def test_basic_2d_affine():
linear_component = np.array([[1, -6],
[-3, 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
affine = Affine(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 = affine.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 = affine.apply(x_copies)
# check that all copies have been transformed correctly
for r in results:
assert_allclose(solution, r)
def test_align_2d_affine():
linear_component = np.array([[1, -6], [-3, 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
affine = Affine(h_matrix)
source = PointCloud(np.array([[0, 1], [1, 1], [-1, -5], [3, -5]]))
target = affine.apply(source)
# estimate the transform from source and target
estimate = AlignmentAffine(source, target)
# check the estimates is correct
assert_allclose(affine.h_matrix, estimate.h_matrix)
def test_align_2d_affine():
linear_component = np.array([[1, -6], [-3, 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
affine = Affine(h_matrix)
source = PointCloud(np.array([[0, 1], [1, 1], [-1, -5], [3, -5]]))
target = affine.apply(source)
# estimate the transform from source and target
estimate = AlignmentAffine(source, target)
# check the estimates is correct
assert_allclose(affine.h_matrix, estimate.h_matrix)
def test_affine_jacobian_2d_with_positions():
params = np.array([0, 0.1, 0.2, 0, 30, 70])
t = Affine.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, jac_solution2d)
def extract_targets(frame, target_centre, target_shape, n_perturbations=10,
noise_std=0.04):
# initialize targets
w, h = target_shape
targets = np.empty((n_perturbations + 1, frame.n_channels, w, h))
# extract original target
targets[0] = frame.extract_patches(
target_centre, patch_size=target_shape,
as_single_array=True)
for j in range(n_perturbations):
# perturb identity affine transform
params = noise_std * np.random.randn(6)
transform = Affine.init_identity(2).from_vector(params)
# warp frame using previous affine transform
perturbed_frame = frame.warp_to_mask(frame.as_masked().mask,
transform)
# apply inverse of affine transform to target centre
perturbed_centre = transform.pseudoinverse().apply(target_centre)
# extract perturbed target + context region from frame
perturbed_target = perturbed_frame.extract_patches(
perturbed_centre, patch_size=target_shape,
as_single_array=True)
# store target
targets[j+1] = perturbed_target
return targets
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 fit_from_bb(self, image, bounding_box, gt_shape=None, **kwargs):
algo_result = self.algorithm.run(image, bounding_box, gt_shape=gt_shape)
# TODO: This should be a basic result instead.
return MultiFitterResult(image, self, [algo_result],
Affine.init_identity(2),
gt_shape=gt_shape)
def extract_targets(frame,
target_centre,
target_shape,
n_perturbations=10,
noise_std=0.04):
# initialize targets
w, h = target_shape
targets = np.empty((n_perturbations + 1, frame.n_channels, w, h))
# extract original target
targets[0] = frame.extract_patches(target_centre,
patch_size=target_shape,
as_single_array=True)
for j in range(n_perturbations):
# perturb identity affine transform
params = noise_std * np.random.randn(6)
transform = Affine.init_identity(2).from_vector(params)
# warp frame using previous affine transform
perturbed_frame = frame.warp_to_mask(frame.as_masked().mask, transform)
# apply inverse of affine transform to target centre
perturbed_centre = transform.pseudoinverse().apply(target_centre)
# extract perturbed target + context region from frame
perturbed_target = perturbed_frame.extract_patches(
perturbed_centre, patch_size=target_shape, as_single_array=True)
# store target
targets[j + 1] = perturbed_target
return targets
def test_warp_multi():
rgb_image = mio.import_builtin_asset('takeo.ppm')
target_transform = Affine.init_identity(2).from_vector(initial_params)
warped_im = rgb_image.warp_to_mask(template_mask, target_transform)
assert (warped_im.shape == rgb_template.shape)
