def crop_image(img, center, scale, res, base=384):
h = base * scale
t = Translation(
[
res[0] * (-center[0] / h + .5),
res[1] * (-center[1] / h + .5)
]) \
.compose_after(
Scale(
(res[0] / h,
res[1] / h)
)).pseudoinverse()
# Upper left point of original image
ul = np.floor(t.apply([0, 0]))
# Bottom right point of original image
br = np.ceil(t.apply(res).astype(np.int))
# crop and rescale
cimg, trans = img.warp_to_shape(br - ul,
Translation(-(br - ul) / 2 +
(br + ul) / 2),
return_transform=True)
c_scale = np.min(cimg.shape) / np.mean(res)
new_img = cimg.rescale(1 / c_scale).resize(res)
return new_img, trans, c_scale
def noisy_alignment_similarity_transform(source, target, noise_type='uniform',
noise_percentage=0.1,
allow_alignment_rotation=False):
r"""
Constructs and perturbs the optimal similarity transform between the source
and target shapes by adding noise to its parameters.
Parameters
----------
source : `menpo.shape.PointCloud`
The source pointcloud instance used in the alignment
target : `menpo.shape.PointCloud`
The target pointcloud instance used in the alignment
noise_type : ``{'uniform', 'gaussian'}``, optional
The type of noise to be added.
noise_percentage : `float` in ``(0, 1)`` or `list` of `len` `3`, optional
The standard percentage of noise to be added. If `float`, then the same
amount of noise is applied to the scale, rotation and translation
parameters of the optimal similarity transform. If `list` of
`float` it must have length 3, where the first, second and third elements
denote the amount of noise to be applied to the scale, rotation and
translation parameters, respectively.
allow_alignment_rotation : `bool`, optional
If ``False``, then the rotation is not considered when computing the
optimal similarity transform between source and target.
Returns
-------
noisy_alignment_similarity_transform : `menpo.transform.Similarity`
The noisy Similarity Transform between source and target.
"""
if isinstance(noise_percentage, float):
noise_percentage = [noise_percentage] * 3
elif len(noise_percentage) == 1:
noise_percentage *= 3
similarity = AlignmentSimilarity(source, target,
rotation=allow_alignment_rotation)
if noise_type is 'gaussian':
s = noise_percentage[0] * (0.5 / 3) * np.asscalar(np.random.randn(1))
r = noise_percentage[1] * (180 / 3) * np.asscalar(np.random.randn(1))
t = noise_percentage[2] * (target.range() / 3) * np.random.randn(2)
s = scale_about_centre(target, 1 + s)
r = rotate_ccw_about_centre(target, r)
t = Translation(t, source.n_dims)
elif noise_type is 'uniform':
s = noise_percentage[0] * 0.5 * (2 * np.asscalar(np.random.randn(1)) - 1)
r = noise_percentage[1] * 180 * (2 * np.asscalar(np.random.rand(1)) - 1)
t = noise_percentage[2] * target.range() * (2 * np.random.rand(2) - 1)
s = scale_about_centre(target, 1. + s)
r = rotate_ccw_about_centre(target, r)
t = Translation(t, source.n_dims)
else:
raise ValueError('Unexpected noise type. '
'Supported values are {gaussian, uniform}')
return similarity.compose_after(t.compose_after(s.compose_after(r)))
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 _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 skew_shape(pointcloud, theta, phi):
r"""
Method that skews the provided pointcloud.
Parameters
----------
pointcloud : `menpo.shape.PointCloud`
The shape to distort.
theta : `float`
The skew angle over x axis (tan(theta)).
phi : `float`
The skew angle over y axis (tan(phi)).
Returns
-------
skewed_shape : `menpo.shape.PointCloud`
The skewed (distorted) pointcloud.
"""
rotate_ccw = Similarity.init_identity(pointcloud.n_dims)
# Create skew matrix
h_matrix = np.ones((3, 3))
h_matrix[0, 1] = np.tan(theta * np.pi / 180.)
h_matrix[1, 0] = np.tan(phi * np.pi / 180.)
h_matrix[:2, 2] = 0.
h_matrix[2, :2] = 0.
r = Affine(h_matrix)
t = Translation(-pointcloud.centre(), skip_checks=True)
# Translate to origin, rotate counter-clockwise, then translate back
rotate_ccw.compose_before_inplace(t)
rotate_ccw.compose_before_inplace(r)
rotate_ccw.compose_before_inplace(t.pseudoinverse())
return rotate_ccw.apply(pointcloud)
def lm_centres_correction(centres):
r"""
Construct a transform that will correct landmarks for a window
iterating feature calculation
Parameters
----------
centres : `ndarray` (H, W, 2)
The location of the window centres in the features
Returns
-------
:map:`Affine`
An affine transform that performs the correction.
Should be applied to the landmarks on the target image.
"""
t = Translation(-centres.min(axis=0).min(axis=0), skip_checks=True)
step_v = centres[0, 0, 0]
if centres.shape[0] > 1:
step_v = centres[1, 0, 0] - centres[0, 0, 0]
step_h = centres[0, 0, 1]
if centres.shape[1] > 1:
step_h = centres[0, 1, 1] - centres[0, 0, 1]
s = NonUniformScale((1. / step_v, 1. / step_h), skip_checks=True)
return t.compose_before(s)
def optimal_cylindrical_unwrap(points):
r"""
Returns a :map:`TransformChain` of
[:map:`Translation`, :map:`CylindricalUnwrap`]
which optimally cylindrically unwraps the points provided. This is done by:
#. Find an optimal :map:`Translation` to centre the points in ``x-z`` plane
#. Use :map:`circle_fit` to find the optimal radius for fitting the points
#. Calculate a :map:`CylindricalUnwrap` using the optimal radius
#. Return a composition of the two.
Parameters
----------
points : :map:`PointCloud`
The 3D points that will be used to find the optimum unwrapping position
Returns
-------
transform: :map:`TransformChain`
A :map:`TransformChain` which performs the optimal translation and
unwrapping.
"""
# find the optimum centre to unwrap
xy = points.points[:, [0, 2]] # just in the x-z plane
centre, radius = radial_fit(xy)
# convert the 2D circle data into the 3D space
translation = np.array([centre[0], 0, centre[1]])
centring_transform = Translation(-translation)
unwrap = CylindricalUnwrap(radius)
return centring_transform.compose_before(unwrap)
def _recursive_procrustes(self):
"""
Recursively calculates a Procrustes alignment
"""
if self.n_iterations > self.max_iterations:
return False
av_aligned_source = sum(t.aligned_source.points
for t in self.transforms) / self.n_sources
new_target = PointCloud(av_aligned_source)
# rescale the new_target to be the same size as the original about
# it's centre
rescale = UniformScale(self.initial_target_scale / new_target.norm(),
self.n_dims)
centre = Translation(-new_target.centre)
rescale_about_centre = centre.compose_before(rescale).compose_before(
centre.pseudoinverse)
rescale_about_centre.apply_inplace(new_target)
# check to see if we have converged yet
delta_target = np.linalg.norm(self.target.points - new_target.points)
if delta_target < 1e-6:
return True
else:
self.n_iterations += 1
for t in self.transforms:
t.set_target(new_target)
self.target = new_target
return self._recursive_procrustes()
def _recursive_procrustes(self):
r"""
Recursively calculates a procrustes alignment.
