def make_neuron_graph(self, skeleton, skeleton_labels,
trunks, branchpoints, endpoints, image):
'''Make a table that captures the graph relationship of the skeleton
skeleton - binary skeleton image + outline of seed objects
skeleton_labels - labels matrix of skeleton
trunks - binary image with trunk points as 1
branchpoints - binary image with branchpoints as 1
endpoints - binary image with endpoints as 1
image - image for intensity measurement
returns two tables.
Table 1: edge table
The edge table is a numpy record array with the following named
columns in the following order:
v1: index into vertex table of first vertex of edge
v2: index into vertex table of second vertex of edge
length: # of intermediate pixels + 2 (for two vertices)
total_intensity: sum of intensities along the edge
Table 2: vertex table
The vertex table is a numpy record array:
i: I coordinate of the vertex
j: J coordinate of the vertex
label: the vertex's label
kind: kind of vertex = "T" for trunk, "B" for branchpoint or "E" for endpoint.
'''
i, j = np.mgrid[0:skeleton.shape[0], 0:skeleton.shape[1]]
#
# Give each point of interest a unique number
#
points_of_interest = trunks | branchpoints | endpoints
number_of_points = np.sum(points_of_interest)
#
# Make up the vertex table
#
tbe = np.zeros(points_of_interest.shape, '|S1')
tbe[trunks] = 'T'
tbe[branchpoints] = 'B'
tbe[endpoints] = 'E'
i_idx = i[points_of_interest]
j_idx = j[points_of_interest]
poe_labels = skeleton_labels[points_of_interest]
tbe = tbe[points_of_interest]
vertex_table = {
self.VF_I: i_idx,
self.VF_J: j_idx,
self.VF_LABELS: poe_labels,
self.VF_KIND: tbe}
#
# First, break the skeleton by removing the branchpoints, endpoints
# and trunks
#
broken_skeleton = skeleton & (~points_of_interest)
#
# Label the broken skeleton: this labels each edge differently
#
edge_labels, nlabels = morph.label_skeleton(skeleton)
#
# Reindex after removing the points of interest
#
edge_labels[points_of_interest] = 0
if nlabels > 0:
indexer = np.arange(nlabels + 1)
unique_labels = np.sort(np.unique(edge_labels))
nlabels = len(unique_labels) - 1
indexer[unique_labels] = np.arange(len(unique_labels))
edge_labels = indexer[edge_labels]
#
# find magnitudes and lengths for all edges
#
magnitudes = fix(scind.sum(image, edge_labels, np.arange(1, nlabels + 1, dtype=np.int32)))
lengths = fix(scind.sum(np.ones(edge_labels.shape),
edge_labels, np.arange(1, nlabels + 1, dtype=np.int32))).astype(int)
else:
magnitudes = np.zeros(0)
lengths = np.zeros(0, int)
#
# combine the edge labels and indexes of points of interest with padding
#
edge_mask = edge_labels != 0
all_labels = np.zeros(np.array(edge_labels.shape) + 2, int)
all_labels[1:-1, 1:-1][edge_mask] = edge_labels[edge_mask] + number_of_points
all_labels[i_idx + 1, j_idx + 1] = np.arange(1, number_of_points + 1)
#
# Collect all 8 neighbors for each point of interest
#
p1 = np.zeros(0, int)
p2 = np.zeros(0, int)
for i_off, j_off in ((0, 0), (0, 1), (0, 2),
(1, 0), (1, 2),
(2, 0), (2, 1), (2, 2)):
p1 = np.hstack((p1, np.arange(1, number_of_points + 1)))
p2 = np.hstack((p2, all_labels[i_idx + i_off, j_idx + j_off]))
#
# Get rid of zeros which are background
#
p1 = p1[p2 != 0]
p2 = p2[p2 != 0]
#
# Find point_of_interest -> point_of_interest connections.
#
p1_poi = p1[(p2 <= number_of_points) & (p1 < p2)]
p2_poi = p2[(p2 <= number_of_points) & (p1 < p2)]
#
# Make sure matches are labeled the same
#
same_labels = (skeleton_labels[i_idx[p1_poi - 1], j_idx[p1_poi - 1]] ==
skeleton_labels[i_idx[p2_poi - 1], j_idx[p2_poi - 1]])
p1_poi = p1_poi[same_labels]
p2_poi = p2_poi[same_labels]
#
# Find point_of_interest -> edge
#
p1_edge = p1[p2 > number_of_points]
edge = p2[p2 > number_of_points]
