def test_basic_2d_similarity():
linear_component = np.array([[2, -6],
[6, 2]])
translation_component = np.array([7, -8])
h_matrix = np.eye(3, 3)
h_matrix[:-1, :-1] = linear_component
h_matrix[:-1, -1] = translation_component
similarity = SimilarityTransform(h_matrix)
x = np.array([[0, 1],
[1, 1],
[-1, -5],
[3, -5]])
# transform x explicitly
solution = np.dot(x, linear_component.T) + translation_component
# transform x using the affine transform
result = similarity.apply(x)
# check that both answers are equivalent
assert_allclose(solution, result)
# create several copies of x
x_copies = np.array([x, x, x, x, x, x, x, x])
# transform all of copies at once using the affine transform
results = similarity.apply(x_copies)
# check that all copies have been transformed correctly
for r in results:
assert_allclose(solution, r)
def test_similarity_2d_from_vector():
params = np.array([0.2, 0.1, 1, 2])
h**o = np.array([[params[0] + 1, -params[1], params[2]],
[params[1], params[0] + 1, params[3]],
[0, 0, 1]])
sim = SimilarityTransform.identity(2).from_vector(params)
assert_equal(sim.h_matrix, h**o)
def test_align_2d_similarity():
linear_component = np.array([[2, -6],
[6, 2]])
translation_component = np.array([7, -8])
h_matrix = np.eye(3, 3)
h_matrix[:-1, :-1] = linear_component
h_matrix[:-1, -1] = translation_component
similarity = SimilarityTransform(h_matrix)
source = PointCloud(np.array([[0, 1],
[1, 1],
[-1, -5],
[3, -5]]))
target = similarity.apply(source)
# estimate the transform from source and target
estimate = SimilarityTransform.align(source, target)
# check the estimates is correct
assert_allclose(similarity.h_matrix,
estimate.h_matrix)
def test_similarity_jacobian_2d():
params = np.ones(4)
t = SimilarityTransform.identity(2).from_vector(params)
explicit_pixel_locations = np.array(
[[0, 0],
[0, 1],
[0, 2],
[1, 0],
[1, 1],
[1, 2]])
dW_dp = t.jacobian(explicit_pixel_locations)
assert_equal(dW_dp, sim_jac_solution2d)
def noisy_align(source, target, noise_std=0.05, rotation=False):
r"""
Constructs and perturbs the optimal similarity transform between source
to the target by adding white noise to its parameters.
Parameters
----------
source: :class:`menpo.shape.PointCloud`
The source pointcloud instance used in the alignment
target: :class:`menpo.shape.PointCloud`
The target pointcloud instance used in the alignment
noise_std: float
The standard deviation of the white noise
Default: 0.05
rotation: boolean
If False the second parameter of the SimilarityTransform,
which captures captures inplane rotations, is set to 0.
Default:False
Returns
-------
noisy_transform : :class: `menpo.transform.SimilarityTransform`
The noisy Similarity Transform
"""
transform = SimilarityTransform.align(source, target)
parameters = transform.as_vector()
if not rotation:
parameters[1] = 0
parameter_range = np.hstack((parameters[:2], target.range()))
noise = (parameter_range * noise_std *
np.random.randn(transform.n_parameters))
parameters += noise
return SimilarityTransform.identity(source.n_dims).from_vector_inplace(
parameters)
def test_similarity_identity_3d():
assert_allclose(SimilarityTransform.identity(3).h_matrix,
np.eye(4))
def test_similarity_2d_points_raises_dimensionalityerror():
params = np.ones(4)
t = SimilarityTransform.identity(2).from_vector(params)
t.jacobian(np.ones([2, 3]))
def test_similarity_jacobian_3d_raises_dimensionalityerror():
t = SimilarityTransform(np.eye(4))
t.jacobian(np.ones([2, 3]))