def test_minimum_spanning_tree():
adjacency_matrix = np.array([[0, 11, 13, 12], [11, 0, 0, 14],
[13, 0, 0, 10], [12, 14, 10, 0]])
g = UndirectedGraph(adjacency_matrix)
t = g.minimum_spanning_tree(root_vertex=0)
assert t.n_edges == 3
assert_allclose(
t.adjacency_matrix.todense(),
csr_matrix(([11., 12., 10.], ([0, 0, 3], [1, 3, 2])),
shape=(4, 4)).todense())
assert t.get_adjacency_list() == [[1, 3], [], [], [2]]
assert t.predecessors_list == [None, 0, 3, 0]
def test_minimum_spanning_tree():
adjacency_matrix = np.array([[0, 11, 13, 12],
[11, 0, 0, 14],
[13, 0, 0, 10],
[12, 14, 10, 0]])
g = UndirectedGraph(adjacency_matrix)
t = g.minimum_spanning_tree(root_vertex=0)
assert t.n_edges == 3
assert_allclose(t.adjacency_matrix.todense(),
csr_matrix(([11., 12., 10.], ([0, 0, 3], [1, 3, 2])),
shape=(4, 4)).todense())
assert t.get_adjacency_list() == [[1, 3], [], [], [2]]
assert t.predecessors_list == [None, 0, 3, 0]
def _compute_minimum_spanning_tree(shapes, root_vertex, level_str, verbose):
# initialize edges and weights matrix
n_vertices = shapes[0].n_points
n_edges = nchoosek(n_vertices, 2)
weights = np.zeros((n_vertices, n_vertices))
edges = np.empty((n_edges, 2), dtype=np.int32)
# fill edges and weights
e = -1
for i in range(n_vertices - 1):
for j in range(i + 1, n_vertices, 1):
# edge counter
e += 1
# print progress
if verbose:
print_dynamic(
'{}Computing complete graph`s weights - {}'.format(
level_str,
progress_bar_str(float(e + 1) / n_edges,
show_bar=False)))
# fill in edges
edges[e, 0] = i
edges[e, 1] = j
# create data matrix of edge
diffs_x = [s.points[i, 0] - s.points[j, 0] for s in shapes]
diffs_y = [s.points[i, 1] - s.points[j, 1] for s in shapes]
coords = np.array([diffs_x, diffs_y])
# compute mean
m = np.mean(coords, axis=1)
# compute covariance
c = np.cov(coords)
# get weight
for im in range(len(shapes)):
weights[i, j] += -np.log(
multivariate_normal.pdf(coords[:, im], mean=m, cov=c))
weights[j, i] = weights[i, j]
# create undirected graph
complete_graph = UndirectedGraph(edges)
if verbose:
print_dynamic('{}Minimum spanning graph computed.\n'.format(level_str))
# compute minimum spanning graph
return complete_graph.minimum_spanning_tree(weights, root_vertex)
def _compute_minimum_spanning_tree(shapes, root_vertex, level_str, verbose):
# initialize edges and weights matrix
n_vertices = shapes[0].n_points
n_edges = nchoosek(n_vertices, 2)
weights = np.zeros((n_vertices, n_vertices))
edges = np.empty((n_edges, 2), dtype=np.int32)
# fill edges and weights
e = -1
for i in range(n_vertices-1):
for j in range(i+1, n_vertices, 1):
# edge counter
e += 1
# print progress
if verbose:
print_dynamic('{}Computing complete graph`s weights - {}'.format(
level_str,
progress_bar_str(float(e + 1) / n_edges,
show_bar=False)))
# fill in edges
edges[e, 0] = i
edges[e, 1] = j
# create data matrix of edge
diffs_x = [s.points[i, 0] - s.points[j, 0] for s in shapes]
diffs_y = [s.points[i, 1] - s.points[j, 1] for s in shapes]
coords = np.array([diffs_x, diffs_y])
# compute mean
m = np.mean(coords, axis=1)
# compute covariance
c = np.cov(coords)
# get weight
for im in range(len(shapes)):
weights[i, j] += -np.log(multivariate_normal.pdf(coords[:, im],
mean=m, cov=c))
weights[j, i] = weights[i, j]
# create undirected graph
complete_graph = UndirectedGraph(edges)
if verbose:
print_dynamic('{}Minimum spanning graph computed.\n'.format(level_str))
