def test_tree_of_shapes_self_dual(self):
np.random.seed(42)
image = np.random.rand(25, 38)
neg_image = -1 * image
tree1, altitudes1 = hg.component_tree_tree_of_shapes_image2d(image)
tree2, altitudes2 = hg.component_tree_tree_of_shapes_image2d(neg_image)
self.assertTrue(hg.test_tree_isomorphism(tree1, tree2))
def test_tree_of_shapes_no_padding(self):
image = np.asarray(
((1, 1, 1, 1, 1, 1), (1, 0, 0, 3, 3, 1), (1, 0, 1, 1, 3, 1),
(1, 0, 0, 3, 3, 1), (1, 1, 1, 1, 1, 1)),
dtype=np.int8)
tree, altitudes = hg.component_tree_tree_of_shapes_image2d(
image, 'none', False)
ref_parents = np.asarray(
(101, 101, 101, 101, 101, 101, 101, 101, 101, 101, 101, 101, 101,
101, 101, 101, 101, 101, 101, 101, 101, 101, 101, 101, 100, 100,
100, 101, 99, 99, 99, 101, 101, 101, 101, 100, 101, 101, 101, 101,
101, 99, 101, 101, 101, 101, 100, 101, 101, 101, 101, 101, 99,
101, 101, 101, 101, 100, 101, 101, 101, 101, 101, 99, 101, 101,
101, 101, 100, 100, 100, 101, 99, 99, 99, 101, 101, 101, 101, 101,
101, 101, 101, 101, 101, 101, 101, 101, 101, 101, 101, 101, 101,
101, 101, 101, 101, 101, 101, 101, 101, 101),
dtype=np.int64)
ref_altitudes = np.asarray(
(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 0, 0, 0, 1, 3, 3, 3, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 3, 1, 1,
1, 1, 0, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 3, 1, 1,
1, 1, 0, 0, 0, 1, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 0, 1),
dtype=np.int8)
self.assertTrue(np.all(tree.parents() == ref_parents))
self.assertTrue(np.all(altitudes == ref_altitudes))
def test_tree_of_shapes_padding_0(self):
image = np.asarray(((1, 1, 1),
(1, -2, 3)), dtype=np.int32)
tree, altitudes = hg.component_tree_tree_of_shapes_image2d(image, 'zero', False)
ref_parents = np.asarray((66, 66, 66, 66, 66, 66, 66, 66, 66,
66, 66, 66, 66, 66, 66, 66, 66, 66,
66, 66, 65, 65, 65, 65, 65, 66, 66,
66, 66, 65, 66, 66, 66, 65, 66, 66,
66, 66, 65, 66, 63, 66, 64, 66, 66,
66, 66, 66, 66, 66, 66, 66, 66, 66,
66, 66, 66, 66, 66, 66, 66, 66, 66,
66, 65, 66, 66), dtype=np.int64)
ref_altitudes = np.asarray((0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 1, 1, 1, 1, 0, 0,
0, 0, 1, 0, 0, 0, 1, 0, 0,
0, 0, 1, 0, -2, 0, 3, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
-2, 3, 1, 0), dtype=np.int32)
self.assertTrue(np.all(tree.parents() == ref_parents))
self.assertTrue(np.all(altitudes == ref_altitudes))
leaf_graph = hg.CptHierarchy.get_leaf_graph(tree)
res_shape = hg.CptGridGraph.get_shape(leaf_graph)
self.assertTrue(len(res_shape) == 2)
self.assertTrue(res_shape[0] * res_shape[1] == tree.num_leaves())
self.assertTrue(res_shape[0] == (image.shape[0] + 2) * 2 - 1)
self.assertTrue(res_shape[1] == (image.shape[1] + 2) * 2 - 1)
def patches_batch_tos_area_p(batch_image, i, j, l):
tree, altitudes = hg.component_tree_tree_of_shapes_image2d(
batch_image[i, :, :, 0])
area = hg.attribute_area(tree)
batch_image[i, :, :,
j + 1] = hg.reconstruct_leaf_data(tree, altitudes, area < l)
return batch_image[i, :, :, j + 1]
def test_tree_of_shapes_no_padding_original_space(self):
image = np.asarray(((1, 1, 1, 1, 1, 1),
(1, 0, 0, 3, 3, 1),
(1, 0, 1, 1, 3, 1),
(1, 0, 0, 3, 3, 1),
(1, 1, 1, 1, 1, 1)), dtype=np.float64)
tree, altitudes = hg.component_tree_tree_of_shapes_image2d(image, 'none', True)
ref_parents = np.asarray((32, 32, 32, 32, 32, 32,
32, 30, 30, 31, 31, 32,
32, 30, 32, 32, 31, 32,
32, 30, 30, 31, 31, 32,
32, 32, 32, 32, 32, 32,
32, 32, 32), dtype=np.int64)
