/usr/lib/python2.7/dist-packages/dipy/align/tests/test_imaffine.py is in python-dipy 0.10.1-1.
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import scipy as sp
import nibabel as nib
import numpy.linalg as npl
from numpy.testing import (assert_array_equal,
assert_array_almost_equal,
assert_almost_equal,
assert_equal,
assert_raises)
from dipy.core import geometry as geometry
from dipy.data import get_data
from dipy.viz import regtools as rt
from dipy.align import floating
from dipy.align import vector_fields as vf
from dipy.align import imaffine
from dipy.align.imaffine import AffineInversionError
from dipy.align.transforms import (Transform,
regtransforms)
from dipy.align.tests.test_parzenhist import (setup_random_transform,
sample_domain_regular)
# For each transform type, select a transform factor (indicating how large the
# true transform between static and moving images will be), a sampling scheme
# (either a positive integer less than or equal to 100, or None) indicating
# the percentage (if int) of voxels to be used for estimating the joint PDFs,
# or dense sampling (if None), and also specify a starting point (to avoid
# starting from the identity)
factors = {('TRANSLATION', 2): (2.0, 0.35, np.array([2.3, 4.5])),
('ROTATION', 2): (0.1, None, np.array([0.1])),
('RIGID', 2): (0.1, .50, np.array([0.12, 1.8, 2.7])),
('SCALING', 2): (0.01, None, np.array([1.05])),
('AFFINE', 2): (0.1, .50, np.array([0.99, -0.05, 1.3, 0.05, 0.99, 2.5])),
('TRANSLATION', 3): (2.0, None, np.array([2.3, 4.5, 1.7])),
('ROTATION', 3): (0.1, 1.0, np.array([0.1, 0.15, -0.11])),
('RIGID', 3): (0.1, None, np.array([0.1, 0.15, -0.11, 2.3, 4.5, 1.7])),
('SCALING', 3): (0.1, .35, np.array([0.95])),
('AFFINE', 3): (0.1, None, np.array([0.99, -0.05, 0.03, 1.3,
0.05, 0.99, -0.10, 2.5,
-0.07, 0.10, 0.99, -1.4]))}
def test_transform_centers_of_mass_3d():
np.random.seed(1246592)
shape = (64, 64, 64)
rm = 8
sp = vf.create_sphere(shape[0]//2, shape[1]//2, shape[2]//2, rm)
moving = np.zeros(shape)
# The center of mass will be (16, 16, 16), in image coordinates
moving[:shape[0]//2, :shape[1]//2, :shape[2]//2] = sp[...]
rs = 16
# The center of mass will be (32, 32, 32), in image coordinates
static = vf.create_sphere(shape[0], shape[1], shape[2], rs)
# Create arbitrary image-to-space transforms
axis = np.array([.5, 2.0, 1.5])
t = 0.15 #translation factor
trans = np.array([[1, 0, 0, -t*shape[0]],
[0, 1, 0, -t*shape[1]],
[0, 0, 1, -t*shape[2]],
[0, 0, 0, 1]])
trans_inv = npl.inv(trans)
for rotation_angle in [-1 * np.pi/6.0, 0.0, np.pi/5.0]:
for scale_factor in [0.83, 1.3, 2.07]: #scale
rot = np.zeros(shape=(4,4))
rot[:3, :3] = geometry.rodrigues_axis_rotation(axis,
rotation_angle)
rot[3,3] = 1.0
scale = np.array([[1 * scale_factor, 0, 0, 0],
[0, 1 * scale_factor, 0, 0],
[0, 0, 1 * scale_factor, 0],
[0, 0, 0, 1]])
static_grid2world = trans_inv.dot(scale.dot(rot.dot(trans)))
moving_grid2world = npl.inv(static_grid2world)
# Expected translation
c_static = static_grid2world.dot((32, 32, 32, 1))[:3]
c_moving = moving_grid2world.dot((16, 16, 16, 1))[:3]