# compute minimum spanning graph
return complete_graph.minimum_spanning_tree(weights, root_vertex)
def test_minimum_spanning_tree():
adjacency_array = np.array([[3, 1], [2, 3], [0, 3], [2, 0], [0, 1]])
weights = np.array([[0, 11, 13, 12], [11, 0, 0, 14], [13, 0, 0, 10],
[12, 14, 10, 0]])
g = UndirectedGraph(adjacency_array)
t = g.minimum_spanning_tree(weights, root_vertex=0)
assert t.n_edges == 3
assert_allclose(t.adjacency_array, np.array([[0, 1], [0, 3], [3, 2]]))
assert t.adjacency_list == [[1, 3], [], [], [2]]
assert_allclose(
t.get_adjacency_matrix(),
np.array([[False, True, False, True], [False, False, False, False],
[False, False, False, False], [False, False, True, False]]))
assert t.predecessors_list == [None, 0, 3, 0]
def _compute_minimum_spanning_tree(shapes,
root_vertex=0,
prefix='',
verbose=False):
# initialize weights matrix
n_vertices = shapes[0].n_points
weights = np.zeros((n_vertices, n_vertices))
# print progress if requested
range1 = range(n_vertices - 1)
if verbose:
range1 = print_progress(
range1,
end_with_newline=False,
prefix='{}Deformation graph - Computing complete graph`s '
'weights'.format(prefix))
# compute weights
for i in range1:
for j in range(i + 1, n_vertices, 1):
# create data matrix of edge
diffs_x = [s.points[i, 0] - s.points[j, 0] for s in shapes]
diffs_y = [s.points[i, 1] - s.points[j, 1] for s in shapes]
coords = np.array([diffs_x, diffs_y])
# compute mean and covariance
m = np.mean(coords, axis=1)
c = np.cov(coords)
# get weight
for im in range(len(shapes)):
weights[i, j] += -np.log(
multivariate_normal.pdf(coords[:, im], mean=m, cov=c))
weights[j, i] = weights[i, j]
# create undirected graph
complete_graph = UndirectedGraph(weights)
if verbose:
print_dynamic('{}Deformation graph - Minimum spanning graph '
'computed.\n'.format(prefix))
# compute minimum spanning graph
return complete_graph.minimum_spanning_tree(root_vertex)
def test_increment():
# arguments values
mode_values = ["concatenation", "subtraction"]
n_features_per_vertex_values = [2, 3]
sparse_values = [True, False]
n_components_values = [None, 30]
# create graph
n_vertices = 6
edges = np.array([[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 0]])
graphs = [
DirectedGraph.init_from_edges(edges, n_vertices),
UndirectedGraph(np.zeros((n_vertices, n_vertices))),
]
for n_features_per_vertex in n_features_per_vertex_values:
# create samples
n_samples = 100
samples = []
for i in range(n_samples):
samples.append(np.random.rand(n_vertices * n_features_per_vertex))
for graph in graphs:
for mode in mode_values:
for sparse in sparse_values:
for n_components in n_components_values:
# Incremental GMRF
gmrf1 = GMRFVectorModel(
samples[:50],
graph,
mode=mode,
sparse=sparse,
n_components=n_components,
dtype=np.float64,
incremental=True,
)
gmrf1.increment(samples[50::])
# Non incremental GMRF
gmrf2 = GMRFVectorModel(
samples,
graph,
mode=mode,
sparse=sparse,
n_components=n_components,
dtype=np.float64,
)
# Compare
if sparse:
assert_array_almost_equal(
gmrf1.precision.todense(),
gmrf2.precision.todense())
assert_array_almost_equal(gmrf1.mean_vector,
gmrf2.mean_vector)
def _compute_minimum_spanning_tree(shapes, root_vertex=0, prefix='',
verbose=False):
# initialize weights matrix
n_vertices = shapes[0].n_points
weights = np.zeros((n_vertices, n_vertices))
# print progress if requested
range1 = range(n_vertices-1)
