def test_cubic_spline_derivative():
# Test derivative of the cubic spline, as defined in [Mattes03] eq. (3) by
# comparing the analytical and numerical derivatives
#
# [Mattes03] Mattes, D., Haynor, D. R., Vesselle, H., Lewellen, T. K.,
# & Eubank, W. PET-CT image registration in the chest using
# free-form deformations. IEEE Transactions on Medical Imaging,
# 22(1), 120-8, 2003.
in_list = []
for epsilon in [-1e-9, 0.0, 1e-9]:
for t in [-2.0, -1.0, 0.0, 1.0, 2.0]:
x = t + epsilon
in_list.append(x)
h = 1e-6
in_list = np.array(in_list)
input_h = in_list + h
s = np.array(cubic_spline(in_list))
s_h = np.array(cubic_spline(input_h))
expected = (s_h - s) / h
actual = cubic_spline_derivative(in_list)
assert_array_almost_equal(actual, expected)
def test_cubic_spline_derivative():
# Test derivative of the cubic spline, as defined in [Mattes03] eq. (3) by
# comparing the analytical and numerical derivatives
#
# [Mattes03] Mattes, D., Haynor, D. R., Vesselle, H., Lewellen, T. K.,
# & Eubank, W. PET-CT image registration in the chest using
# free-form deformations. IEEE Transactions on Medical Imaging,
# 22(1), 120-8, 2003.
in_list = []
for epsilon in [-1e-9, 0.0, 1e-9]:
for t in [-2.0, -1.0, 0.0, 1.0, 2.0]:
x = t + epsilon
in_list.append(x)
h = 1e-6
in_list = np.array(in_list)
input_h = in_list + h
s = np.array(cubic_spline(in_list))
s_h = np.array(cubic_spline(input_h))
expected = (s_h - s) / h
actual = cubic_spline_derivative(in_list)
assert_array_almost_equal(actual, expected)
def test_cubic_spline():
# Cubic spline as defined in [Mattes03] eq. (3)
#
# [Mattes03] Mattes, D., Haynor, D. R., Vesselle, H., Lewellen, T. K.,
# & Eubank, W. PET-CT image registration in the chest using
# free-form deformations. IEEE Transactions on Medical Imaging,
# 22(1), 120-8, 2003.
in_list = []
expected = []
for epsilon in [-1e-9, 0.0, 1e-9]:
for t in [-2.0, -1.0, 0.0, 1.0, 2.0]:
x = t + epsilon
in_list.append(x)
absx = np.abs(x)
sqrx = x * x
if absx < 1:
expected.append((4.0 - 6 * sqrx + 3.0 * (absx**3)) / 6.0)
elif absx < 2:
expected.append(((2 - absx)**3) / 6.0)
else:
expected.append(0.0)
actual = cubic_spline(np.array(in_list, dtype=np.float64))
assert_array_almost_equal(actual, np.array(expected, dtype=np.float64))
def test_cubic_spline():
# Cubic spline as defined in [Mattes03] eq. (3)
#
# [Mattes03] Mattes, D., Haynor, D. R., Vesselle, H., Lewellen, T. K.,
# & Eubank, W. PET-CT image registration in the chest using
# free-form deformations. IEEE Transactions on Medical Imaging,
# 22(1), 120-8, 2003.
in_list = []
expected = []
for epsilon in [-1e-9, 0.0, 1e-9]:
for t in [-2.0, -1.0, 0.0, 1.0, 2.0]:
x = t + epsilon
in_list.append(x)
absx = np.abs(x)
sqrx = x * x
if absx < 1:
expected.append((4.0 - 6 * sqrx + 3.0 * (absx ** 3)) / 6.0)
elif absx < 2:
expected.append(((2 - absx) ** 3) / 6.0)
else:
expected.append(0.0)
actual = cubic_spline(np.array(in_list, dtype=np.float64))
assert_array_almost_equal(actual, np.array(expected, dtype=np.float64))
def test_parzen_densities():
# Test the computation of the joint intensity distribution
# using a dense and a sparse set of values
seed = 1246592
nbins = 32
nr = 30
nc = 35
ns = 20
nvals = 50
for dim in [2, 3]:
if dim == 2:
shape = (nr, nc)
static, moving = create_random_image_pair(shape, nvals, seed)
else:
shape = (ns, nr, nc)
static, moving = create_random_image_pair(shape, nvals, seed)
# Initialize
parzen_hist = ParzenJointHistogram(nbins)
parzen_hist.setup(static, moving)
# Get distributions computed by dense sampling
parzen_hist.update_pdfs_dense(static, moving)
actual_joint_dense = parzen_hist.joint
actual_mmarginal_dense = parzen_hist.mmarginal
actual_smarginal_dense = parzen_hist.smarginal
# Get distributions computed by sparse sampling
sval = static.reshape(-1)
mval = moving.reshape(-1)
parzen_hist.update_pdfs_sparse(sval, mval)
actual_joint_sparse = parzen_hist.joint
actual_mmarginal_sparse = parzen_hist.mmarginal
actual_smarginal_sparse = parzen_hist.smarginal
# Compute the expected joint distribution with dense sampling
expected_joint_dense = np.zeros(shape=(nbins, nbins))
for index in ndindex(shape):
sv = parzen_hist.bin_normalize_static(static[index])
mv = parzen_hist.bin_normalize_moving(moving[index])
sbin = parzen_hist.bin_index(sv)
# The spline is centered at mv, will evaluate for all row
spline_arg = np.array([i - mv for i in range(nbins)])
contribution = cubic_spline(spline_arg)
expected_joint_dense[sbin, :] += contribution
# Compute the expected joint distribution with sparse sampling
expected_joint_sparse = np.zeros(shape=(nbins, nbins))