expected = np.eye(4);
expected[:3, 3] = c_moving - c_static
# Implementation under test
actual = imaffine.transform_centers_of_mass(static, static_grid2world,
moving, moving_grid2world)
assert_array_almost_equal(actual.affine, expected)
def test_transform_geometric_centers_3d():
# Create arbitrary image-to-space transforms
axis = np.array([.5, 2.0, 1.5])
t = 0.15 #translation factor
for theta in [-1 * np.pi/6.0, 0.0, np.pi/5.0]: #rotation angle
for s in [0.83, 1.3, 2.07]: #scale
m_shapes = [(256, 256, 128), (255, 255, 127), (64, 127, 142)]
for shape_moving in m_shapes:
s_shapes = [(256, 256, 128), (255, 255, 127), (64, 127, 142)]
for shape_static in s_shapes:
moving = np.ndarray(shape=shape_moving)
static = np.ndarray(shape=shape_static)
trans = np.array([[1, 0, 0, -t*shape_static[0]],
[0, 1, 0, -t*shape_static[1]],
[0, 0, 1, -t*shape_static[2]],
[0, 0, 0, 1]])
trans_inv = npl.inv(trans)
rot = np.zeros(shape=(4,4))
rot[:3, :3] = geometry.rodrigues_axis_rotation(axis, theta)
rot[3,3] = 1.0
scale = np.array([[1 * s, 0, 0, 0],
[0, 1 * s, 0, 0],
[0, 0, 1 * s, 0],
[0, 0, 0, 1]])
static_grid2world = trans_inv.dot(scale.dot(rot.dot(trans)))
moving_grid2world = npl.inv(static_grid2world)
# Expected translation
c_static = np.array(shape_static, dtype = np.float64) * 0.5
c_static = tuple(c_static)
c_static = static_grid2world.dot(c_static+(1,))[:3]
c_moving = np.array(shape_moving, dtype = np.float64) * 0.5
c_moving = tuple(c_moving)
c_moving = moving_grid2world.dot(c_moving+(1,))[:3]
expected = np.eye(4);
expected[:3, 3] = c_moving - c_static
# Implementation under test
actual = imaffine.transform_geometric_centers(static,
static_grid2world, moving, moving_grid2world)
assert_array_almost_equal(actual.affine, expected)
def test_transform_origins_3d():
# Create arbitrary image-to-space transforms
axis = np.array([.5, 2.0, 1.5])
t = 0.15 #translation factor
for theta in [-1 * np.pi/6.0, 0.0, np.pi/5.0]: #rotation angle
for s in [0.83, 1.3, 2.07]: #scale
m_shapes = [(256, 256, 128), (255, 255, 127), (64, 127, 142)]
for shape_moving in m_shapes:
s_shapes = [(256, 256, 128), (255, 255, 127), (64, 127, 142)]
for shape_static in s_shapes:
moving = np.ndarray(shape=shape_moving)
static = np.ndarray(shape=shape_static)
trans = np.array([[1, 0, 0, -t*shape_static[0]],
[0, 1, 0, -t*shape_static[1]],
[0, 0, 1, -t*shape_static[2]],
[0, 0, 0, 1]])
trans_inv = npl.inv(trans)
rot = np.zeros(shape=(4,4))
rot[:3, :3] = geometry.rodrigues_axis_rotation(axis, theta)
rot[3,3] = 1.0
scale = np.array([[1*s, 0, 0, 0],
[0, 1*s, 0, 0],
[0, 0, 1*s, 0],
[0, 0, 0, 1]])
static_grid2world = trans_inv.dot(scale.dot(rot.dot(trans)))
moving_grid2world = npl.inv(static_grid2world)
# Expected translation
c_static = static_grid2world[:3, 3]
c_moving = moving_grid2world[:3, 3]
expected = np.eye(4);
expected[:3, 3] = c_moving - c_static
# Implementation under test
actual = imaffine.transform_origins(static, static_grid2world,
moving, moving_grid2world)
assert_array_almost_equal(actual.affine, expected)
def test_affreg_all_transforms():
