def test_pca_increment_noncentred():
pca_samples = [np.random.randn(10) for _ in range(10)]
ipca_model = PCAVectorModel(pca_samples[:3], centre=False)
ipca_model.increment(pca_samples[3:6])
ipca_model.increment(pca_samples[6:])
bpca_model = PCAVectorModel(pca_samples, centre=False)
assert_almost_equal(np.abs(ipca_model.components),
np.abs(bpca_model.components))
assert_almost_equal(ipca_model.eigenvalues, bpca_model.eigenvalues)
assert_almost_equal(ipca_model.mean(), bpca_model.mean())
def generate_texture_model_from_image_3d_fits(images_and_fits,
lambda_=0.01,
n_components=0.99):
"""Build an ITW texture model from a list of images with associated dense
3D fits (one per image). Note that the input images should already have an
image feature taken on them, and have all been resized to a consistent
scale."""
f = open("/content/fk.txt", "w")
f.write("shit")
f.close()
feat_img, fit_2d = images_and_fits[0]
n_channels = feat_img.n_channels
n_features = n_channels * fit_2d.n_points
n_samples = len(images_and_fits)
X = np.empty((n_samples, n_features), dtype=feat_img.pixels.dtype)
M = np.empty_like(X, dtype=np.bool)
proportion_masked = []
for i, (img, fit_2d) in enumerate(
print_progress(images_and_fits,
prefix='Extracting masks & features')):
features, mask = extract_per_vertex_colour_with_occlusion(fit_2d, img)
mask_repeated = np.repeat(mask.ravel(), n_channels)
X[i] = features.ravel()
M[i] = mask_repeated.ravel()
proportion_masked.append(mask.sum() / mask.shape[0])
print('Performing R-PCA to complete missing textures')
A, E = rpca_missing(X, M, verbose=True, lambda_=lambda_)
print('R-PCA completed. Building PCA model of features on completed '
'samples.')
model = PCAVectorModel(A, inplace=True)
print('Trimming the components to retain only what was required.')
model.trim_components(n_components=n_components)
return model, X, M
def generate_texture_model_from_itwmm(images, mm, id_ind, exp_ind,
template_camera, p, qs, cs,
lambda_=0.01,
n_components=0.99):
r"""Build a new texture model from an existing model and fitting
information to a collection of images."""
n_channels = images[0].n_channels
n_features = n_channels * mm.n_vertices
n_samples = len(images)
X = np.empty((n_samples, n_features), dtype=mm.texture_model.mean().dtype)
M = np.empty_like(X, dtype=np.bool)
proportion_masked = []
for i, (img, q, c) in enumerate(zip(print_progress(images, 'Extracting '
'masks and '
'features'), qs,
cs)):
i_in_img = instance_for_params(mm, id_ind, exp_ind,
template_camera,
p, q, c)['instance_in_img']
features, mask = extract_per_vertex_colour_with_occlusion(i_in_img, img)
mask_repeated = np.repeat(mask.ravel(), n_channels)
X[i] = features.ravel()
M[i] = mask_repeated.ravel()
proportion_masked.append(mask.sum() / mask.shape[0])
print('Extraction concluded. Self-occlusions on average masked {:.0%} of '
'vertices.'.format(np.array(proportion_masked).mean()))
print('Performing R-PCA to complete missing textures')
A, E = rpca_missing(X, M, verbose=True, lambda_=lambda_)
print('R-PCA completed. Building PCA model of features on completed '
'samples.')
model = PCAVectorModel(A, inplace=True)
print('Trimming the components to retain only what was required.')