"""
from menpo.shape import PointCloud
if self.n_iterations > self.max_iterations:
return False
av_aligned_source = sum(t.aligned_source.points for t in self.transforms) / self.n_sources
new_target = PointCloud(av_aligned_source)
# rescale the new_target to be the same size as the original about
# it's centre
rescale = UniformScale(self.initial_target_scale / new_target.norm(), self.n_dims)
centre = Translation(-new_target.centre)
rescale_about_centre = centre.compose_before(rescale).compose_before(centre.pseudoinverse)
rescale_about_centre.apply_inplace(new_target)
# check to see if we have converged yet
delta_target = np.linalg.norm(self.target.points - new_target.points)
if delta_target < 1e-6:
return True
else:
self.n_iterations += 1
for t in self.transforms:
t.set_target(new_target)
self.target = new_target
return self._recursive_procrustes()
def lm_centres_correction(centres):
r"""
Construct a transform that will correct landmarks for a window
iterating feature calculation
Parameters
----------
centres : `ndarray` (H, W, 2)
The location of the window centres in the features
Returns
-------
:map:`Affine`
An affine transform that performs the correction.
Should be applied to the landmarks on the target image.
"""
t = Translation(-centres.min(axis=0).min(axis=0), skip_checks=True)
step_v = centres[0, 0, 0]
if centres.shape[0] > 1:
step_v = centres[1, 0, 0] - centres[0, 0, 0]
step_h = centres[0, 0, 1]
if centres.shape[1] > 1:
step_h = centres[0, 1, 1] - centres[0, 0, 1]
s = NonUniformScale((1./step_v, 1./step_h), skip_checks=True)
return t.compose_before(s)
def test_translation_compose_after_homog():
# can't do this inplace - so should just give transform chain
homog = Homogeneous(np.array([[0, 1, 0],
[1, 0, 0],
[0, 0, 1]]))
t = Translation([3, 4])
res = t.compose_after(homog)
assert(type(res) == Homogeneous)
def test_align_2d_translation_set_h_matrix_raises_notimplemented_error():
t_vec = np.array([1, 2])
translation = Translation(t_vec)
source = PointCloud(np.array([[0, 1], [1, 1], [-1, -5], [3, -5]]))
target = translation.apply(source)
# estimate the transform from source to source..
estimate = AlignmentTranslation(source, source)
# and change the target.
estimate.set_h_matrix(translation.h_matrix)
def test_align_2d_translation():
t_vec = np.array([1, 2])
translation = Translation(t_vec)
source = PointCloud(np.array([[0, 1], [1, 1], [-1, -5], [3, -5]]))
target = translation.apply(source)
# estimate the transform from source and target
estimate = AlignmentTranslation(source, target)
# check the estimates is correct
assert_allclose(translation.h_matrix, estimate.h_matrix)
def test_align_2d_translation():
t_vec = np.array([1, 2])
translation = Translation(t_vec)
source = PointCloud(np.array([[0, 1], [1, 1], [-1, -5], [3, -5]]))
target = translation.apply(source)
# estimate the transform from source and target
estimate = AlignmentTranslation(source, target)
# check the estimates is correct
assert_allclose(translation.h_matrix, estimate.h_matrix)
def test_align_2d_translation_set_h_matrix_raises_notimplemented_error():
t_vec = np.array([1, 2])
translation = Translation(t_vec)
source = PointCloud(np.array([[0, 1], [1, 1], [-1, -5], [3, -5]]))
target = translation.apply(source)
# estimate the transform from source to source..
estimate = AlignmentTranslation(source, source)
# and change the target.
estimate.set_h_matrix(translation.h_matrix)
def crop(self, min_indices, max_indices, constrain_to_boundary=True):
r"""
Crops this image using the given minimum and maximum indices.
Landmarks are correctly adjusted so they maintain their position
relative to the newly cropped image.
Parameters
-----------
min_indices: (n_dims, ) ndarray
The minimum index over each dimension
max_indices: (n_dims, ) ndarray
The maximum index over each dimension
constrain_to_boundary: boolean, optional
If True the crop will be snapped to not go beyond this images
boundary. If False, an ImageBoundaryError will be raised if an
attempt is made to go beyond the edge of the image.
Default: True
Returns
-------
cropped_image : :class:`type(self)`
This image, but cropped.
Raises
------
ValueError
min_indices and max_indices both have to be of length n_dims.
All max_indices must be greater than min_indices.
ImageBoundaryError
Raised if constrain_to_boundary is False, and an attempt is made
to crop the image in a way that violates the image bounds.
"""
min_indices = np.floor(min_indices)
max_indices = np.ceil(max_indices)
if not (min_indices.size == max_indices.size == self.n_dims):
raise ValueError(
"Both min and max indices should be 1D numpy arrays of" " length n_dims ({})".format(self.n_dims)
)
elif not np.all(max_indices > min_indices):
raise ValueError("All max indices must be greater that the min " "indices")
min_bounded = self.constrain_points_to_bounds(min_indices)
max_bounded = self.constrain_points_to_bounds(max_indices)
if not constrain_to_boundary and not (np.all(min_bounded == min_indices) or np.all(max_bounded == max_indices)):
# points have been constrained and the user didn't want this -
raise ImageBoundaryError(min_indices, max_indices, min_bounded, max_bounded)
slices = [slice(int(min_i), int(max_i)) for min_i, max_i in zip(list(min_bounded), list(max_bounded))]
self.pixels = self.pixels[slices].copy()
# update all our landmarks
lm_translation = Translation(-min_bounded)
lm_translation.apply_inplace(self.landmarks)
return self
def _build_reference_frame(landmarks, boundary=3, group='source'):
# translate landmarks to the origin
minimum = landmarks.bounds(boundary=boundary)[0]
landmarks = Translation(-minimum).apply(landmarks)
resolution = landmarks.range(boundary=boundary)
reference_frame = MaskedImage.blank(resolution)
reference_frame.landmarks[group] = landmarks
return reference_frame
def test_align_2d_translation_from_vector_inplace():
t_vec = np.array([1, 2])
translation = Translation(t_vec)
source = PointCloud(np.array([[0, 1], [1, 1], [-1, -5], [3, -5]]))
target = translation.apply(source)
# estimate the transform from source to source..
estimate = AlignmentTranslation(source, source)
# and update from_vector
estimate._from_vector_inplace(t_vec)
# check the estimates is correct
assert_allclose(target.points, estimate.target.points)
def init_from_pointcloud(cls,
pointcloud,
group=None,
boundary=0,
constrain=True,
fill=True):
r"""
Create an Image that is big enough to contain the given pointcloud.