if verbose:
range1 = print_progress(
range1, end_with_newline=False,
prefix='{}Deformation graph - Computing complete graph`s '
'weights'.format(prefix))
# compute weights
for i in range1:
for j in range(i+1, n_vertices, 1):
# create data matrix of edge
diffs_x = [s.points[i, 0] - s.points[j, 0] for s in shapes]
diffs_y = [s.points[i, 1] - s.points[j, 1] for s in shapes]
coords = np.array([diffs_x, diffs_y])
# compute mean and covariance
m = np.mean(coords, axis=1)
c = np.cov(coords)
# get weight
for im in range(len(shapes)):
weights[i, j] += -np.log(multivariate_normal.pdf(coords[:, im],
mean=m, cov=c))
weights[j, i] = weights[i, j]
# create undirected graph
complete_graph = UndirectedGraph(weights)
if verbose:
print_dynamic('{}Deformation graph - Minimum spanning graph '
'computed.\n'.format(prefix))
# compute minimum spanning graph
return complete_graph.minimum_spanning_tree(root_vertex)
def test_minimum_spanning_tree():
adjacency_array = np.array([[3, 1],
[2, 3],
[0, 3],
[2, 0],
[0, 1]])
weights = np.array([[0, 11, 13, 12],
[11, 0, 0, 14],
[13, 0, 0, 10],
[12, 14, 10, 0]])
g = UndirectedGraph(adjacency_array)
t = g.minimum_spanning_tree(weights, root_vertex=0)
assert t.n_edges == 3
assert_allclose(t.adjacency_array, np.array([[0, 1], [0, 3], [3, 2]]))
assert t.adjacency_list == [[1, 3], [], [], [2]]
assert_allclose(t.get_adjacency_matrix(),
np.array([[False, True, False, True],
[False, False, False, False],
[False, False, False, False],
[False, False, True, False]]))
assert t.predecessors_list == [None, 0, 3, 0]
def test_mahalanobis_distance():
# arguments values
mode_values = ['concatenation', 'subtraction']
n_features_per_vertex_values = [2, 3]
sparse_values = [True, False]
subtract_mean_values = [True, False]
n_components_values = [None, 30]
# create graph
n_vertices = 6
edges = np.array([[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 0]])
graphs = [
DirectedGraph.init_from_edges(edges, n_vertices),
UndirectedGraph(np.zeros((n_vertices, n_vertices)))
]
for n_features_per_vertex in n_features_per_vertex_values:
# create samples
n_samples = 50
samples = []
for i in range(n_samples):
samples.append(
PointCloud(np.random.rand(n_vertices, n_features_per_vertex)))
test_sample = PointCloud(
np.random.rand(n_vertices, n_features_per_vertex))
for graph in graphs:
for mode in mode_values:
for sparse in sparse_values:
for n_components in n_components_values:
# train GMRF
gmrf = GMRFModel(samples,
graph,
mode=mode,
sparse=sparse,
n_components=n_components,
dtype=np.float64)
for subtract_mean in subtract_mean_values:
# compute costs
if graph.n_edges == 0:
cost1 = _compute_sum_cost_block_diagonal(
samples, test_sample, graph,
n_features_per_vertex, subtract_mean)
else:
cost1 = _compute_sum_cost_block_sparse(
samples, test_sample, graph,
n_features_per_vertex, subtract_mean, mode)
cost2 = gmrf.mahalanobis_distance(
test_sample, subtract_mean=subtract_mean)
assert_almost_equal(cost1, cost2)
def __init__(self,
adjacency_array_appearance=None,
gaussian_per_patch=True,
adjacency_array_deformation=None,
root_vertex_deformation=None,
adjacency_array_shape=None,
features=no_op,
patch_shape=(17, 17),
normalization_diagonal=None,
n_levels=2,
downscale=2,
scaled_shape_models=False,
use_procrustes=True,
max_shape_components=None,
n_appearance_parameters=None):
# check parameters
checks.check_n_levels(n_levels)