# Test affine registration using all transforms with typical settings
# Make sure dictionary entries are processed in the same order regardless of
# the platform. Otherwise any random numbers drawn within the loop would make
# the test non-deterministic even if we fix the seed before the loop.
# Right now, this test does not draw any samples, but we still sort the entries
# to prevent future related failures.
for ttype in sorted(factors):
dim = ttype[1]
if dim == 2:
nslices = 1
else:
nslices = 45
factor = factors[ttype][0]
sampling_pc = factors[ttype][1]
transform = regtransforms[ttype]
static, moving, static_grid2world, moving_grid2world, smask, mmask, T = \
setup_random_transform(transform, factor, nslices, 1.0)
# Sum of absolute differences
start_sad = np.abs(static - moving).sum()
metric = imaffine.MutualInformationMetric(32, sampling_pc)
affreg = imaffine.AffineRegistration(metric,
[1000, 100, 50],
[3, 1, 0],
[4, 2, 1],
'L-BFGS-B',
None,
options=None)
x0 = transform.get_identity_parameters()
affine_map = affreg.optimize(static, moving, transform, x0,
static_grid2world, moving_grid2world)
transformed = affine_map.transform(moving)
# Sum of absolute differences
end_sad = np.abs(static - transformed).sum()
reduction = 1 - end_sad / start_sad
print("%s>>%f"%(ttype, reduction))
assert(reduction > 0.9)
# Verify that exception is raised if level_iters is empty
metric = imaffine.MutualInformationMetric(32)
assert_raises(ValueError, imaffine.AffineRegistration, metric, [])
def test_affreg_defaults():
# Test all default arguments with an arbitrary transform
# Select an arbitrary transform (all of them are already tested
# in test_affreg_all_transforms)
transform_name = 'TRANSLATION'
dim = 2
ttype = (transform_name, dim)
aff_options = ['mass', 'voxel-origin', 'centers', None, np.eye(dim+1)]
for starting_affine in aff_options:
if dim == 2:
nslices = 1
else:
nslices = 45
factor = factors[ttype][0]
sampling_pc = factors[ttype][1]
transform = regtransforms[ttype]
id_param = transform.get_identity_parameters()
static, moving, static_grid2world, moving_grid2world, smask, mmask, T = \
setup_random_transform(transform, factor, nslices, 1.0)
# Sum of absolute differences
start_sad = np.abs(static - moving).sum()
metric = None
x0 = None
sigmas = None
scale_factors = None
level_iters = None
static_grid2world = None
moving_grid2world = None
for ss_sigma_factor in [1.0, None]:
affreg = imaffine.AffineRegistration(metric,
level_iters,
sigmas,
scale_factors,
'L-BFGS-B',
ss_sigma_factor,
options=None)
affine_map = affreg.optimize(static, moving, transform, x0,
static_grid2world, moving_grid2world,
starting_affine)
transformed = affine_map.transform(moving)
# Sum of absolute differences
end_sad = np.abs(static - transformed).sum()
reduction = 1 - end_sad / start_sad
print("%s>>%f"%(ttype, reduction))
assert(reduction > 0.9)
transformed_inv = affine_map.transform_inverse(static)
# Sum of absolute differences
end_sad = np.abs(moving - transformed_inv).sum()
reduction = 1 - end_sad / start_sad
print("%s>>%f"%(ttype, reduction))
assert(reduction > 0.9)
def test_mi_gradient():
np.random.seed(2022966)
# Test the gradient of mutual information
h = 1e-5
# Make sure dictionary entries are processed in the same order regardless of
# the platform. Otherwise any random numbers drawn within the loop would make
# the test non-deterministic even if we fix the seed before the loop:
# in this case the samples are drawn with `np.random.randn` below
for ttype in sorted(factors):
transform = regtransforms[ttype]
dim = ttype[1]
if dim == 2:
nslices = 1
else:
nslices = 45
factor = factors[ttype][0]
sampling_proportion = factors[ttype][1]
theta = factors[ttype][2]
# Start from a small rotation
start = regtransforms[('ROTATION', dim)]
nrot = start.get_number_of_parameters()
starting_affine = start.param_to_matrix(0.25 * np.random.randn(nrot))
# Get data (pair of images related to each other by an known transform)
static, moving, static_g2w, moving_g2w, smask, mmask, M = \
setup_random_transform(transform, factor, nslices, 2.0)
# Prepare a MutualInformationMetric instance
mi_metric = imaffine.MutualInformationMetric(32, sampling_proportion)
mi_metric.setup(transform, static, moving, starting_affine=starting_affine)
# Compute the gradient with the implementation under test
actual = mi_metric.gradient(theta)
# Compute the gradient using finite-diferences
n = transform.get_number_of_parameters()
expected = np.empty(n, dtype=np.float64)
val0 = mi_metric.distance(theta)
for i in range(n):
dtheta = theta.copy()
dtheta[i] += h
val1 = mi_metric.distance(dtheta)
expected[i] = (val1 - val0) / h
dp = expected.dot(actual)
enorm = npl.norm(expected)
anorm = npl.norm(actual)
nprod = dp / (enorm * anorm)
assert(nprod >= 0.99)
def create_affine_transforms(dim, translations, rotations, scales, rot_axis=None):
r""" Creates a list of affine transforms with all combinations of params
This function is intended to be used for testing only. It generates
affine transforms for all combinations of the input parameters in the
following order: let T be a translation, R a rotation and S a scale. The
generated affine will be:
A = T.dot(S).dot(R).dot(T^{-1})
Translation is handled this way because it is convenient to provide
the translation parameters in terms of the center of rotation we wish
to generate.