The pointcloud will be translated to the origin and then translated
according to its bounds in order to fit inside the new image.
An optional boundary can be provided in order to increase the space
around the boundary of the pointcloud. The boundary will be added
to *all sides of the image* and so a boundary of 5 provides 10 pixels
of boundary total for each dimension.
By default, the mask will be constrained to the convex hull of the
provided pointcloud.
Parameters
----------
pointcloud : :map:`PointCloud`
Pointcloud to place inside the newly created image.
group : `str`, optional
If ``None``, the pointcloud will only be used to create the image.
If a `str` then the pointcloud will be attached as a landmark
group to the image, with the given string as key.
boundary : `float`
A optional padding distance that is added to the pointcloud bounds.
Default is ``0``, meaning the max/min of tightest possible
containing image is returned.
fill : `int`, optional
The value to fill all pixels with.
constrain : `bool`, optional
If ``True``, the ``True`` values will be image will be constrained
to the convex hull of the provided pointcloud. If ``False``,
the mask will be the value of ``fill``.
Returns
-------
image : :map:`MaskedImage`
A new image with the same size as the given pointcloud, optionally
with the pointcloud attached as landmarks and the mask constrained
to the convex hull of the pointcloud.
"""
# Translate pointcloud to the origin
minimum = pointcloud.bounds(boundary=boundary)[0]
origin_pc = Translation(-minimum).apply(pointcloud)
image_shape = origin_pc.range(boundary=boundary)
new_image = cls.init_blank(image_shape, fill=fill)
if constrain:
new_image = new_image.constrain_to_pointcloud(origin_pc)
if group is not None:
new_image.landmarks[group] = origin_pc
return new_image
def test_align_2d_translation_from_vector_inplace():
t_vec = np.array([1, 2])
translation = Translation(t_vec)
source = PointCloud(np.array([[0, 1], [1, 1], [-1, -5], [3, -5]]))
target = translation.apply(source)
# estimate the transform from source to source..
estimate = AlignmentTranslation(source, source)
# and update from_vector
estimate.from_vector_inplace(t_vec)
# check the estimates is correct
assert_allclose(target.points, estimate.target.points)
def mask_pc(pc):
t = Translation(-pc.centre())
p = t.apply(pc)
(y1, x1), (y2, x2) = p.bounds()
a, b = np.meshgrid(np.arange(np.floor(y1), np.ceil(y2)),
np.arange(np.floor(x1), np.ceil(x2)))
mask = np.vstack([a.flatten(), b.flatten()]).T
return PointCloud(t.pseudoinverse().apply(mask[matpath(
p.points).contains_points(mask)]).astype(int))
def chain_compose_after_inplace_chain_test():
a = PointCloud(np.random.random([10, 2]))
b = PointCloud(np.random.random([10, 2]))
t = Translation([3, 4])
s = Scale([4, 2])
chain_1 = TransformChain([t, s])
chain_2 = TransformChain([s.pseudoinverse(), t.pseudoinverse()])
chain_1.compose_before_inplace(chain_2)
points = PointCloud(np.random.random([10, 2]))
chain_res = chain_1.apply(points)
assert(np.allclose(points.points, chain_res.points))
def init_from_pointcloud(cls, pointcloud, group=None, boundary=0,
constrain=True, fill=True):
r"""
Create an Image that is big enough to contain the given pointcloud.
The pointcloud will be translated to the origin and then translated
according to its bounds in order to fit inside the new image.
An optional boundary can be provided in order to increase the space
around the boundary of the pointcloud. The boundary will be added
to *all sides of the image* and so a boundary of 5 provides 10 pixels
of boundary total for each dimension.
By default, the mask will be constrained to the convex hull of the
provided pointcloud.
Parameters
----------
pointcloud : :map:`PointCloud`
Pointcloud to place inside the newly created image.
group : `str`, optional
If ``None``, the pointcloud will only be used to create the image.
If a `str` then the pointcloud will be attached as a landmark
group to the image, with the given string as key.
boundary : `float`
A optional padding distance that is added to the pointcloud bounds.
Default is ``0``, meaning the max/min of tightest possible
containing image is returned.
fill : `int`, optional
The value to fill all pixels with.
constrain : `bool`, optional
If ``True``, the ``True`` values will be image will be constrained
to the convex hull of the provided pointcloud. If ``False``,
the mask will be the value of ``fill``.
Returns
-------
image : :map:`MaskedImage`
A new image with the same size as the given pointcloud, optionally
with the pointcloud attached as landmarks and the mask constrained
to the convex hull of the pointcloud.
"""
# Translate pointcloud to the origin
minimum = pointcloud.bounds(boundary=boundary)[0]
origin_pc = Translation(-minimum).apply(pointcloud)
image_shape = origin_pc.range(boundary=boundary)
new_image = cls.init_blank(image_shape, fill=fill)
if constrain:
new_image = new_image.constrain_to_pointcloud(origin_pc)
if group is not None:
new_image.landmarks[group] = origin_pc
return new_image
def test_align_2d_translation_from_vector():
t_vec = np.array([1, 2])
translation = Translation(t_vec)
source = PointCloud(np.array([[0, 1], [1, 1], [-1, -5], [3, -5]]))
target = translation.apply(source)
# estimate the transform from source to source..
estimate = AlignmentTranslation(source, source)
# and update from_vector
new_est = estimate.from_vector(t_vec)
# check the original is unchanged
assert_allclose(estimate.source.points, source.points)
assert_allclose(estimate.target.points, source.points)
# check the new estimate has the source and target correct
assert_allclose(new_est.source.points, source.points)
assert_allclose(new_est.target.points, target.points)
def test_chain_compose_after_inplace_tps():
a = PointCloud(np.random.random([10, 2]))
b = PointCloud(np.random.random([10, 2]))
tps = ThinPlateSplines(a, b)
t = Translation([3, 4])
s = Scale([4, 2])
chain = TransformChain([t, s])
chain.compose_after_inplace(tps)
points = PointCloud(np.random.random([10, 2]))
manual_res = s.apply(t.apply(tps.apply(points)))
chain_res = chain.apply(points)
assert (np.all(manual_res.points == chain_res.points))
def test_align_2d_translation_from_vector():
t_vec = np.array([1, 2])
translation = Translation(t_vec)
source = PointCloud(np.array([[0, 1], [1, 1], [-1, -5], [3, -5]]))
target = translation.apply(source)