checks.check_downscale(downscale)
checks.check_normalization_diagonal(normalization_diagonal)
max_shape_components = checks.check_max_components(
max_shape_components, n_levels, 'max_shape_components')
features = checks.check_features(features, n_levels)
n_appearance_parameters = _check_n_parameters(
n_appearance_parameters, n_levels, 'n_appearance_parameters')
# appearance graph
if adjacency_array_appearance is None:
self.graph_appearance = None
elif adjacency_array_appearance == 'yorgos':
self.graph_appearance = 'yorgos'
else:
self.graph_appearance = UndirectedGraph(adjacency_array_appearance)
# shape graph
if adjacency_array_shape is None:
self.graph_shape = None
else:
self.graph_shape = UndirectedGraph(adjacency_array_shape)
# check adjacency_array_deformation, root_vertex_deformation
if adjacency_array_deformation is None:
self.graph_deformation = None
if root_vertex_deformation is None:
self.root_vertex = 0
else:
if root_vertex_deformation is None:
self.graph_deformation = DirectedGraph(
adjacency_array_deformation)
else:
self.graph_deformation = Tree(adjacency_array_deformation,
root_vertex_deformation)
# store parameters
self.features = features
self.patch_shape = patch_shape
self.normalization_diagonal = normalization_diagonal
self.n_levels = n_levels
self.downscale = downscale
self.scaled_shape_models = scaled_shape_models
self.max_shape_components = max_shape_components
self.n_appearance_parameters = n_appearance_parameters
self.use_procrustes = use_procrustes
self.gaussian_per_patch = gaussian_per_patch
def test_create_graph_exception():
adj = np.array([[0, 1, 3], [0, 2, 4]])
with raises(ValueError):
UndirectedGraph(adj)
]
)
point = np.array([[10, 10]])
# Define undirected graph and pointgraph
adj_undirected = np.array(
[
[0, 1, 1, 0, 0, 0],
[1, 0, 1, 1, 0, 0],
[1, 1, 0, 0, 1, 0],
[0, 1, 0, 0, 1, 1],
[0, 0, 1, 1, 0, 0],
[0, 0, 0, 1, 0, 0],
]
)
g_undirected = UndirectedGraph(adj_undirected)
pg_undirected = PointUndirectedGraph(points, adj_undirected)
# Define directed graph and pointgraph
adj_directed = csr_matrix(
([1] * 8, ([1, 2, 1, 2, 1, 2, 3, 3], [0, 0, 2, 1, 3, 4, 4, 5])), shape=(6, 6)
)
g_directed = DirectedGraph(adj_directed)
pg_directed = PointDirectedGraph(points, adj_directed)
# Define tree and pointtree
adj_tree = np.array(
[
[0, 1, 1, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 1, 1, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 1, 0, 0, 0],
def test_create_graph_exception():
adj = np.array([[0, 1, 3], [0, 2, 4]])
UndirectedGraph(adj)
import numpy as np
from numpy.testing import assert_allclose
from nose.tools import raises
from menpo.shape import UndirectedGraph, DirectedGraph, Tree
# Define adjacency arrays
adj_undirected = np.array([[0, 1], [0, 2], [1, 2], [1, 3], [2, 4], [3, 4],
[3, 5]])
g_undirected = UndirectedGraph(adj_undirected)
adj_directed = np.array([[1, 0], [2, 0], [1, 2], [2, 1], [1, 3], [2, 4],
[3, 4], [3, 5]])
g_directed = DirectedGraph(adj_directed)
adj_tree = np.array([[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [3, 6], [4, 7],
[5, 8]])
g_tree = Tree(adj_tree, 0)
@raises(ValueError)
def test_create_graph_exception():
adj = np.array([[0, 1, 3], [0, 2, 4]])
UndirectedGraph(adj)
@raises(ValueError)
def test_create_tree_exception_1():
adj = np.array([[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [3, 6], [4, 7],
[5, 8], [0, 4]])
Tree(adj, 0)
