def octahedron_tetrahedra(side_length=15.):
points = {}
points[2] = np.array([1, 0, 0]) + 0.1 * np.random.rand(3)
points[3] = np.array([0, 1, 0]) + 0.1 * np.random.rand(3)
points[4] = np.array([-1, 0, 0]) + 0.1 * np.random.rand(3)
points[5] = np.array([0, -1, 0]) + 0.1 * np.random.rand(3)
points[6] = np.array([0, 0, 1]) + 0.1 * np.random.rand(3)
points[7] = np.array([0, 0, -1]) + 0.1 * np.random.rand(3)
tetrahedra = []
tetrahedra += [[2, 3, 4, 6]]
tetrahedra += [[2, 4, 5, 6]]
tetrahedra += [[2, 3, 4, 7]]
tetrahedra += [[2, 4, 5, 7]]
return tetrahedra_topomesh(tetrahedra, points)
def octahedron_tetrahedra(side_length=15.):
points = {}
points[2] = np.array([1,0,0]) + 0.1*np.random.rand(3)
points[3] = np.array([0,1,0]) + 0.1*np.random.rand(3)
points[4] = np.array([-1,0,0]) + 0.1*np.random.rand(3)
points[5] = np.array([0,-1,0]) + 0.1*np.random.rand(3)
points[6] = np.array([0,0,1]) + 0.1*np.random.rand(3)
points[7] = np.array([0,0,-1]) + 0.1*np.random.rand(3)
tetrahedra = []
tetrahedra += [[2,3,4,6]]
tetrahedra += [[2,4,5,6]]
tetrahedra += [[2,3,4,7]]
tetrahedra += [[2,4,5,7]]
return tetrahedra_topomesh(tetrahedra,points)
def compute_image_adjacency(self):
"""Compute the adjacency relationships between cells in the tissue image.
By default, the DRACO adjacency complex is set to the cell_vertices tetrahedra (!!NOT A VALID CELL COMPLEX!!)
!!STRONG RISK OF TOPOLOGICAL ERRORS IF DUALIZING AT THIS STAGE!!
Updates:
image_graph (PropertyGraph): adjacency graph connecting adjacent cells by edges
image_cell_vertex (dict): cell vertices representing 4 co-adjacent cells by the point where they meet
cell_layer (int): information whether the cell belong to the first layer of cells (L1), the second one (L2) or lower layers (0)
layer_edge_topomesh (PropertyTopomesh): adjacency graphs restricted to the L1 and L2 layers
layer_triangle_topomesh (PropertyTopomesh): adjacency triangles between L1 and L2 layers (**TO BE COMPLETED**)
triangulation_topomesh (PropertyTopomesh): the tetrahedra representing adjacencies between cells
Returns:
None
"""
self.image_graph = graph_from_image(
self.segmented_image,
spatio_temporal_properties=["volume", "barycenter", "L1"],
ignore_cells_at_stack_margins=False,
property_as_real=True,
)
self.image_labels = np.array(list(self.image_graph.vertices()))
self.image_cell_volumes = array_dict(
[self.image_graph.vertex_property("volume")[v] for v in self.image_labels], self.image_labels
)
img_center = np.nanmean(self.image_graph.vertex_property("barycenter").values(), axis=0)
self.positions = array_dict(self.image_graph.vertex_property("barycenter"))
self.point_topomesh = vertex_topomesh(self.positions)
img_analysis = SpatialImageAnalysis(self.segmented_image)
exterior_cells = np.array(list(img_analysis.neighbors(1)))
self.image_wall_surfaces = img_analysis.wall_areas(real=True)
self.image_graph.add_vertex(1)
for c in exterior_cells:
self.image_graph.add_edge(1, c)
for v in self.image_cell_vertex.keys():
self.image_cell_vertex[v] = self.image_cell_vertex[v] * self.resolution
image_cell_vertex_tetrahedra = np.sort(self.image_cell_vertex.keys())