# estimate the transform from source to source..
estimate = AlignmentTranslation(source, source)
# and update from_vector
new_est = estimate.from_vector(t_vec)
# check the original is unchanged
assert_allclose(estimate.source.points, source.points)
assert_allclose(estimate.target.points, source.points)
# check the new estimate has the source and target correct
assert_allclose(new_est.source.points, source.points)
assert_allclose(new_est.target.points, target.points)
def chain_compose_before_tps_test():
a = PointCloud(np.random.random([10, 2]))
b = PointCloud(np.random.random([10, 2]))
tps = ThinPlateSplines(a, b)
t = Translation([3, 4])
s = Scale([4, 2])
chain = TransformChain([t, s])
chain_mod = chain.compose_before(tps)
points = PointCloud(np.random.random([10, 2]))
manual_res = tps.apply(s.apply(t.apply(points)))
chain_res = chain_mod.apply(points)
assert(np.all(manual_res.points == chain_res.points))
def __init__(self, batch_size=1):
super().__init__(batch_size)
from menpo.transform import Translation, scale_about_centre
import menpo3d.io as m3dio
self.name = 'LFPW'
self.batch_size = batch_size
self.root = Path('/vol/atlas/databases/lfpw/trainset')
template = m3dio.import_mesh(
'/vol/construct3dmm/regression/src/template.obj')
template = Translation(-template.centre()).apply(template)
self.template = scale_about_centre(template, 1. /
1000.).apply(template)
self.image_extension = '.png'
self.lms_extension = '.pts'
def clip_to_image_transform(width, height):
r"""
Affine transform that converts 3D clip space coordinates into 2D image
space coordinates. Note that the z axis of the clip space coordinates is
ignored.
Parameters
----------
width: int
The width of the image
height: int
The height of the image
Returns
-------
:map`Homogeneous`
A homogeneous transform that moves clip space coordinates into image
space.
"""
# 1. Remove the z axis from the clip space
rem_z = dims_3to2()
# 2. invert the y direction (up becomes down)
invert_y = Scale([1, -1])
# 3. [-1, 1] [-1, 1] -> [0, 2] [0, 2]
t = Translation([1, 1])
# 4. [0, 2] [0, 2] -> [0, 1] [0, 1]
unit_scale = Scale(0.5, n_dims=2)
# 5. [0, 1] [0, 1] -> [0, w - 1] [0, h - 1]
im_scale = Scale([width - 1, height - 1])
# 6. [0, w] [0, h] -> [0, h] [0, w]
xy_yx = Homogeneous(
np.array([[0, 1, 0], [1, 0, 0], [0, 0, 1]], dtype=np.float))
# reduce the full transform chain to a single affine matrix
transforms = [rem_z, invert_y, t, unit_scale, im_scale, xy_yx]
return reduce(lambda a, b: a.compose_before(b), transforms)
def retrieve_view_projection_transforms(image, mesh, group=None):
rows = image.shape[0]
cols = image.shape[1]
max_d = max(rows, cols)
camera_matrix = np.array([[max_d, 0, cols / 2.0], [0, max_d, rows / 2.0],
[0, 0, 1.0]])
distortion_coeffs = np.zeros(4)
converged, r_vec, t_vec = cv2.solvePnP(
mesh.landmarks[group].lms.points,
image.landmarks[group].lms.points[:, ::-1], camera_matrix,
distortion_coeffs)
rotation_matrix = cv2.Rodrigues(r_vec)[0]
h_camera_matrix = np.eye(4)
h_camera_matrix[:3, :3] = camera_matrix
c = Homogeneous(h_camera_matrix)
t = Translation(t_vec.ravel())
r = Rotation(rotation_matrix)
view_t_flipped = r.compose_before(t)
view_t = view_t_flipped.compose_before(axes_flip_t)
proj_t = Homogeneous(
weak_projection_matrix(image.width, image.height,
view_t_flipped.apply(mesh)))
return view_t, proj_t, r
def build_shape_model(shapes, max_components=None):
r"""
Builds a shape model given a set of shapes.
Parameters
----------
shapes: list of :map:`PointCloud`
The set of shapes from which to build the model.
max_components: None or int or float
Specifies the number of components of the trained shape model.
If int, it specifies the exact number of components to be retained.
If float, it specifies the percentage of variance to be retained.
If None, all the available components are kept (100% of variance).
Returns
-------
shape_model: :class:`menpo.model.pca`
The PCA shape model.
"""
# centralize shapes
centered_shapes = [Translation(-s.centre()).apply(s) for s in shapes]
# align centralized shape using Procrustes Analysis
gpa = GeneralizedProcrustesAnalysis(centered_shapes)
aligned_shapes = [s.aligned_source() for s in gpa.transforms]
# build shape model
shape_model = PCAModel(aligned_shapes)
if max_components is not None:
# trim shape model if required
shape_model.trim_components(max_components)
return shape_model
def compose_tps_after_translation_test():
a = PointCloud(np.random.random([10, 2]))
b = PointCloud(np.random.random([10, 2]))
t = Translation([3, 4])
tps = ThinPlateSplines(a, b)
chain = tps.compose_after(t)
assert(isinstance(chain, TransformChain))
def test_translation_2d_from_vector():
params = np.array([1, 2])
h**o = np.array([[1, 0, params[0]], [0, 1, params[1]], [0, 0, 1]])
tr = Translation.init_identity(2).from_vector(params)
assert_equal(tr.h_matrix, h**o)
def __init__(self, batch_size=1):
super().__init__(batch_size)
from menpo.transform import Translation, scale_about_centre
import menpo3d.io as m3dio
self.name = 'FDDB'
self.root = Path('/vol/atlas/databases/fddb_ibug')
template = m3dio.import_mesh(
'/vol/construct3dmm/regression/src/template.obj')
template = Translation(-template.centre()).apply(template)
self.template = scale_about_centre(template, 1. /
1000.).apply(template)
pca_path = '/homes/gt108/Projects/ibugface/pose_settings/pca_params.pkl'
self.eigenvectors, self.eigenvalues, self.h_mean, self.h_max = mio.import_pickle(
pca_path)
self.image_extension = '.jpg'
self.lms_extension = '.ljson'
def test_translation_3d_from_vector():
params = np.array([1, 2, 3])
h**o = np.array([[1, 0, 0, params[0]], [0, 1, 0, params[1]],
[0, 0, 1, params[2]], [0, 0, 0, 1]])
tr = Translation.identity(3).from_vector(params)
assert_almost_equal(tr.h_matrix, h**o)
def rescale(mesh, center, var):
"""
Rescale mesh according to given variances.
