def _recursive_procrustes(self):
r"""
Recursively calculates a procrustes alignment.
"""
from menpo.shape import mean_pointcloud
from menpo.transform import Similarity
if self.n_iterations > self.max_iterations:
return False
new_tgt = mean_pointcloud([t.aligned_source.points
for t in self.transforms])
# rescale the new_target to be the same size as the original about
# it's centre
rescale = Similarity.identity(new_tgt.n_dims)
s = UniformScale(self.initial_target_scale / new_tgt.norm(),
self.n_dims, skip_checks=True)
t = Translation(-new_tgt.centre, skip_checks=True)
rescale.compose_before_inplace(t)
rescale.compose_before_inplace(s)
rescale.compose_before_inplace(t.pseudoinverse)
rescale.apply_inplace(new_tgt)
# check to see if we have converged yet
delta_target = np.linalg.norm(self.target.points - new_tgt.points)
if delta_target < 1e-6:
return True
else:
self.n_iterations += 1
for t in self.transforms:
t.set_target(new_tgt)
self.target = new_tgt
return self._recursive_procrustes()
def noisy_align(source, target, noise_std=0.04, rotation=False):
r"""
Constructs and perturbs the optimal similarity transform between source
to the target by adding white noise to its weights.
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: 0.04
rotation: boolean
If False the second parameter of the Similarity,
which captures captures inplane rotations, is set to 0.
Default:False
Returns
-------
noisy_transform : :class: `menpo.transform.Similarity`
The noisy Similarity Transform
"""
transform = AlignmentSimilarity(source, target, rotation=rotation)
parameters = transform.as_vector()
parameter_range = np.hstack((parameters[:2], target.range()))
noise = (parameter_range * noise_std *
np.random.randn(transform.n_parameters))
return Similarity.identity(source.n_dims).from_vector(parameters + noise)
def noisy_align(source, target, noise_std=0.04, rotation=False):
r"""
Constructs and perturbs the optimal similarity transform between source
to the target by adding white noise to its weights.
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: 0.04
rotation: boolean
If False the second parameter of the Similarity,
which captures captures inplane rotations, is set to 0.
Default:False
Returns
-------
noisy_transform : :class: `menpo.transform.Similarity`
The noisy Similarity Transform
"""
transform = AlignmentSimilarity(source, target, rotation=rotation)
parameters = transform.as_vector()
parameter_range = np.hstack((parameters[:2], target.range()))
noise = (parameter_range * noise_std *
np.random.randn(transform.n_parameters))
return Similarity.identity(source.n_dims).from_vector(parameters + noise)
def _recursive_procrustes(self):
r"""
Recursively calculates a procrustes alignment.
"""
from menpo.shape import mean_pointcloud
from menpo.transform import Similarity
if self.n_iterations > self.max_iterations:
return False
new_tgt = mean_pointcloud(
[t.aligned_source.points for t in self.transforms])
# rescale the new_target to be the same size as the original about
# it's centre
rescale = Similarity.identity(new_tgt.n_dims)
s = UniformScale(self.initial_target_scale / new_tgt.norm(),
self.n_dims,
skip_checks=True)
t = Translation(-new_tgt.centre, skip_checks=True)
rescale.compose_before_inplace(t)
rescale.compose_before_inplace(s)
rescale.compose_before_inplace(t.pseudoinverse)
rescale.apply_inplace(new_tgt)
# check to see if we have converged yet
delta_target = np.linalg.norm(self.target.points - new_tgt.points)
if delta_target < 1e-6:
return True
else:
self.n_iterations += 1
for t in self.transforms:
t.set_target(new_tgt)
self.target = new_tgt
return self._recursive_procrustes()
def test_similarity_jacobian_2d():
params = np.ones(4)
t = Similarity.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 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 = Similarity.identity(2).from_vector(params)
assert_equal(sim.h_matrix, h**o)
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 = Similarity.identity(2).from_vector(params)
assert_equal(sim.h_matrix, h**o)
def test_similarity_jacobian_2d():
params = np.ones(4)
t = Similarity.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.d_dp(explicit_pixel_locations)
assert_equal(dW_dp, sim_jac_solution2d)
def test_similarity_2d_points_raises_dimensionalityerror():
params = np.ones(4)
t = Similarity.identity(2).from_vector(params)
t.d_dp(np.ones([2, 3]))
def test_similarity_identity_3d():
assert_allclose(Similarity.identity(3).h_matrix,
np.eye(4))
def test_similarity_identity_3d():
assert_allclose(Similarity.identity(3).h_matrix,
np.eye(4))
def test_similarity_2d_points_raises_dimensionalityerror():
params = np.ones(4)
t = Similarity.identity(2).from_vector(params)
t.d_dp(np.ones([2, 3]))