ref_altitudes = np.asarray((1, 1, 1, 1, 1, 1,
1, 0, 0, 3, 3, 1,
1, 0, 1, 1, 3, 1,
1, 0, 0, 3, 3, 1,
1, 1, 1, 1, 1, 1,
0, 3, 1), dtype=np.float64)
self.assertTrue(np.all(tree.parents() == ref_parents))
self.assertTrue(np.all(altitudes == ref_altitudes))
leaf_graph = hg.CptHierarchy.get_leaf_graph(tree)
res_shape = hg.CptGridGraph.get_shape(leaf_graph)
self.assertTrue(len(res_shape) == 2)
self.assertTrue(res_shape[0] * res_shape[1] == tree.num_leaves())
self.assertTrue(res_shape[0] == image.shape[0])
self.assertTrue(res_shape[1] == image.shape[1])
def patches_batch_tos_area(batch_image, batch_size, lambdas):
for i in range(batch_size):
tree, altitudes = hg.component_tree_tree_of_shapes_image2d(
batch_image[i, :, :, 0])
area = hg.attribute_area(tree)
for j in range(len(lambdas)):
batch_image[i, :, :, j + 1] = hg.reconstruct_leaf_data(
tree, altitudes, area < lambdas[j])
return batch_image
def test_component_tree_multivariate_tree_of_shapes_image2d_sanity(self):
image = np.asarray(((1, 1),
(1, -2),
(1, 7)), dtype=np.float64)
tree, _ = hg.component_tree_tree_of_shapes_image2d(image, 'mean')
image3d = np.dstack((image, image, image))
tree2 = hg.component_tree_multivariate_tree_of_shapes_image2d(image3d, 'mean')
self.assertTrue(hg.test_tree_isomorphism(tree, tree2))
def test_tree_of_shapes_padding_0_original_space(self):
image = np.asarray(((1, 1, 1), (1, -2, 3)), dtype=np.int32)
tree, altitudes = hg.component_tree_tree_of_shapes_image2d(
image, 'zero', True)
ref_parents = np.asarray((8, 8, 8, 8, 6, 7, 9, 8, 9, 9),
dtype=np.int64)
ref_altitudes = np.asarray((1, 1, 1, 1, -2, 3, -2, 3, 1, 0),
dtype=np.int32)
self.assertTrue(np.all(tree.parents() == ref_parents))
self.assertTrue(np.all(altitudes == ref_altitudes))
def test_tree_of_shapes_padding_mean_original_space(self):
image = np.asarray(((1, 1), (1, -2), (1, 7)), dtype=np.float64)
tree, altitudes = hg.component_tree_tree_of_shapes_image2d(
image, 'mean', True)
ref_parents = np.asarray((8, 8, 8, 7, 8, 6, 9, 8, 9, 9),
dtype=np.int64)
ref_altitudes = np.asarray((1., 1., 1., -2., 1., 7., 7., -2., 1., 1.5),
dtype=np.float64)
self.assertTrue(np.all(tree.parents() == ref_parents))
self.assertTrue(np.allclose(altitudes, ref_altitudes))
def test_contour_length_tree_of_shapes(self):
image = np.asarray(
((0, 0, 0, 0), (0, -2, 2, 0), (0, -1, 1, 0), (0, 0, 0, 0)))
tree, altitudes = hg.component_tree_tree_of_shapes_image2d(image)
res = hg.attribute_contour_length(tree)
ref = np.asarray(
(4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6, 6, 16),
dtype=np.float64)
self.assertTrue(np.all(res == ref))
def test_tree_of_shapes_no_padding_original_space(self):
image = np.asarray(
((1, 1, 1, 1, 1, 1), (1, 0, 0, 3, 3, 1), (1, 0, 1, 1, 3, 1),
(1, 0, 0, 3, 3, 1), (1, 1, 1, 1, 1, 1)),
dtype=np.float64)
tree, altitudes = hg.component_tree_tree_of_shapes_image2d(
image, 'none', True)
ref_parents = np.asarray((32, 32, 32, 32, 32, 32, 32, 31, 31, 30, 30,
32, 32, 31, 32, 32, 30, 32, 32, 31, 31, 30,
30, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32),
dtype=np.int64)
ref_altitudes = np.asarray(
(1, 1, 1, 1, 1, 1, 1, 0, 0, 3, 3, 1, 1, 0, 1, 1, 3, 1, 1, 0, 0, 3,
3, 1, 1, 1, 1, 1, 1, 1, 3, 0, 1),
dtype=np.float64)
self.assertTrue(np.all(tree.parents() == ref_parents))
self.assertTrue(np.all(altitudes == ref_altitudes))
def test_tree_of_shapes_no_immersion_no_padding_no_original_space(self):
image = np.asarray(((1, 1, 1, 1, 1),
(1, 0, 1, 2, 1),
