def labelisation_seeded_watershed(graph, edge_weights, vertex_seeds):
"""
Seeded watershed cut on an edge weighted graph.
Seeds are defined as vertex weights: any flat zone of value strictly greater than 0 is considered as a seed.
Note that if two different seeds are places in a minima of the edge weighted graph, and if the altitude of this minima
is equal to the smallest representable value for the given `dtype` of the edge weights, then the algorithm won't be able
to produce two different regions for these two seeds.
:param graph: input graph
:param edge_weights: Weights on the edges of the graph
:param vertex_seeds: Seeds on the vertices of the graph
:return: A labelisation of the graph vertices
"""
# edges inside a seed take the value of the seed and 0 otherwise
edges_in_or_between_seeds = hg.weight_graph(graph, vertex_seeds,
hg.WeightFunction.L0)
edges_outside_seeds = hg.weight_graph(graph, vertex_seeds,
hg.WeightFunction.min)
edges_in_seed = np.logical_and(edges_outside_seeds > 0,
1 - edges_in_or_between_seeds)
# set edges inside seeds at minimum level
edge_weights = edge_weights.copy()
edge_weights[edges_in_seed > 0] = hg.dtype_info(edge_weights.dtype).min
tree, altitudes = hg.watershed_hierarchy_by_attribute(
graph, edge_weights, lambda tree, _: hg.accumulate_sequential(
tree, vertex_seeds, hg.Accumulators.max))
return hg.labelisation_hierarchy_supervertices(tree, altitudes)
def watershed_hierarchy_by_number_of_parents(graph, edge_weights):
"""
Watershed hierarchy by number of parents.
The definition of *number of parents* was proposed in:
B. Perret, J. Cousty, S. J. F. Guimarães and D. S. Maia,
`Evaluation of Hierarchical Watersheds <https://hal.archives-ouvertes.fr/hal-01430865/file/PCGM%20-%20TIP%202018%20-%20Evaluation%20of%20hierarchical%20watersheds.pdf>`_ ,
in IEEE Transactions on Image Processing, vol. 27, no. 4, pp. 1676-1688, April 2018.
doi: 10.1109/TIP.2017.2779604
The definition of hierarchical watershed follows the one given in:
J. Cousty, L. Najman.
`Incremental algorithm for hierarchical minimum spanning forests and saliency of watershed cuts <https://hal-upec-upem.archives-ouvertes.fr/hal-00622505/document>`_.
ISMM 2011: 272-283.
The algorithm used is described in:
Laurent Najman, Jean Cousty, Benjamin Perret.
`Playing with Kruskal: Algorithms for Morphological Trees in Edge-Weighted Graphs <https://hal.archives-ouvertes.fr/file/index/docid/798621/filename/ismm2013-algo.pdf>`_.
ISMM 2013: 135-146.
:param graph: input graph
:param edge_weights: edge weights of the input graph
:return: a tree (Concept :class:`~higra.CptHierarchy`) and its node altitudes
"""
def num_parents(bpt_tree, altitudes):
# construct quasi flat zone hierarchy from input bpt
tree, node_map = hg.simplify_tree(
bpt_tree, altitudes == altitudes[bpt_tree.parents()])
# determine inner nodes of the min tree, i.e. nodes of qfz having at least one node that is not a leaf
num_children = tree.num_children(np.arange(tree.num_vertices()))
num_children_leaf = np.zeros((tree.num_vertices(), ), dtype=np.int64)
np.add.at(num_children_leaf, tree.parents()[:tree.num_leaves()], 1)
inner_nodes = num_children != num_children_leaf
# go back into bpt space
inner_nodes_bpt = np.zeros((bpt_tree.num_vertices(), ), dtype=np.int64)
inner_nodes_bpt[node_map] = inner_nodes
inner_nodes = inner_nodes_bpt
# count number of min tree inner nodes in the subtree rooted in the given node
res = hg.accumulate_and_add_sequential(bpt_tree, inner_nodes,
inner_nodes[:tree.num_leaves()],
hg.Accumulators.sum)
# add 1 to avoid having a zero measure in a minima
res[bpt_tree.num_leaves():] = res[bpt_tree.num_leaves():] + 1
return res
return hg.watershed_hierarchy_by_attribute(graph, edge_weights,
num_parents)
def test_watershed_hierarchy_by_attribute(self):
g = hg.get_4_adjacency_graph((1, 19))
edge_weights = np.asarray(
(0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0))
# watershed hierarchy by area...
t, altitudes = hg.watershed_hierarchy_by_attribute(
g, edge_weights, lambda tree, _: hg.attribute_area(tree))
ref_parents = np.asarray(
(19, 19, 20, 20, 20, 21, 21, 21, 21, 21, 21, 22, 22, 22, 22, 22,
23, 23, 23, 24, 24, 25, 26, 26, 25, 27, 27, 27),
dtype=np.int64)
ref_tree = hg.Tree(ref_parents)
ref_altitudes = np.asarray((0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 3, 5))
self.assertTrue(hg.test_tree_isomorphism(t, ref_tree))
self.assertTrue(np.allclose(altitudes, ref_altitudes))