#
# Now, each value that p2_edge takes forms a group and all
# p1_edge whose p2_edge are connected together by the edge.
# Possibly they touch each other without the edge, but we will
# take the minimum distance connecting each pair to throw out
# the edge.
#
edge, p1_edge, p2_edge = morph.pairwise_permutations(edge, p1_edge)
indexer = edge - number_of_points - 1
lengths = lengths[indexer]
magnitudes = magnitudes[indexer]
#
# OK, now we make the edge table. First poi<->poi. Length = 2,
# magnitude = magnitude at each point
#
poi_length = np.ones(len(p1_poi)) * 2
poi_magnitude = (image[i_idx[p1_poi - 1], j_idx[p1_poi - 1]] +
image[i_idx[p2_poi - 1], j_idx[p2_poi - 1]])
#
# Now the edges...
#
poi_edge_length = lengths + 2
poi_edge_magnitude = (image[i_idx[p1_edge - 1], j_idx[p1_edge - 1]] +
image[i_idx[p2_edge - 1], j_idx[p2_edge - 1]] +
magnitudes)
#
# Put together the columns
#
v1 = np.hstack((p1_poi, p1_edge))
v2 = np.hstack((p2_poi, p2_edge))
lengths = np.hstack((poi_length, poi_edge_length))
magnitudes = np.hstack((poi_magnitude, poi_edge_magnitude))
#
# Sort by p1, p2 and length in order to pick the shortest length
#
indexer = np.lexsort((lengths, v1, v2))
v1 = v1[indexer]
v2 = v2[indexer]
lengths = lengths[indexer]
magnitudes = magnitudes[indexer]
if len(v1) > 0:
to_keep = np.hstack(([True],
(v1[1:] != v1[:-1]) |
(v2[1:] != v2[:-1])))
v1 = v1[to_keep]
v2 = v2[to_keep]
lengths = lengths[to_keep]
magnitudes = magnitudes[to_keep]
#
# Put it all together into a table
#
edge_table = {
self.EF_V1: v1,
self.EF_V2: v2,
self.EF_LENGTH: lengths,
self.EF_TOTAL_INTENSITY: magnitudes
}
return edge_table, vertex_table
def make_objskeleton_graph(self, skeleton, skeleton_labels, trunks,
branchpoints, endpoints, image):
'''Make a table that captures the graph relationship of the skeleton
skeleton - binary skeleton image + outline of seed objects
skeleton_labels - labels matrix of skeleton
trunks - binary image with trunk points as 1
branchpoints - binary image with branchpoints as 1
endpoints - binary image with endpoints as 1
image - image for intensity measurement
returns two tables.
Table 1: edge table
The edge table is a numpy record array with the following named
columns in the following order:
v1: index into vertex table of first vertex of edge
v2: index into vertex table of second vertex of edge
length: # of intermediate pixels + 2 (for two vertices)
total_intensity: sum of intensities along the edge
Table 2: vertex table
The vertex table is a numpy record array:
i: I coordinate of the vertex
j: J coordinate of the vertex
label: the vertex's label
kind: kind of vertex = "T" for trunk, "B" for branchpoint or "E" for endpoint.