(1, 1, 1, 1, 1)), dtype=np.float64)
tree, altitudes = hg.component_tree_tree_of_shapes_image2d(image, 'none', original_size=False, immersion=False)
ref_parents = np.asarray((17, 17, 17, 17, 17,
17, 16, 17, 15, 17,
17, 17, 17, 17, 17, 17, 17, 17), dtype=np.int64)
ref_altitudes = np.asarray((1, 1, 1, 1, 1,
1, 0, 1, 2, 1,
1, 1, 1, 1, 1, 2, 0, 1), dtype=np.float64)
self.assertTrue(np.all(tree.parents() == ref_parents))
self.assertTrue(np.allclose(altitudes, ref_altitudes))
g = hg.CptHierarchy.get_leaf_graph(tree)
s = hg.CptGridGraph.get_shape(g)
self.assertTrue(s[0] * s[1] == tree.num_leaves())
def test_tree_of_shapes_padding_0(self):
image = np.asarray(((1, 1, 1), (1, -2, 3)), dtype=np.int32)
tree, altitudes = hg.component_tree_tree_of_shapes_image2d(
image, 'zero', False)
ref_parents = np.asarray(
(66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66,
66, 66, 66, 66, 65, 65, 65, 65, 65, 66, 66, 66, 66, 65, 66, 66,
66, 65, 66, 66, 66, 66, 65, 66, 63, 66, 64, 66, 66, 66, 66, 66,
66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66,
65, 66, 66),
dtype=np.int64)
ref_altitudes = np.asarray(
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1,
1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, -2, 0, 3, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 3, 1,
0),
dtype=np.int32)
self.assertTrue(np.all(tree.parents() == ref_parents))
self.assertTrue(np.all(altitudes == ref_altitudes))
def test_tree_of_shapes_padding_0_original_space(self):
image = np.asarray(((1, 1, 1),
(1, -2, 3)), dtype=np.int32)
tree, altitudes = hg.component_tree_tree_of_shapes_image2d(image, 'zero', True)
ref_parents = np.asarray((7, 7, 7,
7, 8, 6,
7, 9, 9, 9), dtype=np.int64)
ref_altitudes = np.asarray((1, 1, 1,
1, -2, 3,
3, 1, -2, 0), dtype=np.int32)
self.assertTrue(np.all(tree.parents() == ref_parents))
self.assertTrue(np.all(altitudes == ref_altitudes))
leaf_graph = hg.CptHierarchy.get_leaf_graph(tree)
res_shape = hg.CptGridGraph.get_shape(leaf_graph)
self.assertTrue(len(res_shape) == 2)
self.assertTrue(res_shape[0] * res_shape[1] == tree.num_leaves())
self.assertTrue(res_shape[0] == image.shape[0])
self.assertTrue(res_shape[1] == image.shape[1])
def test_tree_of_shapes_no_padding(self):
image = np.asarray(((1, 1, 1, 1, 1, 1),
(1, 0, 0, 3, 3, 1),
(1, 0, 1, 1, 3, 1),
(1, 0, 0, 3, 3, 1),
(1, 1, 1, 1, 1, 1)), dtype=np.int8)
tree, altitudes = hg.component_tree_tree_of_shapes_image2d(image, 'none', False)
ref_parents = np.asarray((101, 101, 101, 101, 101, 101, 101, 101, 101, 101, 101,
101, 101, 101, 101, 101, 101, 101, 101, 101, 101, 101,
101, 101, 100, 100, 100, 101, 99, 99, 99, 101, 101,
101, 101, 100, 101, 101, 101, 101, 101, 99, 101, 101,
101, 101, 100, 101, 101, 101, 101, 101, 99, 101, 101,
101, 101, 100, 101, 101, 101, 101, 101, 99, 101, 101,
101, 101, 100, 100, 100, 101, 99, 99, 99, 101, 101,
101, 101, 101, 101, 101, 101, 101, 101, 101, 101, 101,
101, 101, 101, 101, 101, 101, 101, 101, 101, 101, 101,
101, 101, 101), dtype=np.int64)
ref_altitudes = np.asarray((1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 0, 0, 0, 1, 3, 3, 3, 1, 1,
1, 1, 0, 1, 1, 1, 1, 1, 3, 1, 1,
1, 1, 0, 1, 1, 1, 1, 1, 3, 1, 1,
1, 1, 0, 1, 1, 1, 1, 1, 3, 1, 1,
1, 1, 0, 0, 0, 1, 3, 3, 3, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
3, 0, 1), dtype=np.int8)
self.assertTrue(np.all(tree.parents() == ref_parents))
self.assertTrue(np.all(altitudes == ref_altitudes))
leaf_graph = hg.CptHierarchy.get_leaf_graph(tree)