Parameters
----------
dim: int (either dim=2 or dim=3)
dimension of the affine transforms
translations: sequence of dim-tuples
each dim-tuple represents a translation parameter
rotations: sequence of floats
each number represents a rotation angle in radians
scales: sequence of floats
each number represents a scale
rot_axis: rotation axis (used for dim=3 only)
Returns
-------
transforms: sequence of (dim + 1)x(dim + 1) matrices
each matrix correspond to an affine transform with a combination
of the input parameters
"""
transforms = []
for t in translations:
trans_inv = np.eye(dim + 1)
trans_inv[:dim, dim] = -t[:dim]
trans = npl.inv(trans_inv)
for theta in rotations: # rotation angle
if dim == 2:
ct = np.cos(theta)
st = np.sin(theta)
rot = np.array([[ct, -st, 0],
[st, ct, 0],
[0, 0, 1]])
else:
rot = np.eye(dim + 1)
rot[:3, :3] = geometry.rodrigues_axis_rotation(rot_axis, theta)
for s in scales: # scale
scale = np.eye(dim + 1) * s
scale[dim,dim] = 1
affine = trans.dot(scale.dot(rot.dot(trans_inv)))
transforms.append(affine)
return transforms
def test_affine_map():
np.random.seed(2112927)
dom_shape = np.array([64, 64, 64], dtype=np.int32)
cod_shape = np.array([80, 80, 80], dtype=np.int32)
nx = dom_shape[0]
ny = dom_shape[1]
nz = dom_shape[2]
# Radius of the circle/sphere (testing image)
radius = 16
# Rotation axis (used for 3D transforms only)
rot_axis = np.array([.5, 2.0, 1.5])
# Arbitrary transform parameters
t = 0.15
rotations = [-1 * np.pi / 10.0, 0.0, np.pi / 10.0]
scales = [0.9, 1.0, 1.1]
for dim in [2, 3]:
# Setup current dimension
if dim == 2:
# Create image of a circle
img = vf.create_circle(cod_shape[0], cod_shape[1], radius)
oracle_linear = vf.transform_2d_affine
oracle_nn = vf.transform_2d_affine_nn
else:
# Create image of a sphere
img = vf.create_sphere(cod_shape[0], cod_shape[1], cod_shape[2],
radius)
oracle_linear = vf.transform_3d_affine
oracle_nn = vf.transform_3d_affine_nn
img = np.array(img)
# Translation is the only parameter differing for 2D and 3D
translations = [t * dom_shape[:dim]]
# Generate affine transforms
gt_affines = create_affine_transforms(dim, translations, rotations,
scales, rot_axis)
# Include the None case
gt_affines.append(None)
for affine in gt_affines:
# make both domain point to the same physical region
# It's ok to use the same transform, we just want to test
# that this information is actually being considered
domain_grid2world = affine
codomain_grid2world = affine
grid2grid_transform = affine
# Evaluate the transform with vector_fields module (already tested)
expected_linear = oracle_linear(img, dom_shape[:dim],
grid2grid_transform)
expected_nn = oracle_nn(img, dom_shape[:dim], grid2grid_transform)
# Evaluate the transform with the implementation under test
affine_map = imaffine.AffineMap(affine,
dom_shape[:dim], domain_grid2world,
cod_shape[:dim], codomain_grid2world)
actual_linear = affine_map.transform(img, interp='linear')
actual_nn = affine_map.transform(img, interp='nearest')
assert_array_almost_equal(actual_linear, expected_linear)
assert_array_almost_equal(actual_nn, expected_nn)
# Test set_affine with valid matrix
affine_map.set_affine(affine)
if affine is None:
assert(affine_map.affine is None)
assert(affine_map.affine_inv is None)
else:
assert_array_equal(affine, affine_map.affine)
actual = affine_map.affine.dot(affine_map.affine_inv)
assert_array_almost_equal(actual, np.eye(dim+1))