Parameters:
mesh (menpo.shape.mesh.base.TriMesh): mesh to be rescaled
center (numpy.array of 3 floats): center on 3 dimensions
var (numpy.array of 3 floats): variance on 3 dimensions
Returns:
mesh (menpo.shape.mesh.base.TriMesh): rescaled source
"""
tr = Translation(center)
sc = UniformScale(np.mean(var / mesh.range()), 3)
prepare = tr.compose_after(sc)
return prepare.apply(mesh)
def model_to_clip_transform(points, xy_scale=0.9, z_scale=0.3):
r"""
Produces an Affine Transform which centres and scales 3D points to fit
into the OpenGL clipping space ([-1, 1], [-1, 1], [1, 1-]). This can be
used to construct an appropriate projection matrix for use in an
orthographic Rasterizer. Note that the z-axis is flipped as is default in
OpenGL - as a result this transform converts the right handed coordinate
input into a left hand one.
Parameters
----------
points: :map:`PointCloud`
The points that should be adjusted.
xy_scale: `float` 0-1, optional
Amount by which the boundary is relaxed so the points are not
right against the edge. A value of 1 means the extremities of the
point cloud will be mapped onto [-1, 1] [-1, 1] exactly (no boarder)
A value of 0.5 means the points will be mapped into the range
[-0.5, 0.5].
Default: 0.9 (map to [-0.9, 0.9])
z_scale: float 0-1, optional
Scale factor by which the z-dimension is squeezed. A value of 1
means the z-range of the points will be mapped to exactly fit in
[1, -1]. A scale of 0.1 means the z-range is compressed to fit in the
range [0.1, -0.1].
Returns
-------
:map:`Affine`
The affine transform that creates this mapping
"""
# 1. Centre the points on the origin
center = Translation(points.centre_of_bounds()).pseudoinverse()
# 2. Scale the points to exactly fit the boundaries
scale = Scale(points.range() / 2.0)
# 3. Apply the relaxations requested - note the flip in the z axis!!
# This is because OpenGL by default evaluates depth as bigger number ==
# further away. Thus not only do we need to get to clip space [-1, 1] in
# all dims) but we must invert the z axis so depth buffering is correctly
# applied.
b_scale = NonUniformScale([xy_scale, xy_scale, -z_scale])
return center.compose_before(scale.pseudoinverse()).compose_before(b_scale)
def align_shapes(shapes):
r"""
"""
# centralize shapes
centered_shapes = [Translation(-s.centre()).apply(s) for s in shapes]
# align centralized shape using Procrustes Analysis
gpa = GeneralizedProcrustesAnalysis(centered_shapes)
return [s.aligned_source() for s in gpa.transforms]
def model_to_clip_transform(points, xy_scale=0.9, z_scale=0.3):
r"""
Produces an Affine Transform which centres and scales 3D points to fit
into the OpenGL clipping space ([-1, 1], [-1, 1], [1, 1-]). This can be
used to construct an appropriate projection matrix for use in an
orthographic Rasterizer. Note that the z-axis is flipped as is default in
OpenGL - as a result this transform converts the right handed coordinate
input into a left hand one.
Parameters
----------
points: :map:`PointCloud`
The points that should be adjusted.
xy_scale: `float` 0-1, optional
Amount by which the boundary is relaxed so the points are not
right against the edge. A value of 1 means the extremities of the
point cloud will be mapped onto [-1, 1] [-1, 1] exactly (no boarder)
A value of 0.5 means the points will be mapped into the range
[-0.5, 0.5].
Default: 0.9 (map to [-0.9, 0.9])
z_scale: float 0-1, optional
Scale factor by which the z-dimension is squeezed. A value of 1
means the z-range of the points will be mapped to exactly fit in
[1, -1]. A scale of 0.1 means the z-range is compressed to fit in the
range [0.1, -0.1].
Returns
-------
:map:`Affine`
The affine transform that creates this mapping
"""
# 1. Centre the points on the origin
center = Translation(points.centre_of_bounds()).pseudoinverse()
# 2. Scale the points to exactly fit the boundaries
scale = Scale(points.range() / 2.0)
# 3. Apply the relaxations requested - note the flip in the z axis!!
# This is because OpenGL by default evaluates depth as bigger number ==
# further away. Thus not only do we need to get to clip space [-1, 1] in
# all dims) but we must invert the z axis so depth buffering is correctly
# applied.
b_scale = NonUniformScale([xy_scale, xy_scale, -z_scale])
return center.compose_before(scale.pseudoinverse()).compose_before(b_scale)
def test_translation_2d_from_vector():
params = np.array([1, 2])
h**o = np.array([[1, 0, params[0]],
[0, 1, params[1]],
[0, 0, 1]])
tr = Translation.init_identity(2).from_vector(params)
assert_equal(tr.h_matrix, h**o)
def prepare_template_reference_space(template):
r"""Return a copy of the template centred at the origin
and with max radial distance from centre of 1.
This means the template is:
1. fully contained by a bounding sphere of radius 1 at the origin
2. centred at the origin.
This isn't necessary, but it's nice to have a meaningful reference space
for our models.
"""
max_radial = np.sqrt(
((template.points - template.centre())**2).sum(axis=1)).max()
translation = Translation(-template.centre())
scale = Scale(1 / max_radial, n_dims=3)
adjustment = translation.compose_before(scale)
adjustment.apply(template)
return adjustment.apply(template)
def test_translation_3d_from_vector():
params = np.array([1, 2, 3])
h**o = np.array([[1, 0, 0, params[0]],
[0, 1, 0, params[1]],
[0, 0, 1, params[2]],
[0, 0, 0, 1]])
tr = Translation.identity(3).from_vector(params)
assert_almost_equal(tr.h_matrix, h**o)
def perspective_camera_for_template(img_shape,
focal_length_mult=1.1,
pose_angle_deg=0):
f = np.array(img_shape).max() * focal_length_mult
rot_z = rotation_from_3d_ccw_angle_around_z(180)
rot_y = rotation_from_3d_ccw_angle_around_y(180 + pose_angle_deg)
rotation = rot_z.compose_before(rot_y)
translation = Translation([0, 0, +3])
projection = PerspectiveProjection(f, img_shape)
return PerspectiveCamera(rotation, translation, projection)
def test_translation():
t_vec = np.array([1, 2, 3])
starting_vector = np.random.rand(10, 3)
transform = Translation(t_vec)
transformed = transform.apply(starting_vector)
assert_allclose(starting_vector + t_vec, transformed)
def normalize(gt):
from menpo.transform import Translation, NonUniformScale
t = Translation(gt.centre()).pseudoinverse()
s = NonUniformScale(gt.range()).pseudoinverse()
return t.compose_before(s)
def test_translation_set_h_matrix_raises_notimplementederror():
t = Translation([3, 4])
t.set_h_matrix(t.h_matrix)
def non_rigid_icp_generator(source, target, eps=1e-3,
stiffness_weights=None, data_weights=None,
landmark_group=None, landmark_weights=None,
v_i_update_func=None, verbose=False):
r"""
Deforms the source trimesh to align with to optimally the target.