res_shape = hg.CptGridGraph.get_shape(leaf_graph)
self.assertTrue(len(res_shape) == 2)
self.assertTrue(res_shape[0] * res_shape[1] == tree.num_leaves())
self.assertTrue(res_shape[0] == image.shape[0] * 2 - 1)
self.assertTrue(res_shape[1] == image.shape[1] * 2 - 1)
def component_tree_multivariate_tree_of_shapes_image2d(image,
padding='mean',
original_size=True,
immersion=True):
"""
Multivariate tree of shapes for a 2d multi-band image. This tree is defined as a fusion of the marginal
trees of shapes. The method is described in:
E. Carlinet.
`A Tree of shapes for multivariate images <https://pastel.archives-ouvertes.fr/tel-01280131/file/TH2015PESC1118.pdf>`_.
PhD Thesis, Université Paris-Est, 2015.
The input :attr:`image` must be a 3d array of shape :math:`(height, width, channel)`.
Note that the constructed hierarchy doesn't have natural altitudes associated to its node: as a node is generally
a fusion of several marginal nodes, we can't associate a single canonical value from the original image to this node.
The parameters :attr:`padding`, :attr:`original_size`, and :attr:`immersion` are forwarded to the function
:func:`~higra.component_tree_tree_of_shapes_image2d`: please look at this function documentation for more details.
:Complexity:
The worst case runtime complexity of this method is :math:`\mathcal{O}(N^2D^2)` with :math:`N` the number of pixels
and :math:`D` the number of bands. If the image pixel values are quantized on :math:`K<<N` different values
(eg. with a color image in :math:`[0..255]^D`), then the worst case runtime complexity can be tightened to
:math:`\mathcal{O}(NKD^2)`.
:See:
This function relies on :func:`~higra.tree_fusion_depth_map` to compute the fusion of the marinal trees.
:param image: input *color* 2d image
:param padding: possible values are `'none'`, `'zero'`, and `'mean'` (default = `'mean'`)
:param original_size: remove all nodes corresponding to interpolated/padded pixels (default = `True`)
:param immersion: performs a plain map continuous immersion fo the original image (default = `True`)
:return: a tree (Concept :class:`~higra.CptHierarchy`)
"""
assert len(
image.shape
) == 3, "This multivariate tree of shapes implementation only supports multichannel 2d images."
ndim = image.shape[2]
trees = tuple(
hg.component_tree_tree_of_shapes_image2d(
image[:, :,
k], padding, original_size=False, immersion=immersion)[0]
for k in range(ndim))
g = hg.CptHierarchy.get_leaf_graph(trees[0])
shape = hg.CptGridGraph.get_shape(g)
depth_map = hg.tree_fusion_depth_map(trees)
tree, altitudes = hg.component_tree_tree_of_shapes_image2d(
np.reshape(depth_map, shape),
padding="none",
original_size=False,
immersion=False)
if original_size and (immersion or padding != "none"):
deleted_vertices = np.ones((tree.num_leaves(), ), dtype=np.bool)
deleted = np.reshape(deleted_vertices, shape)
if immersion:
if padding != "none":
deleted[2:-2:2, 2:-2:2] = False
else:
deleted[0::2, 0::2] = False
else:
if padding != "none":
deleted[1:-1, 1::-1] = False
all_deleted = hg.accumulate_sequential(tree, deleted_vertices,
hg.Accumulators.min)
shape = (image.shape[0], image.shape[1])
else:
all_deleted = np.zeros((tree.num_vertices(), ), dtype=np.bool)
holes = altitudes < altitudes[tree.parents()]
all_deleted = np.logical_or(all_deleted, holes)
tree, _ = hg.simplify_tree(tree, all_deleted, process_leaves=True)
g = hg.get_4_adjacency_graph(shape)
hg.CptHierarchy.link(tree, g)
return tree
