def test_triangle_variance_space_3D_case(sphere):
"""Test the values of the barycentric coordinates (variance space).
alpha and beta must be close to 0. (so gamme close to 1.)
"""
pca = PCA().fit(sphere)
norm_eigenvalues = sum_normalize(pca.singular_values_**2)
alpha, beta = triangle_variance_space(norm_eigenvalues)
assert 1 - (alpha + beta) >= 0.95
def test_triangle_variance_space_2D_case(plane):
"""Test the values of the barycentric coordinates (variance space).
beta must be > alpha and close to 1.0
"""
pca = PCA().fit(plane)
norm_eigenvalues = sum_normalize(pca.singular_values_**2)
alpha, beta = triangle_variance_space(norm_eigenvalues)
assert alpha < beta
assert beta >= 0.95
def test_triangle_variance_space_1D_case(line):
"""Test the values of the barycentric coordinates (variance space).
'alpha' must be >> to 'beta'
"""
pca = PCA().fit(line)
norm_eigenvalues = sum_normalize(pca.singular_values_**2)
alpha, beta = triangle_variance_space(norm_eigenvalues)
assert alpha > beta
assert abs(alpha - 1) < 1e-3
def test_3d_features_line(line):
"""Test curvature change, linearity, planarity and scattering for a line.
"""
pca = PCA().fit(line)
norm_eigenvalues = sum_normalize(pca.singular_values_**2)
# close to 1
assert linearity(norm_eigenvalues) >= 0.9
# close to zero
assert curvature_change(norm_eigenvalues) <= 5e-3
assert planarity(norm_eigenvalues) <= 0.05
assert scattering(norm_eigenvalues) <= 0.05
def test_3d_features_sphere(sphere):
"""Test curvature change, linearity, planarity and scattering for a sphere.
"""
pca = PCA().fit(sphere)
norm_eigenvalues = sum_normalize(pca.singular_values_**2)
# close to 1/3
assert abs(curvature_change(norm_eigenvalues) - 1 / 3) <= 0.05
# close to 1
assert scattering(norm_eigenvalues) >= 0.9
# close to 0
assert linearity(norm_eigenvalues) <= 0.05
assert planarity(norm_eigenvalues) <= 0.05
def test_sum_triangle_variance_space(plane):
"""Test the values of the barycentric coordinates (variance space).
The function returns the first two barycentric coordinates but you should have
`alpha + beta + gamma = 1`
"""
pca = PCA().fit(plane)
norm_eigenvalues = sum_normalize(pca.singular_values_**2)
print(pca.singular_values_)
print(pca.singular_values_**2)
print(norm_eigenvalues)
alpha, beta = triangle_variance_space(norm_eigenvalues)
assert alpha + beta <= 1.0
def process_full(neighbors, dist_to_neighbors, extra):
"""Build the full feature set for a single point
Parameters
----------
neighbors : numpy.array
Coordinates of all points within the point neighborhood; must be a
2D-shaped array with `point_cloud.shape[1] == 3`
dist_to_neighbors : numpy.array
Gives distance between the point and all its neighbors
extra : ExtraFeatures
Names and values of extra input features, e.g. the RGB color
Returns
------
list, OrderedDict generator (features for each point)
"""
num_neighbors = neighbors.shape[0] - 1
x, y, z = neighbors[0]
rad_2D = radius_2D(neighbors[0, :2], neighbors[:, :2])
rad_3D = radius_3D(dist_to_neighbors)
if len(neighbors) <= 2:
return (
FeatureTuple(
x, y, z,
np.nan, np.nan, # alpha, beta
rad_3D,
val_range(neighbors[:, 2]), # z_range
std_deviation(neighbors[:, 2]), # std_dev
density_3D(rad_3D, len(neighbors)),
np.nan, np.nan, np.nan, np.nan, np.nan,
np.nan, np.nan, np.nan, np.nan,
rad_2D,
density_2D(rad_2D, len(neighbors)),
np.nan, # eigenvalue_sum_2D
np.nan, # eigenvalue_ratio_2D
),
extra
)
else:
pca = fit_pca(neighbors) # PCA on the x,y,z coords
eigenvalues_3D = pca.singular_values_ ** 2
norm_eigenvalues_3D = sum_normalize(eigenvalues_3D)
alpha, beta = triangle_variance_space(norm_eigenvalues_3D)
pca_2d = fit_pca(neighbors[:, :2]) # PCA just on the x,y coords
eigenvalues_2D = pca_2d.singular_values_ ** 2
return (
FeatureTuple(
x, y, z,
num_neighbors,
alpha, beta,
rad_3D,
val_range(neighbors[:, 2]), # z_range
std_deviation(neighbors[:, 2]), # std_dev
density_3D(rad_3D, len(neighbors)),
verticality_coefficient(pca),
curvature_change(norm_eigenvalues_3D),
linearity(norm_eigenvalues_3D),
planarity(norm_eigenvalues_3D),
scattering(norm_eigenvalues_3D),
omnivariance(norm_eigenvalues_3D),
anisotropy(norm_eigenvalues_3D),
eigenentropy(norm_eigenvalues_3D),
val_sum(eigenvalues_3D), # eigenvalue sum
rad_2D,
density_2D(rad_2D, len(neighbors)),
val_sum(eigenvalues_2D), # eigenvalue_sum_2D
eigenvalue_ratio_2D(eigenvalues_2D)
),
extra
)