"""
# If landmarks are provided, we should always start with a simple
# AlignmentSimilarity between the landmarks to initialize optimally.
if landmark_group is not None:
if verbose:
print("'{}' landmarks will be used as "
"a landmark constraint.".format(landmark_group))
print("performing similarity alignment using landmarks")
lm_align = AlignmentSimilarity(source.landmarks[landmark_group],
target.landmarks[landmark_group]).as_non_alignment()
source = lm_align.apply(source)
# Scale factors completely change the behavior of the algorithm - always
# rescale the source down to a sensible size (so it fits inside box of
# diagonal 1) and is centred on the origin. We'll undo this after the fit
# so the user can use whatever scale they prefer.
tr = Translation(-1 * source.centre())
sc = UniformScale(1.0 / np.sqrt(np.sum(source.range() ** 2)), 3)
prepare = tr.compose_before(sc)
source = prepare.apply(source)
target = prepare.apply(target)
# store how to undo the similarity transform
restore = prepare.pseudoinverse()
n_dims = source.n_dims
# Homogeneous dimension (1 extra for translation effects)
h_dims = n_dims + 1
points, trilist = source.points, source.trilist
n = points.shape[0] # record number of points
edge_tris = source.boundary_tri_index()
M_s, unique_edge_pairs = node_arc_incidence_matrix(source)
# weight matrix
G = np.identity(n_dims + 1)
M_kron_G_s = sp.kron(M_s, G)
# build octree for finding closest points on target.
target_vtk = trimesh_to_vtk(target)
closest_points_on_target = VTKClosestPointLocator(target_vtk)
# save out the target normals. We need them for the weight matrix.
target_tri_normals = target.tri_normals()
# init transformation
X_prev = np.tile(np.zeros((n_dims, h_dims)), n).T
v_i = points
if stiffness_weights is not None:
if verbose:
print('using user-defined stiffness_weights')
validate_weights('stiffness_weights', stiffness_weights,
source.n_points, verbose=verbose)
else:
# these values have been empirically found to perform well for well
# rigidly aligned facial meshes
stiffness_weights = [50, 20, 5, 2, 0.8, 0.5, 0.35, 0.2]
if verbose:
print('using default '
'stiffness_weights: {}'.format(stiffness_weights))
n_iterations = len(stiffness_weights)
if landmark_weights is not None:
if verbose:
print('using user defined '
'landmark_weights: {}'.format(landmark_weights))
elif landmark_group is not None:
# these values have been empirically found to perform well for well
# rigidly aligned facial meshes
landmark_weights = [5, 2, .5, 0, 0, 0, 0, 0]
if verbose:
print('using default '
'landmark_weights: {}'.format(landmark_weights))
else:
# no landmark_weights provided - no landmark_group in use. We still
# need a landmark group for the iterator
landmark_weights = [None] * n_iterations
# We should definitely have some landmark weights set now - check the
# number is correct.
# Note we say verbose=False, as we have done custom reporting above, and
# per-vertex landmarks are not supported.
validate_weights('landmark_weights', landmark_weights, source.n_points,
n_iterations=n_iterations, verbose=False)
if data_weights is not None:
if verbose:
print('using user-defined data_weights')
validate_weights('data_weights', data_weights,
source.n_points, n_iterations=n_iterations,
verbose=verbose)
else:
data_weights = [None] * n_iterations
if verbose:
print('Not customising data_weights')
# we need to prepare some indices for efficient construction of the D
# sparse matrix.
row = np.hstack((np.repeat(np.arange(n)[:, None], n_dims, axis=1).ravel(),
np.arange(n)))
x = np.arange(n * h_dims).reshape((n, h_dims))
col = np.hstack((x[:, :n_dims].ravel(),
x[:, n_dims]))
o = np.ones(n)
if landmark_group is not None:
source_lm_index = source.distance_to(
source.landmarks[landmark_group]).argmin(axis=0)
target_lms = target.landmarks[landmark_group]
U_L = target_lms.points
n_landmarks = target_lms.n_points
lm_mask = np.in1d(row, source_lm_index)
col_lm = col[lm_mask]
# pull out the rows for the lms - but the values are
# all wrong! need to map them back to the order of the landmarks
row_lm_to_fix = row[lm_mask]
source_lm_index_l = list(source_lm_index)
row_lm = np.array([source_lm_index_l.index(r) for r in row_lm_to_fix])
for i, (alpha, beta, gamma) in enumerate(zip(stiffness_weights,
landmark_weights,
data_weights), 1):
alpha_is_per_vertex = isinstance(alpha, np.ndarray)
if alpha_is_per_vertex:
# stiffness is provided per-vertex
if alpha.shape[0] != source.n_points:
raise ValueError()
alpha_per_edge = alpha[unique_edge_pairs].mean(axis=1)
alpha_M_s = sp.diags(alpha_per_edge).dot(M_s)
alpha_M_kron_G_s = sp.kron(alpha_M_s, G)
else:
# stiffness is global - just a scalar multiply. Note that here
# we don't have to recalculate M_kron_G_s
alpha_M_kron_G_s = alpha * M_kron_G_s
if verbose:
a_str = (alpha if not alpha_is_per_vertex
else 'min: {:.2f}, max: {:.2f}'.format(alpha.min(),
alpha.max()))
i_str = '{}/{}: stiffness: {}'.format(i, len(stiffness_weights), a_str)
if landmark_group is not None:
i_str += ' lm_weight: {}'.format(beta)
print(i_str)
j = 0
while True: # iterate until convergence
j += 1 # track the iterations for this alpha/landmark weight
# find nearest neighbour and the normals
U, tri_indices = closest_points_on_target(v_i)
# ---- WEIGHTS ----
# 1. Edges
# Are any of the corresponding tris on the edge of the target?
# Where they are we return a false weight (we *don't* want to
# include these points in the solve)
w_i_e = np.in1d(tri_indices, edge_tris, invert=True)
# 2. Normals
# Calculate the normals of the current v_i
v_i_tm = TriMesh(v_i, trilist=trilist)
v_i_n = v_i_tm.vertex_normals()
# Extract the corresponding normals from the target
u_i_n = target_tri_normals[tri_indices]