assert_allclose(warped_im.pixels, rgb_template.pixels)
def test_warp_multi():
rgb_image = mio.import_builtin_asset('takeo.ppm')
target_transform = Affine.init_identity(2).from_vector(initial_params)
warped_im = rgb_image.warp_to_mask(template_mask, target_transform)
assert(warped_im.shape == rgb_template.shape)
assert_allclose(warped_im.pixels, rgb_template.pixels)
def test_c_warp_gray():
target_transform = Affine.identity(2).from_vector(initial_params)
warped_im = gray_image.warp_to(template_mask, target_transform,
interpolator='c')
assert(warped_im.shape == gray_template.shape)
assert_allclose(warped_im.pixels, gray_template.pixels)
def test_warp_to_mask_masked_image_all_true():
img = MaskedImage.init_blank((10, 10), fill=2.5)
template_mask = BooleanImage.init_blank((10, 10), fill=False)
template_mask.pixels[:, :5, :5] = True
t = Affine.init_identity(2)
warped_img = img.warp_to_mask(template_mask, t)
assert (type(warped_img) == MaskedImage)
def residual_wrapper(residual, algorithm, interpolator, expected_error):
image, template, initial_params = setup_conditions(interpolator)
align_algorithm = algorithm(template, residual,
Affine.identity(2).from_vector(initial_params))
fitting = align_algorithm.fit(image, initial_params)
transform = fitting.final_transform
rms_error = compute_fixed_error(transform)
assert_approx_equal(rms_error, expected_error)
def setup_error():
target_transform = Affine.identity(2).from_vector(target_params)
original_box = np.array([[0, 0], [target_shape[0], 0],
[target_shape[0], target_shape[1]],
[0, target_shape[1]]]).T
target_pts = target_transform.apply(original_box.T)
return target_pts, original_box
def test_warp_to_mask_masked_image_all_true():
img = MaskedImage.init_blank((10, 10), fill=2.5)
template_mask = BooleanImage.init_blank((10, 10), fill=False)
template_mask.pixels[:, :5, :5] = True
t = Affine.init_identity(2)
warped_img = img.warp_to_mask(template_mask, t)
assert(type(warped_img) == MaskedImage)
def residual_wrapper(residual, algorithm, interpolator, expected_error):
image, template, initial_params = setup_conditions(interpolator)
align_algorithm = algorithm(
template, residual, Affine.identity(2).from_vector(
initial_params))
fitting = align_algorithm.fit(image, initial_params)
transform = fitting.final_transform
rms_error = compute_fixed_error(transform)
assert_approx_equal(rms_error, expected_error)
def test_warp_gray_batch():
rgb_image = mio.import_builtin_asset('takeo.ppm')
gray_image = rgb_image.as_greyscale()
target_transform = Affine.init_identity(2).from_vector(initial_params)
warped_im = gray_image.warp_to_mask(template_mask, target_transform,
batch_size=100)
assert(warped_im.shape == gray_template.shape)
assert_allclose(warped_im.pixels, gray_template.pixels)
def test_warp_gray_batch():
rgb_image = mio.import_builtin_asset('takeo.ppm')
gray_image = rgb_image.as_greyscale()
target_transform = Affine.init_identity(2).from_vector(initial_params)
warped_im = gray_image.warp_to_mask(template_mask, target_transform,
batch_size=100)
assert(warped_im.shape == gray_template.shape)
assert_allclose(warped_im.pixels, gray_template.pixels)
def test_affine_jacobian_3d_with_positions():
params = np.ones(12)
t = Affine.identity(3).from_vector(params)
explicit_pixel_locations = np.array([[0, 0, 0], [0, 0, 1], [0, 1, 0],
[0, 1, 1], [0, 2, 0], [0, 2, 1],
[1, 0, 0], [1, 0, 1], [1, 1, 0],
[1, 1, 1], [1, 2, 0], [1, 2, 1]])
dW_dp = t.d_dp(explicit_pixel_locations)
assert_equal(dW_dp, jac_solution3d)
def setup_error():
target_transform = Affine.identity(2).from_vector(target_params)
original_box = np.array([[0, 0],
[target_shape[0], 0],
[target_shape[0], target_shape[1]],
[0, target_shape[1]]]).T
target_pts = target_transform.apply(original_box.T)
return target_pts, original_box
def fit_from_bb(self, image, bounding_box, gt_shape=None, **kwargs):
algo_result = self.algorithm.run(image,
bounding_box,
gt_shape=gt_shape)