image_cell_vertex_tetrahedra = np.delete(
image_cell_vertex_tetrahedra, np.where(image_cell_vertex_tetrahedra[:, 0] == 1)[0], axis=0
)
self.image_cell_vertex_topomesh = tetrahedra_topomesh(image_cell_vertex_tetrahedra, self.positions)
self.triangulation_topomesh = deepcopy(self.image_cell_vertex_topomesh)
truncated_image = self.segmented_image[:, :, :]
truncated_image_graph = graph_from_image(
truncated_image,
spatio_temporal_properties=["barycenter", "L1"],
background=1,
ignore_cells_at_stack_margins=True,
property_as_real=True,
)
self.cell_layer = array_dict(np.zeros_like(self.positions.keys()), self.positions.keys())
for c in truncated_image_graph.vertices():
if c > 1 and truncated_image_graph.vertex_property("L1")[c]:
self.cell_layer[c] = 1
for c in self.cell_layer.keys():
if c > 1 and self.cell_layer[c] == 1:
for n in truncated_image_graph.neighbors(c):
if n > 1 and self.cell_layer[n] != 1:
self.cell_layer[n] = 2
self.point_topomesh.update_wisp_property(
"layer", 0, self.cell_layer.values(list(self.point_topomesh.wisps(0))), list(self.point_topomesh.wisps(0))
)
self.layer_edge_topomesh = {}
if (self.cell_layer.values() == 1).sum() > 1:
L1_edges = np.array(
[
[(c, n) for n in self.image_graph.neighbors(c) if n > 1 and self.cell_layer[n] == 1]
for c in self.cell_layer.keys()
if self.cell_layer[c] == 1
]
)
L1_edges = np.concatenate([e for e in L1_edges if len(e) > 0])
L1_edges = L1_edges[L1_edges[:, 1] > L1_edges[:, 0]]
L1_edge_topomesh = edge_topomesh(L1_edges, self.positions)
self.layer_edge_topomesh["L1"] = L1_edge_topomesh
if (self.cell_layer.values() == 2).sum() > 1:
L2_edges = np.array(
[
[(c, n) for n in self.image_graph.neighbors(c) if n > 1 and self.cell_layer[n] == 2]
for c in self.cell_layer.keys()
if self.cell_layer[c] == 2
]
)
L2_edges = np.concatenate([e for e in L2_edges if len(e) > 0])
L2_edges = L2_edges[L2_edges[:, 1] > L2_edges[:, 0]]
L2_edge_topomesh = edge_topomesh(L2_edges, self.positions)
self.layer_edge_topomesh["L2"] = L2_edge_topomesh
self.layer_triangle_topomesh = {}
if (self.cell_layer.values() == 1).sum() > 1 and (self.cell_layer.values() == 2).sum() > 1:
L1_L2_edges = np.array(
[
[(c, n) for n in self.image_graph.neighbors(c) if n > 1 and self.cell_layer[n] in [1, 2]]
for c in self.cell_layer.keys()
if self.cell_layer[c] in [1, 2]
]
)
L1_L2_edges = np.concatenate([e for e in L1_L2_edges if len(e) > 0])
L1_L2_edges = L1_L2_edges[L1_L2_edges[:, 1] > L1_L2_edges[:, 0]]
L1_L2_additional_edges = np.array(
[
[
(c, n)
for n in np.unique(
np.array(self.image_cell_vertex.keys())[
np.where(np.array(self.image_cell_vertex.keys()) == c)[0]
]
)
if n > 1
and n != c
and (n not in self.image_graph.neighbors(c))
and (self.cell_layer[n] in [1, 2])
]
for c in self.cell_layer.keys()
if self.cell_layer[c] in [1, 2]
]
)
L1_L2_additional_edges = np.concatenate([e for e in L1_L2_additional_edges if len(e) > 0])
L1_L2_additional_edges = L1_L2_additional_edges[L1_L2_additional_edges[:, 1] > L1_L2_additional_edges[:, 0]]
self.layer_triangle_topomesh["L1_L2"] = triangle_topomesh(
triangles_from_adjacency_edges(np.concatenate([L1_L2_edges, L1_L2_additional_edges])), self.positions
)