# If the dot of the normals is lt 0.9 don't contrib to deformation
w_i_n = (u_i_n * v_i_n).sum(axis=1) > 0.9
# 3. Self-intersection
# This adds approximately 12% to the running cost and doesn't seem
# to be very critical in helping mesh fitting performance so for
# now it's removed. Revisit later.
# # Build an intersector for the current deformed target
# intersect = build_intersector(to_vtk(v_i_tm))
# # budge the source points 1% closer to the target
# source = v_i + ((U - v_i) * 0.5)
# # if the vector from source to target intersects the deformed
# # template we don't want to include it in the optimisation.
# problematic = [i for i, (s, t) in enumerate(zip(source, U))
# if len(intersect(s, t)[0]) > 0]
# print(len(problematic) * 1.0 / n)
# w_i_i = np.ones(v_i_tm.n_points, dtype=np.bool)
# w_i_i[problematic] = False
# Form the overall w_i from the normals, edge case
# for now disable the edge constraint (it was noisy anyway)
w_i = w_i_n
# w_i = np.logical_and(w_i_n, w_i_e).astype(np.float)
# we could add self intersection at a later date too...
# w_i = np.logical_and(np.logical_and(w_i_n,
# w_i_e,
# w_i_i).astype(np.float)
prop_w_i = (n - w_i.sum() * 1.0) / n
prop_w_i_n = (n - w_i_n.sum() * 1.0) / n
prop_w_i_e = (n - w_i_e.sum() * 1.0) / n
if data_weights is not None:
w_i = w_i * gamma
# Build the sparse diagonal weight matrix
W_s = sp.diags(w_i.astype(np.float)[None, :], [0])
data = np.hstack((v_i.ravel(), o))
D_s = sp.coo_matrix((data, (row, col)))
to_stack_A = [alpha_M_kron_G_s, W_s.dot(D_s)]
to_stack_B = [np.zeros((alpha_M_kron_G_s.shape[0], n_dims)),
U * w_i[:, None]] # nullify nearest points by w_i
if landmark_group is not None:
D_L = sp.coo_matrix((data[lm_mask], (row_lm, col_lm)),
shape=(n_landmarks, D_s.shape[1]))
to_stack_A.append(beta * D_L)
to_stack_B.append(beta * U_L)
A_s = sp.vstack(to_stack_A).tocsr()
B_s = sp.vstack(to_stack_B).tocsr()
X = spsolve(A_s, B_s)
# deform template
v_i_prev = v_i
v_i = D_s.dot(X)
delta_v_i = v_i - v_i_prev
if v_i_update_func:
# custom logic is provided to update the current template
# deformation. This is typically used by Active NICP.
# take the v_i points matrix and convert back to a TriMesh in
# the original space
def_template = restore.apply(source.from_vector(v_i.ravel()))
# perform the update
updated_def_template = v_i_update_func(def_template)
# convert back to points in the NICP space
v_i = prepare.apply(updated_def_template.points)
err = np.linalg.norm(X_prev - X, ord='fro')
stop_criterion = err / np.sqrt(np.size(X_prev))
if landmark_group is not None:
src_lms = v_i[source_lm_index]
lm_err = np.sqrt((src_lms - U_L) ** 2).sum(axis=1).mean()
if verbose:
v_str = (' - {} stop crit: {:.3f} '
'total: {:.0%} norms: {:.0%} '
'edges: {:.0%}'.format(j, stop_criterion,
prop_w_i, prop_w_i_n,
prop_w_i_e))
if landmark_group is not None:
v_str += ' lm_err: {:.4f}'.format(lm_err)
print(v_str)
X_prev = X
# track the progress of the algorithm per-iteration
info_dict = {
'alpha': alpha,
'iteration': j,
'prop_omitted': prop_w_i,
'prop_omitted_norms': prop_w_i_n,
'prop_omitted_edges': prop_w_i_e,
'delta': err,
'mask_normals': w_i_n,
'mask_edges': w_i_e,
'mask_all': w_i,
'nearest_points': restore.apply(U),
'deformation_per_step': delta_v_i
}
current_instance = source.copy()
current_instance.points = v_i.copy()
if landmark_group:
info_dict['beta'] = beta
info_dict['lm_err'] = lm_err
current_instance.landmarks[landmark_group] = PointCloud(src_lms)
yield restore.apply(current_instance), info_dict
if stop_criterion < eps:
break
def manual_no_op_chain_test():
points = PointCloud(np.random.random([10, 2]))
t = Translation([3, 4])
chain = TransformChain([t, t.pseudoinverse()])
points_applied = chain.apply(points)
assert(np.allclose(points_applied.points, points.points))
def test_translation_identity_2d():
assert_allclose(Translation.identity(2).h_matrix, np.eye(3))
def test_init_from_pointcloud_return_transform():
correct_tr = Translation([5, 5])
pc = correct_tr.apply(PointCloud.init_2d_grid((10, 10)))
im, tr = Image.init_from_pointcloud(pc, return_transform=True)
assert im.shape == (9, 9)
assert_allclose(tr.as_vector(), -correct_tr.as_vector())
def non_rigid_icp(source, target, eps=1e-3, stiffness_values=None,
verbose=False, landmarks=None, lm_weight=None):
r"""
Deforms the source trimesh to align with to optimally the target.
"""
# Scale factors completely change the behavior of the algorithm - always
# rescale the source down to a sensible size (so it fits inside box of
# diagonal 1) and is centred on the origin. We'll undo this after the fit
# so the user can use whatever scale they prefer.
tr = Translation(-1 * source.centre())
sc = UniformScale(1.0 / np.sqrt(np.sum(source.range() ** 2)), 3)
prepare = tr.compose_before(sc)
source = prepare.apply(source)
target = prepare.apply(target)
# store how to undo the similarity transform
restore = prepare.pseudoinverse()
n_dims = source.n_dims
# Homogeneous dimension (1 extra for translation effects)
h_dims = n_dims + 1
points, trilist = source.points, source.trilist
n = points.shape[0] # record number of points
edge_tris = source.boundary_tri_index()
M_s = node_arc_incidence_matrix(source)
# weight matrix
G = np.identity(n_dims + 1)
M_kron_G_s = sp.kron(M_s, G)
# build octree for finding closest points on target.
target_vtk = trimesh_to_vtk(target)
closest_points_on_target = VTKClosestPointLocator(target_vtk)