# TODO: This should be a basic result instead.
return MultiFitterResult(image,
self, [algo_result],
Affine.init_identity(2),
gt_shape=gt_shape)
def test_warp_to_mask_image():
img = Image.init_blank((10, 10), n_channels=2)
img.pixels[:, :, :5] = 0.5
template_mask = BooleanImage.init_blank((10, 10))
template_mask.pixels[:, 5:, :] = False
t = Affine.init_identity(2)
warped_img = img.warp_to_mask(template_mask, t)
assert(type(warped_img) == MaskedImage)
result = Image.init_blank((10, 10), n_channels=2).pixels
result[:, :5, :5] = 0.5
assert(np.all(result == warped_img.pixels))
def test_warp_to_mask_boolean():
b = BooleanImage.init_blank((10, 10))
b.pixels[:, :5] = False
template_mask = BooleanImage.init_blank((10, 10))
template_mask.pixels[:5, :] = False
t = Affine.init_identity(2)
warped_mask = b.warp_to_mask(template_mask, t)
assert(type(warped_mask) == BooleanImage)
result = template_mask.pixels.copy()
result[:, :5] = False
assert(np.all(result == warped_mask.pixels))
def test_warp_to_mask_boolean():
b = BooleanImage.init_blank((10, 10))
b.pixels[:, :5] = False
template_mask = BooleanImage.init_blank((10, 10))
template_mask.pixels[:5, :] = False
t = Affine.init_identity(2)
warped_mask = b.warp_to_mask(template_mask, t)
assert (type(warped_mask) == BooleanImage)
result = template_mask.pixels.copy()
result[:, :5] = False
assert (np.all(result == warped_mask.pixels))
def test_warp_to_mask_image():
img = Image.init_blank((10, 10), n_channels=2)
img.pixels[:, :, :5] = 0.5
template_mask = BooleanImage.init_blank((10, 10))
template_mask.pixels[:, 5:, :] = False
t = Affine.init_identity(2)
warped_img = img.warp_to_mask(template_mask, t)
assert (type(warped_img) == MaskedImage)
result = Image.init_blank((10, 10), n_channels=2).pixels
result[:, :5, :5] = 0.5
assert (np.all(result == warped_img.pixels))
def test_affine_jacobian_2d_with_positions():
params = np.array([0, 0.1, 0.2, 0, 30, 70])
t = Affine.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, jac_solution2d)
def _produce_affine_transforms_per_tri(self):
r"""
Compute the affine transformation between each triangle in the source
and target. This is calculated analytically.
"""
# we permute the axes of the indexed point set to have shape
# [3, n_dims, n_tris] for ease of indexing in.
s = np.transpose(self.source.points[self.trilist],
axes=[1, 2, 0])
t = np.transpose(self.target.points[self.trilist],
axes=[1, 2, 0])
# sik
# ^^^
# ||\- the k'th point
# ||
# |vector between end (j or k) and i
# source [target]
# if i is absent, it is the position of the ijk point.
# (not a _vector_ between points)
# get vectors ij ik for source and target
sij, sik = s[1] - s[0], s[2] - s[0]
tij, tik = t[1] - t[0], t[2] - t[0]
# source vertex positions
si, sj, sk = s[0], s[1], s[2]
ti = t[0]
d = (sij[0] * sik[1]) - (sij[1] * sik[0])
c_x = (sik[1] * tij - sij[1] * tik) / d
c_y = (sij[0] * tik - sik[0] * tij) / d
c_t = ti + (tij * (si[1] * sik[0] - si[0] * sik[1]) +
tik * (si[0] * sij[1] - si[1] * sij[0])) / d
ht = np.repeat(np.eye(3)[..., None], self.n_tris, axis=2)
ht[:2, 0] = c_x
ht[:2, 1] = c_y
ht[:2, 2] = c_t
transforms = []
for i in range(self.n_tris):
transforms.append(Affine(ht[..., i]))
# store our state out
self.transforms = transforms
self.s, self.t = s, t
self.sij, self.sik = sij, sik
self.tij, self.tik = tij, tik
def test_warp_to_mask_masked_image():
mask = BooleanImage.init_blank((15, 15))
# make a truncated mask on the original image
mask.pixels[0, -1, -1] = False
img = MaskedImage.init_blank((15, 15), n_channels=2, mask=mask, fill=2.5)
template_mask = BooleanImage.init_blank((10, 10), fill=False)
template_mask.pixels[:, :5, :5] = True
t = Affine.init_identity(2)
warped_img = img.warp_to_mask(template_mask, t)
assert (type(warped_img) == MaskedImage)
result = Image.init_blank((10, 10), n_channels=2).pixels
result[:, :5, :5] = 2.5
result_mask = BooleanImage.init_blank((10, 10), fill=False).pixels
result_mask[:, :5, :5] = True
assert (warped_img.n_true_pixels() == 25)
assert_allclose(result, warped_img.pixels)
assert_allclose(result_mask, warped_img.mask.pixels)
def test_warp_to_mask_masked_image():
mask = BooleanImage.blank((10, 10))
# make a funny mask on the original image
mask.pixels[2:, :] = False
img = MaskedImage.blank((10, 10), n_channels=2, mask=mask)
img.pixels[...] = 2.5
template_mask = BooleanImage.blank((10, 10), fill=False)
