtype=np.int32)
indices = (isamples[:, 0] * shape[1] * shape[2] +
isamples[:, 1] * shape[2] + isamples[:, 2])
# Verify correct number of points sampled
assert_array_equal(samples.shape, [n // k, dim])
# Verify all sampled points are different
assert_equal(len(set(indices)), len(indices))
# Verify the sampling was regular at rate k
assert_equal((indices % k).sum(), 0)
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_joint_pdf_gradients_sparse():
h = 1e-4
for ttype in factors:
dim = ttype[1]
if dim == 2:
nslices = 1
interp_method = vf.interpolate_scalar_2d
else:
nslices = 45
interp_method = vf.interpolate_scalar_3d
transform = regtransforms[ttype]
factor = factors[ttype]
theta = transform.get_identity_parameters()
static, moving, static_g2w, moving_g2w, smask, mmask, M = \
setup_random_transform(transform, factor, nslices, 5.0)
metric = MattesBase(32)
metric.setup(static, moving, smask, mmask)
# Sample the fixed-image 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)
# The routines in vector_fields operate, mostly, with float32 because
# they were thought to be used for non-linear registration. We may need
# to write some float64 counterparts for affine registration, where
# memory is not so big issue
intensities_static = np.array(intensities_static, dtype=np.float64)
# Compute the gradient at theta with the implementation under test
M = transform.param_to_matrix(theta)
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)
# Get the joint distribution evaluated at theta
J0 = np.copy(metric.joint)
spacing = np.ones(dim + 1, dtype=np.float64)
mgrad, inside = vf.sparse_gradient(moving.astype(np.float32),
sp_to_moving, spacing, samples)
metric.update_gradient_sparse(theta, transform, intensities_static,
intensities_moving, samples[..., :dim],
mgrad)
# Get the gradient of the joint distribution w.r.t. the transform
# parameters
actual = np.copy(metric.joint_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
# Update the joint distribution with the warped moving image
M = transform.param_to_matrix(dtheta)
sp_to_moving = np.linalg.inv(moving_g2w).dot(M)
samples_moving_grid = sp_to_moving.dot(samples.T).T
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)
J1 = np.copy(metric.joint)
expected[..., i] = (J1 - J0) / h
# Dot product and norms of gradients of each joint histogram cell
# i.e. the derivatives of each cell w.r.t. all parameters
P = (expected * actual).sum(2)
enorms = np.sqrt((expected ** 2).sum(2))
anorms = np.sqrt((actual ** 2).sum(2))
prodnorms = enorms*anorms
# Cosine of angle between the expected and actual gradients.
# Exclude very small gradients
P[prodnorms > 1e-6] /= (prodnorms[prodnorms > 1e-6])
P[prodnorms <= 1e-6] = 0
# Verify that a large proportion of the gradients point almost in
# the same direction. Disregard very small gradients
mean_cosine = P[P != 0].mean()
std_cosine = P[P != 0].std()
assert(mean_cosine > 0.99)
assert(std_cosine < 0.15)
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_joint_pdf_gradients_sparse():
h = 1e-4
for ttype in factors:
dim = ttype[1]
if dim == 2:
nslices = 1
interp_method = vf.interpolate_scalar_2d
else:
nslices = 45
interp_method = vf.interpolate_scalar_3d
transform = regtransforms[ttype]
factor = factors[ttype]
theta = transform.get_identity_parameters()
static, moving, static_g2w, moving_g2w, smask, mmask, M = \
setup_random_transform(transform, factor, nslices, 5.0)
metric = MattesBase(32)
metric.setup(static, moving, smask, mmask)
# Sample the fixed-image 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)
# The routines in vector_fields operate, mostly, with float32 because
# they were thought to be used for non-linear registration. We may need
# to write some float64 counterparts for affine registration, where
# memory is not so big issue
intensities_static = np.array(intensities_static, dtype=np.float64)
# Compute the gradient at theta with the implementation under test
M = transform.param_to_matrix(theta)
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)
# Get the joint distribution evaluated at theta
J0 = np.copy(metric.joint)
spacing = np.ones(dim + 1, dtype=np.float64)
mgrad, inside = vf.sparse_gradient(moving.astype(np.float32),
sp_to_moving, spacing, samples)
metric.update_gradient_sparse(theta, transform, intensities_static,
intensities_moving, samples[..., :dim],
mgrad)
# Get the gradient of the joint distribution w.r.t. the transform
# parameters
actual = np.copy(metric.joint_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
# Update the joint distribution with the warped moving image
M = transform.param_to_matrix(dtheta)
sp_to_moving = np.linalg.inv(moving_g2w).dot(M)
samples_moving_grid = sp_to_moving.dot(samples.T).T
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)
J1 = np.copy(metric.joint)
expected[..., i] = (J1 - J0) / h
# Dot product and norms of gradients of each joint histogram cell
# i.e. the derivatives of each cell w.r.t. all parameters
P = (expected * actual).sum(2)
enorms = np.sqrt((expected**2).sum(2))
anorms = np.sqrt((actual**2).sum(2))
prodnorms = enorms * anorms
# Cosine of angle between the expected and actual gradients.
# Exclude very small gradients
P[prodnorms > 1e-6] /= (prodnorms[prodnorms > 1e-6])
P[prodnorms <= 1e-6] = 0
# Verify that a large proportion of the gradients point almost in
# the same direction. Disregard very small gradients
mean_cosine = P[P != 0].mean()
std_cosine = P[P != 0].std()
assert (mean_cosine > 0.99)
assert (std_cosine < 0.15)