# save out the target normals. We need them for the weight matrix.
target_tri_normals = target.tri_normals()
# init transformation
X_prev = np.tile(np.zeros((n_dims, h_dims)), n).T
v_i = points
if stiffness_values is not None:
stiffness = stiffness_values
if verbose:
print('using user defined stiffness values: {}'.format(stiffness))
else:
# these values have been empirically found to perform well for well
# rigidly aligned facial meshes
stiffness = [50, 20, 5, 2, 0.8, 0.5, 0.35, 0.2]
if verbose:
print('using default stiffness values: {}'.format(stiffness))
if lm_weight is not None:
lm_weight = lm_weight
if verbose:
print('using user defined lm_weight values: {}'.format(lm_weight))
else:
# these values have been empirically found to perform well for well
# rigidly aligned facial meshes
lm_weight = [5, 2, .5, 0, 0, 0, 0, 0]
if verbose:
print('using default lm_weight values: {}'.format(lm_weight))
# to store per iteration information
info = []
# we need to prepare some indices for efficient construction of the D
# sparse matrix.
row = np.hstack((np.repeat(np.arange(n)[:, None], n_dims, axis=1).ravel(),
np.arange(n)))
x = np.arange(n * h_dims).reshape((n, h_dims))
col = np.hstack((x[:, :n_dims].ravel(),
x[:, n_dims]))
if landmarks is not None:
if verbose:
print("'{}' landmarks will be used as a landmark constraint.".format(landmarks))
source_lm_index = source.distance_to(
source.landmarks[landmarks].lms).argmin(axis=0)
target_lms = target.landmarks[landmarks].lms
U_L = target_lms.points
n_landmarks = target_lms.n_points
lm_mask = np.in1d(row, source_lm_index)
col_lm = col[lm_mask]
# pull out the rows for the lms - but the values are
# all wrong! need to map them back to the order of the landmarks
row_lm_to_fix = row[lm_mask]
source_lm_index_l = list(source_lm_index)
row_lm = np.array([source_lm_index_l.index(r) for r in row_lm_to_fix])
o = np.ones(n)
for alpha, beta in zip(stiffness, lm_weight):
alpha_M_kron_G_s = alpha * M_kron_G_s # get the term for stiffness
j = 0
while True: # iterate until convergence
# find nearest neighbour and the normals
U, tri_indices = closest_points_on_target(v_i)
# ---- WEIGHTS ----
# 1. Edges
# Are any of the corresponding tris on the edge of the target?
# Where they are we return a false weight (we *don't* want to
# include these points in the solve)
w_i_e = np.in1d(tri_indices, edge_tris, invert=True)
# 2. Normals
# Calculate the normals of the current v_i
v_i_tm = TriMesh(v_i, trilist=trilist, copy=False)
v_i_n = v_i_tm.vertex_normals()
# Extract the corresponding normals from the target
u_i_n = target_tri_normals[tri_indices]
# If the dot of the normals is lt 0.9 don't contrib to deformation
w_i_n = (u_i_n * v_i_n).sum(axis=1) > 0.9
# 3. Self-intersection
# This adds approximately 12% to the running cost and doesn't seem
# to be very critical in helping mesh fitting performance so for
# now it's removed. Revisit later.
# # Build an intersector for the current deformed target
# intersect = build_intersector(to_vtk(v_i_tm))
# # budge the source points 1% closer to the target
# source = v_i + ((U - v_i) * 0.5)
# # if the vector from source to target intersects the deformed
# # template we don't want to include it in the optimisation.
# problematic = [i for i, (s, t) in enumerate(zip(source, U))
# if len(intersect(s, t)[0]) > 0]
# print(len(problematic) * 1.0 / n)
# w_i_i = np.ones(v_i_tm.n_points, dtype=np.bool)
# w_i_i[problematic] = False
# Form the overall w_i from the normals, edge case
w_i = np.logical_and(w_i_n, w_i_e)
# we could add self intersection at a later date too...
# w_i = np.logical_and(np.logical_and(w_i_n, w_i_e), w_i_i)
prop_w_i = (n - w_i.sum() * 1.0) / n
prop_w_i_n = (n - w_i_n.sum() * 1.0) / n
prop_w_i_e = (n - w_i_e.sum() * 1.0) / n
j = j + 1
# Build the sparse diagonal weight matrix
W_s = sp.diags(w_i.astype(np.float)[None, :], [0])
data = np.hstack((v_i.ravel(), o))
D_s = sp.coo_matrix((data, (row, col)))
# nullify the masked U values
U[~w_i] = 0
to_stack_A = [alpha_M_kron_G_s, W_s.dot(D_s)]
to_stack_B = [np.zeros((alpha_M_kron_G_s.shape[0], n_dims)), U]
if landmarks:
D_L = sp.coo_matrix((data[lm_mask], (row_lm, col_lm)),
shape=(n_landmarks, D_s.shape[1]))
to_stack_A.append(beta * D_L)
to_stack_B.append(beta * U_L)
A_s = sp.vstack(to_stack_A).tocsr()
B_s = sp.vstack(to_stack_B).tocsr()
X = spsolve(A_s, B_s)
# deform template
v_i = D_s.dot(X)
err = np.linalg.norm(X_prev - X, ord='fro')
if landmarks is not None:
src_lms = v_i[source_lm_index]
lm_err = np.sqrt((src_lms - U_L) ** 2).sum(axis=1).mean()
if verbose:
v_str = ('a: {}, ({}) - total : {:.0%} norms: {:.0%} '
'edges: {:.0%}'.format(alpha, j, prop_w_i,
prop_w_i_n, prop_w_i_e))
if landmarks is not None:
v_str += ' beta: {}, lm_err: {:.5f}'.format(beta, lm_err)
print(v_str)
info_dict = {
'alpha': alpha,
'iteration': j + 1,
'prop_omitted': prop_w_i,
'prop_omitted_norms': prop_w_i_n,
'prop_omitted_edges': prop_w_i_e,
'delta': err
}
if landmarks:
info_dict['beta'] = beta
info_dict['lm_err'] = lm_err
info.append(info_dict)
X_prev = X
if err / np.sqrt(np.size(X_prev)) < eps:
break
# final result if we choose closest points
point_corr = closest_points_on_target(v_i)[0]
result = {
'deformed_source': restore.apply(v_i),
'matched_target': restore.apply(point_corr),
'matched_tri_indices': tri_indices,
'info': info
}
if landmarks is not None:
result['source_lm_index'] = source_lm_index
return result
def test_translation_compose_after_uniformscale():
t = Translation([3, 4])
s = UniformScale(2, 2)
res = t.compose_after(s)
assert(type(res) == Similarity)
def test_translation_identity_3d():
assert_allclose(Translation.init_identity(3).h_matrix, np.eye(4))
def test_translation_decompose_optional():
t = Translation.init_identity(2)
d = t.decompose()
assert np.all(d[0].h_matrix == t.h_matrix)
def init_from_image_shape_and_vector(cls, image_shape, vector):
r = Rotation.init_identity(n_dims=3)
t = Translation.init_identity(n_dims=3)
p = PerspectiveProjection(focal_length=1, image_shape=image_shape)
return cls(r, t, p).from_vector(vector)