# Evaluate via the inverse transform
# AffineMap will use the inverse of the input matrix when we call
# `transform_inverse`. Since the inverse of the inverse of a matrix
# is not exactly equal to the original matrix (numerical limitations)
# we need to invert the matrix twice to make sure the oracle and the
# implementation under test apply the same transform
aff_inv = None if affine is None else npl.inv(affine)
aff_inv_inv = None if aff_inv is None else npl.inv(aff_inv)
expected_linear = oracle_linear(img, dom_shape[:dim],
aff_inv_inv)
expected_nn = oracle_nn(img, dom_shape[:dim], aff_inv_inv)
affine_map = imaffine.AffineMap(aff_inv,
cod_shape[:dim], codomain_grid2world,
dom_shape[:dim], domain_grid2world)
actual_linear = affine_map.transform_inverse(img, interp='linear')
actual_nn = affine_map.transform_inverse(img, interp='nearest')
assert_array_almost_equal(actual_linear, expected_linear)
assert_array_almost_equal(actual_nn, expected_nn)
# Verify AffineMap cannot be created with a non-invertible matrix
invalid_nan = np.zeros((dim + 1, dim + 1), dtype=np.float64)
invalid_nan[1, 1] = np.nan
invalid_zeros = np.zeros((dim + 1, dim + 1), dtype=np.float64)
assert_raises(imaffine.AffineInversionError, imaffine.AffineMap, invalid_nan)
assert_raises(imaffine.AffineInversionError, imaffine.AffineMap, invalid_zeros)
# Test exception is raised when the affine transform matrix is not valid
invalid_shape = np.eye(dim)
affmap_invalid_shape = imaffine.AffineMap(invalid_shape,
dom_shape[:dim], None,
cod_shape[:dim], None)
assert_raises(ValueError, affmap_invalid_shape.transform, img)
assert_raises(ValueError, affmap_invalid_shape.transform_inverse, img)
# Verify exception is raised when sampling info is not provided
valid = np.eye(3)
affmap_invalid_shape = imaffine.AffineMap(valid)
assert_raises(ValueError, affmap_invalid_shape.transform, img)
assert_raises(ValueError, affmap_invalid_shape.transform_inverse, img)
# Verify exception is raised when requesting an invalid interpolation
assert_raises(ValueError, affine_map.transform, img, 'invalid')
assert_raises(ValueError, affine_map.transform_inverse, img, 'invalid')
# Verify exception is raised when attempting to warp an image of
# invalid dimension
for dim in [2, 3]:
affine_map = imaffine.AffineMap(np.eye(dim),
cod_shape[:dim], None,
dom_shape[:dim], None)
for sh in [(2,), (2,2,2,2)]:
img = np.zeros(sh)
assert_raises(ValueError, affine_map.transform, img)
assert_raises(ValueError, affine_map.transform_inverse, img)
aff_sing = np.zeros((dim + 1, dim + 1))
aff_nan = np.zeros((dim + 1, dim + 1))
aff_nan[...] = np.nan
aff_inf = np.zeros((dim + 1, dim + 1))
aff_inf[...] = np.inf
assert_raises(AffineInversionError, affine_map.set_affine, aff_sing)
assert_raises(AffineInversionError, affine_map.set_affine, aff_nan)
assert_raises(AffineInversionError, affine_map.set_affine, aff_inf)
def test_MIMetric_invalid_params():
transform = regtransforms[('AFFINE', 3)]
static = np.random.rand(20,20,20)
moving = np.random.rand(20,20,20)
n = transform.get_number_of_parameters()
sampling_proportion = 0.3
theta_sing = np.zeros(n)
theta_nan = np.zeros(n)
theta_nan[...] = np.nan
theta_inf = np.zeros(n)
theta_nan[...] = np.inf
mi_metric = imaffine.MutualInformationMetric(32, sampling_proportion)
mi_metric.setup(transform, static, moving)
for theta in [theta_sing, theta_nan, theta_inf]:
# Test metric value at invalid params
actual_val = mi_metric.distance(theta)
assert(np.isinf(actual_val))
# Test gradient at invalid params
expected_grad = np.zeros(n)
actual_grad = mi_metric.gradient(theta)
assert_equal(actual_grad, expected_grad)
# Test both
actual_val, actual_grad = mi_metric.distance_and_gradient(theta)
assert(np.isinf(actual_val))
assert_equal(actual_grad, expected_grad)
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