def test_diffeomorphic_map_simplification_2d():
r"""
Create an invertible deformation field, and define a DiffeomorphicMap
using different voxel-to-space transforms for domain, codomain, and
reference discretizations, also use a non-identity pre-aligning matrix.
Warp a circle using the diffeomorphic map to obtain the expected warped
circle. Now simplify the DiffeomorphicMap and warp the same circle using
this simplified map. Verify that the two warped circles are equal up to
numerical precision.
"""
#create a simple affine transformation
dom_shape = (64, 64)
cod_shape = (80, 80)
nr = dom_shape[0]
nc = dom_shape[1]
s = 1.1
t = 0.25
trans = np.array([[1, 0, -t*nr],
[0, 1, -t*nc],
[0, 0, 1]])
trans_inv = np.linalg.inv(trans)
scale = np.array([[1*s, 0, 0],
[0, 1*s, 0],
[0, 0, 1]])
gt_affine = trans_inv.dot(scale.dot(trans))
# Create the invertible displacement fields and the circle
radius = 16
circle = vfu.create_circle(cod_shape[0], cod_shape[1], radius)
d, dinv = vfu.create_harmonic_fields_2d(dom_shape[0], dom_shape[1], 0.3, 6)
#Define different voxel-to-space transforms for domain, codomain and
#reference grid, also, use a non-identity pre-align transform
D = gt_affine
C = imwarp.mult_aff(gt_affine, gt_affine)
R = np.eye(3)
P = gt_affine
#Create the original diffeomorphic map
diff_map = imwarp.DiffeomorphicMap(2, dom_shape, R,
dom_shape, D,
cod_shape, C,
P)
diff_map.forward = np.array(d, dtype = floating)
diff_map.backward = np.array(dinv, dtype = floating)
#Warp the circle to obtain the expected image
expected = diff_map.transform(circle, 'linear')
#Simplify
simplified = diff_map.get_simplified_transform()
#warp the circle
warped = simplified.transform(circle, 'linear')
#verify that the simplified map is equivalent to the
#original one
assert_array_almost_equal(warped, expected)
#And of course, it must be simpler...
assert_equal(simplified.domain_affine, None)
assert_equal(simplified.codomain_affine, None)
assert_equal(simplified.disp_affine, None)
assert_equal(simplified.domain_affine_inv, None)
assert_equal(simplified.codomain_affine_inv, None)
assert_equal(simplified.disp_affine_inv, None)
def test_mult_aff():
r""" Test matrix multiplication using None as identity
"""
A = np.array([[1.0, 2.0], [3.0, 4.0]])
B = np.array([[2.0, 0.0], [0.0, 2.0]])
C = imwarp.mult_aff(A, B)
expected_mult = np.array([[2.0, 4.0], [6.0, 8.0]])
assert_array_almost_equal(C, expected_mult)
C = imwarp.mult_aff(A, None)
assert_array_almost_equal(C, A)
C = imwarp.mult_aff(None, B)
assert_array_almost_equal(C, B)
C = imwarp.mult_aff(None, None)
assert_equal(C, None)
def test_mult_aff():
r""" Test matrix multiplication using None as identity
"""
A = np.array([[1.0, 2.0], [3.0, 4.0]])
B = np.array([[2.0, 0.0], [0.0, 2.0]])
C = imwarp.mult_aff(A, B)
expected_mult = np.array([[2.0, 4.0], [6.0, 8.0]])
assert_array_almost_equal(C, expected_mult)
C = imwarp.mult_aff(A, None)
assert_array_almost_equal(C, A)
C = imwarp.mult_aff(None, B)
assert_array_almost_equal(C, B)
C = imwarp.mult_aff(None, None)
assert_equal(C, None)
def test_mult_aff():
r"""mult_aff from imwarp returns the matrix product A.dot(B) considering
None as the identity
"""
A = np.array([[1.0, 2.0], [3.0, 4.0]])
B = np.array([[2.0, 0.0], [0.0, 2.0]])
C = imwarp.mult_aff(A, B)
expected_mult = np.array([[2.0, 4.0], [6.0, 8.0]])
assert_array_almost_equal(C, expected_mult)
C = imwarp.mult_aff(A, None)
assert_array_almost_equal(C, A)
C = imwarp.mult_aff(None, B)
assert_array_almost_equal(C, B)
C = imwarp.mult_aff(None, None)
assert_equal(C, None)