model.trim_components(n_components=n_components)
return model, X, M
def test_pca_orthogonalize_against():
pca_samples = np.random.randn(10, 10)
pca_model = PCAVectorModel(pca_samples)
lm_samples = np.asarray([np.random.randn(10) for _ in range(4)])
lm_model = LinearVectorModel(np.asarray(lm_samples))
# orthogonalize
pca_model.orthonormalize_against_inplace(lm_model)
# number of active components must remain the same
assert_equal(pca_model.n_active_components, 6)
def test_pca_n_active_components_too_many():
samples = [np.random.randn(10) for _ in range(10)]
model = PCAVectorModel(samples)
# too many components
model.n_active_components = 100
assert_equal(model.n_active_components, 9)
# reset too smaller number of components
model.n_active_components = 5
assert_equal(model.n_active_components, 5)
# reset to too many components
model.n_active_components = 100
assert_equal(model.n_active_components, 9)
def test_pca_variance_after_trim():
samples = [np.random.randn(10) for _ in range(10)]
model = PCAVectorModel(samples)
# set number of active components
model.trim_components(5)
# kept variance must be smaller than total variance
assert model.variance() < model.original_variance()
# kept variance ratio must be smaller than 1.0
assert model.variance_ratio() < 1.0
# noise variance must be bigger than 0.0
assert model.noise_variance() > 0.0
# noise variance ratio must also be bigger than 0.0
assert model.noise_variance_ratio() > 0.0
# inverse noise variance is computable
assert model.inverse_noise_variance() == 1 / model.noise_variance()
def test_pca_vector_init_from_covariance():
n_samples = 30
n_features = 10
centre_values = [True, False]
for centre in centre_values:
# generate samples matrix and mean vector
samples = np.random.randn(n_samples, n_features)
mean = np.mean(samples, axis=0)
# compute covariance matrix
if centre:
X = samples - mean
C = np.dot(X.T, X) / (n_samples - 1)
else:
C = np.dot(samples.T, samples) / (n_samples - 1)
# create the 2 pca models
pca1 = PCAVectorModel.init_from_covariance_matrix(C,
mean,
centred=centre,
n_samples=n_samples)
pca2 = PCAVectorModel(samples, centre=centre, inplace=False)
# compare them
assert_array_almost_equal(pca1.mean(), pca2.mean())
assert_array_almost_equal(pca1.component(0, with_mean=False),
pca2.component(0, with_mean=False))
assert_array_almost_equal(pca1.component(7), pca2.component(7))
assert_array_almost_equal(pca1.components, pca2.components)
assert_array_almost_equal(pca1.eigenvalues, pca2.eigenvalues)
assert_array_almost_equal(pca1.eigenvalues_cumulative_ratio(),
pca2.eigenvalues_cumulative_ratio())
assert_array_almost_equal(pca1.eigenvalues_ratio(),
pca2.eigenvalues_ratio())
weights = np.random.randn(pca1.n_active_components - 4)
assert_array_almost_equal(pca1.instance(weights),
pca2.instance(weights))
assert pca1.n_active_components == pca2.n_active_components
assert pca1.n_components == pca2.n_components
assert pca1.n_features == pca2.n_features
assert pca1.n_samples == pca2.n_samples
assert pca1.noise_variance() == pca2.noise_variance()
assert pca1.noise_variance_ratio() == pca2.noise_variance_ratio()
assert_allclose(pca1.variance(), pca2.variance())
assert pca1.variance_ratio() == pca2.variance_ratio()
assert_array_almost_equal(pca1.whitened_components(),
pca2.whitened_components())
def test_pca_trim_variance_limit():
samples = [np.random.randn(10) for _ in range(10)]
model = PCAVectorModel(samples)
with raises(ValueError):
# impossible to keep more than 1.0 ratio variance
model.trim_components(2.5)
def test_pca_n_active_components_negative():
samples = [np.random.randn(10) for _ in range(10)]
model = PCAVectorModel(samples)
with raises(ValueError):
model.n_active_components = -5
def test_pca_n_active_components():
samples = [np.random.randn(10) for _ in range(10)]
model = PCAVectorModel(samples)
# integer
model.n_active_components = 5
assert_equal(model.n_active_components, 5)
def test_pca_n_active_components_negative():
samples = [np.random.randn(10) for _ in range(10)]
model = PCAVectorModel(samples)
# not sufficient components
model.n_active_components = -5