for index in range(sval.shape[0]):
sv = parzen_hist.bin_normalize_static(sval[index])
mv = parzen_hist.bin_normalize_moving(mval[index])
sbin = parzen_hist.bin_index(sv)
# The spline is centered at mv, will evaluate for all row
spline_arg = np.array([i - mv for i in range(nbins)])
contribution = cubic_spline(spline_arg)
expected_joint_sparse[sbin, :] += contribution
# Verify joint distributions
expected_joint_dense /= expected_joint_dense.sum()
expected_joint_sparse /= expected_joint_sparse.sum()
assert_array_almost_equal(actual_joint_dense, expected_joint_dense)
assert_array_almost_equal(actual_joint_sparse, expected_joint_sparse)
# Verify moving marginals
expected_mmarginal_dense = expected_joint_dense.sum(0)
expected_mmarginal_dense /= expected_mmarginal_dense.sum()
expected_mmarginal_sparse = expected_joint_sparse.sum(0)
expected_mmarginal_sparse /= expected_mmarginal_sparse.sum()
assert_array_almost_equal(actual_mmarginal_dense,
expected_mmarginal_dense)
assert_array_almost_equal(actual_mmarginal_sparse,
expected_mmarginal_sparse)
# Verify static marginals
expected_smarginal_dense = expected_joint_dense.sum(1)
expected_smarginal_dense /= expected_smarginal_dense.sum()
expected_smarginal_sparse = expected_joint_sparse.sum(1)
expected_smarginal_sparse /= expected_smarginal_sparse.sum()
assert_array_almost_equal(actual_smarginal_dense,
expected_smarginal_dense)
assert_array_almost_equal(actual_smarginal_sparse,
expected_smarginal_sparse)
def test_parzen_densities():
# Test the computation of the joint intensity distribution
# using a dense and a sparse set of values
seed = 1246592
nbins = 32
nr = 30
nc = 35
ns = 20
nvals = 50
for dim in [2, 3]:
if dim == 2:
shape = (nr, nc)
static, moving = create_random_image_pair(shape, nvals, seed)
else:
shape = (ns, nr, nc)
static, moving = create_random_image_pair(shape, nvals, seed)
# Initialize
parzen_hist = ParzenJointHistogram(nbins)
parzen_hist.setup(static, moving)
# Get distributions computed by dense sampling
parzen_hist.update_pdfs_dense(static, moving)
actual_joint_dense = parzen_hist.joint
actual_mmarginal_dense = parzen_hist.mmarginal
actual_smarginal_dense = parzen_hist.smarginal
# Get distributions computed by sparse sampling
sval = static.reshape(-1)
mval = moving.reshape(-1)
parzen_hist.update_pdfs_sparse(sval, mval)
actual_joint_sparse = parzen_hist.joint
actual_mmarginal_sparse = parzen_hist.mmarginal
actual_smarginal_sparse = parzen_hist.smarginal
# Compute the expected joint distribution with dense sampling
expected_joint_dense = np.zeros(shape=(nbins, nbins))
for index in ndindex(shape):
sv = parzen_hist.bin_normalize_static(static[index])
mv = parzen_hist.bin_normalize_moving(moving[index])
sbin = parzen_hist.bin_index(sv)
# The spline is centered at mv, will evaluate for all row
spline_arg = np.array([i - mv for i in range(nbins)])
contribution = cubic_spline(spline_arg)
expected_joint_dense[sbin, :] += contribution
# Compute the expected joint distribution with sparse sampling
expected_joint_sparse = np.zeros(shape=(nbins, nbins))
for index in range(sval.shape[0]):
sv = parzen_hist.bin_normalize_static(sval[index])
mv = parzen_hist.bin_normalize_moving(mval[index])
sbin = parzen_hist.bin_index(sv)
# The spline is centered at mv, will evaluate for all row
spline_arg = np.array([i - mv for i in range(nbins)])
contribution = cubic_spline(spline_arg)
expected_joint_sparse[sbin, :] += contribution
# Verify joint distributions
expected_joint_dense /= expected_joint_dense.sum()
expected_joint_sparse /= expected_joint_sparse.sum()
assert_array_almost_equal(actual_joint_dense, expected_joint_dense)
assert_array_almost_equal(actual_joint_sparse, expected_joint_sparse)
# Verify moving marginals
expected_mmarginal_dense = expected_joint_dense.sum(0)
expected_mmarginal_dense /= expected_mmarginal_dense.sum()
expected_mmarginal_sparse = expected_joint_sparse.sum(0)
expected_mmarginal_sparse /= expected_mmarginal_sparse.sum()
assert_array_almost_equal(actual_mmarginal_dense,
expected_mmarginal_dense)
assert_array_almost_equal(actual_mmarginal_sparse,
expected_mmarginal_sparse)
# Verify static marginals
expected_smarginal_dense = expected_joint_dense.sum(1)
expected_smarginal_dense /= expected_smarginal_dense.sum()
expected_smarginal_sparse = expected_joint_sparse.sum(1)
expected_smarginal_sparse /= expected_smarginal_sparse.sum()
assert_array_almost_equal(actual_smarginal_dense,
expected_smarginal_dense)
assert_array_almost_equal(actual_smarginal_sparse,
expected_smarginal_sparse)