'''
i, j = np.mgrid[0:skeleton.shape[0], 0:skeleton.shape[1]]
#
# Give each point of interest a unique number
#
points_of_interest = trunks | branchpoints | endpoints
number_of_points = np.sum(points_of_interest)
#
# Make up the vertex table
#
tbe = np.zeros(points_of_interest.shape, '|S1')
tbe[trunks] = 'T'
tbe[branchpoints] = 'B'
tbe[endpoints] = 'E'
i_idx = i[points_of_interest]
j_idx = j[points_of_interest]
poe_labels = skeleton_labels[points_of_interest]
tbe = tbe[points_of_interest]
vertex_table = {
self.VF_I: i_idx,
self.VF_J: j_idx,
self.VF_LABELS: poe_labels,
self.VF_KIND: tbe
}
#
# First, break the skeleton by removing the branchpoints, endpoints
# and trunks
#
broken_skeleton = skeleton & (~points_of_interest)
#
# Label the broken skeleton: this labels each edge differently
#
edge_labels, nlabels = morph.label_skeleton(skeleton)
#
# Reindex after removing the points of interest
#
edge_labels[points_of_interest] = 0
if nlabels > 0:
indexer = np.arange(nlabels + 1)
unique_labels = np.sort(np.unique(edge_labels))
nlabels = len(unique_labels) - 1
indexer[unique_labels] = np.arange(len(unique_labels))
edge_labels = indexer[edge_labels]
#
# find magnitudes and lengths for all edges
#
magnitudes = fix(
scind.sum(image, edge_labels,
np.arange(1, nlabels + 1, dtype=np.int32)))
lengths = fix(
scind.sum(np.ones(edge_labels.shape), edge_labels,
np.arange(1, nlabels + 1,
dtype=np.int32))).astype(int)
else:
magnitudes = np.zeros(0)
lengths = np.zeros(0, int)
#
# combine the edge labels and indexes of points of interest with padding
#
edge_mask = edge_labels != 0
all_labels = np.zeros(np.array(edge_labels.shape) + 2, int)
all_labels[1:-1,
1:-1][edge_mask] = edge_labels[edge_mask] + number_of_points
all_labels[i_idx + 1, j_idx + 1] = np.arange(1, number_of_points + 1)
#
# Collect all 8 neighbors for each point of interest
#
p1 = np.zeros(0, int)
p2 = np.zeros(0, int)
for i_off, j_off in ((0, 0), (0, 1), (0, 2), (1, 0), (1, 2), (2, 0),
(2, 1), (2, 2)):
p1 = np.hstack((p1, np.arange(1, number_of_points + 1)))
p2 = np.hstack((p2, all_labels[i_idx + i_off, j_idx + j_off]))
#
# Get rid of zeros which are background
#
p1 = p1[p2 != 0]
p2 = p2[p2 != 0]
#
# Find point_of_interest -> point_of_interest connections.
#
p1_poi = p1[(p2 <= number_of_points) & (p1 < p2)]
p2_poi = p2[(p2 <= number_of_points) & (p1 < p2)]
#
# Make sure matches are labeled the same
#
same_labels = (
skeleton_labels[i_idx[p1_poi - 1],
j_idx[p1_poi -
1]] == skeleton_labels[i_idx[p2_poi - 1],
j_idx[p2_poi - 1]])
p1_poi = p1_poi[same_labels]
p2_poi = p2_poi[same_labels]
#
# Find point_of_interest -> edge
#
p1_edge = p1[p2 > number_of_points]
edge = p2[p2 > number_of_points]
#
# Now, each value that p2_edge takes forms a group and all
# p1_edge whose p2_edge are connected together by the edge.
# Possibly they touch each other without the edge, but we will
# take the minimum distance connecting each pair to throw out
# the edge.
#
edge, p1_edge, p2_edge = morph.pairwise_permutations(edge, p1_edge)
indexer = edge - number_of_points - 1
lengths = lengths[indexer]
magnitudes = magnitudes[indexer]
#
# OK, now we make the edge table. First poi<->poi. Length = 2,
# magnitude = magnitude at each point
#
poi_length = np.ones(len(p1_poi)) * 2
poi_magnitude = (image[i_idx[p1_poi - 1], j_idx[p1_poi - 1]] +
image[i_idx[p2_poi - 1], j_idx[p2_poi - 1]])
#
# Now the edges...
#
poi_edge_length = lengths + 2
poi_edge_magnitude = (image[i_idx[p1_edge - 1], j_idx[p1_edge - 1]] +
image[i_idx[p2_edge - 1], j_idx[p2_edge - 1]] +
magnitudes)
#
# Put together the columns
#
v1 = np.hstack((p1_poi, p1_edge))
v2 = np.hstack((p2_poi, p2_edge))
lengths = np.hstack((poi_length, poi_edge_length))
magnitudes = np.hstack((poi_magnitude, poi_edge_magnitude))
#
# Sort by p1, p2 and length in order to pick the shortest length
#
indexer = np.lexsort((lengths, v1, v2))
v1 = v1[indexer]
v2 = v2[indexer]
lengths = lengths[indexer]
magnitudes = magnitudes[indexer]
if len(v1) > 0:
to_keep = np.hstack(
([True], (v1[1:] != v1[:-1]) | (v2[1:] != v2[:-1])))
v1 = v1[to_keep]
v2 = v2[to_keep]
lengths = lengths[to_keep]
magnitudes = magnitudes[to_keep]
#
# Put it all together into a table
#
edge_table = {
self.EF_V1: v1,
self.EF_V2: v2,
self.EF_LENGTH: lengths,
self.EF_TOTAL_INTENSITY: magnitudes
}
return edge_table, vertex_table