template_mask.pixels[:5, :5] = True
t = Affine.identity(2)
warped_img = img.warp_to_mask(template_mask, t)
assert(type(warped_img) == MaskedImage)
result = Image.blank((10, 10), n_channels=2).pixels
result[:5, :5, :] = 2.5
result_mask = BooleanImage.blank((10, 10), fill=False).pixels
result_mask[:2, :5] = True
assert(warped_img.n_true_pixels() == 10)
assert(np.all(result == warped_img.pixels))
assert(np.all(result_mask == warped_img.mask.pixels))
def test_affine_jacobian_3d_with_positions():
params = np.ones(12)
t = Affine.identity(3).from_vector(params)
explicit_pixel_locations = np.array(
[[0, 0, 0],
[0, 0, 1],
[0, 1, 0],
[0, 1, 1],
[0, 2, 0],
[0, 2, 1],
[1, 0, 0],
[1, 0, 1],
[1, 1, 0],
[1, 1, 1],
[1, 2, 0],
[1, 2, 1]])
dW_dp = t.d_dp(explicit_pixel_locations)
assert_equal(dW_dp, jac_solution3d)
def test_warp_to_mask_masked_image():
mask = BooleanImage.init_blank((15, 15))
# make a truncated mask on the original image
mask.pixels[0, -1, -1] = False
img = MaskedImage.init_blank((15, 15), n_channels=2, mask=mask,
fill=2.5)
template_mask = BooleanImage.init_blank((10, 10), fill=False)
template_mask.pixels[:, :5, :5] = True
t = Affine.init_identity(2)
warped_img = img.warp_to_mask(template_mask, t)
assert(type(warped_img) == MaskedImage)
result = Image.init_blank((10, 10), n_channels=2).pixels
result[:, :5, :5] = 2.5
result_mask = BooleanImage.init_blank((10, 10), fill=False).pixels
result_mask[:, :5, :5] = True
assert(warped_img.n_true_pixels() == 25)
assert_allclose(result, warped_img.pixels)
assert_allclose(result_mask, warped_img.mask.pixels)
def setup_conditions(interpolator):
target_transform = Affine.identity(2).from_vector(target_params)
image_warped = image.warp_to(template_mask,
target_transform,
interpolator=interpolator)
return image, image_warped, initial_params
def target_transform():
initial_params = np.array([0, 0, 0, 0, 70, 30])
return Affine.init_identity(2).from_vector(initial_params)
def test_affine_identity_3d():
assert_allclose(Affine.identity(3).h_matrix, np.eye(4))
def test_affine_incorrect_bottom_row():
h**o = np.random.rand(4, 4)
Affine(h**o)
def test_affine_3d_n_parameters():
h**o = np.eye(4)
t = Affine(h**o)
assert(t.n_parameters == 12)
def test_affine_2d_n_parameters():
h**o = np.eye(3)
t = Affine(h**o)
assert(t.n_parameters == 6)
def setup_conditions(interpolator):
target_transform = Affine.identity(2).from_vector(target_params)
image_warped = image.warp_to(template_mask, target_transform,
interpolator=interpolator)
return image, image_warped, initial_params
def test_scipy_warp_multi():
target_transform = Affine.identity(2).from_vector(initial_params)
warped_im = rgb_image.warp_to(template_mask, target_transform)
assert(warped_im.shape == rgb_template.shape)
assert_allclose(warped_im.pixels, rgb_template.pixels)
def test_affine_identity_2d():
assert_allclose(Affine.init_identity(2).h_matrix, np.eye(3))
def test_affine_pseudoinverse():
s = NonUniformScale([4, 3])
inv_man = NonUniformScale([1. / 4, 1. / 3])
b = Affine(s.h_matrix)
i = b.pseudoinverse()
assert_allclose(i.h_matrix, inv_man.h_matrix)
def test_affine_compose_inplace_affine():
a = Affine.init_identity(2)
b = Affine.init_identity(2)
a.compose_before_inplace(b)
assert (np.all(a.h_matrix == b.h_matrix))
def test_affine_non_square_h_matrix():
h**o = np.random.rand(4, 6)
Affine(h**o)
def test_affine_identity_3d():
assert_allclose(Affine.identity(3).h_matrix, np.eye(4))
def test_scipy_warp_multi():
target_transform = Affine.identity(2).from_vector(initial_params)
warped_im = rgb_image.warp_to(template_mask, target_transform)
assert (warped_im.shape == rgb_template.shape)
assert_allclose(warped_im.pixels, rgb_template.pixels)
def test_affine_compose_inplace_affine():
a = Affine.init_identity(2)
b = Affine.init_identity(2)
a.compose_before_inplace(b)
assert(np.all(a.h_matrix == b.h_matrix))
def test_affine_2d_n_dims_output():
h**o = np.eye(3)
t = Affine(h**o)
assert(t.n_dims_output == 2)
def test_affine_non_square_h_matrix():
h**o = np.random.rand(4, 6)
with raises(ValueError):
Affine(h**o)
def test_affine_pseudoinverse():
s = NonUniformScale([4, 3])
inv_man = NonUniformScale([1./4, 1./3])
b = Affine(s.h_matrix)
i = b.pseudoinverse()
assert_allclose(i.h_matrix, inv_man.h_matrix)
def test_affine_identity_2d():
assert_allclose(Affine.init_identity(2).h_matrix, np.eye(3))
