def find_edges_to_link(mesh,
vert_ind_a,
vert_ind_b,
distance_upper_bound=2500,
verbose=False):
'''Given a mesh and two points on that mesh
find a way to add edges to the mesh graph so that those indices
are on the same connected component
Parameters
----------
mesh: trimesh_io.Mesh
a mesh to find edges on
vert_ind_a: int
one index into mesh.vertices, the first point
vert_ind_b: int
a second index into mesh.vertices, the second point
distance_upper_bound: float
a maximum distance to (default 2500 in units of mesh.vertices)
verbose: bool
whether to print debug info
Returns
-------
np.array
a Kx2 array of mesh indices that represent edges to add to the mesh to link the two points
in a way that creates the shortest path between the points across mututally closest vertices
from connected components.. not adding edges if they are larger than distance_upper_bound
TODO: distance_upper_bound not presently implemented
'''
timings = {}
start_time = time.time()
# find the distance between the merge points and their center
d = np.linalg.norm(mesh.vertices[vert_ind_a, :] -
mesh.vertices[vert_ind_b, :])
c = np.mean(mesh.vertices[[vert_ind_a, vert_ind_b], :], axis=0)
# cut down the mesh to only include mesh vertices near the center of this
# merge edge and within 2x the euclidean length of the edge
inds = mesh.kdtree.query_ball_point(c, d * 2)
# convert this to a mask
mask = np.zeros(len(mesh.vertices), dtype=np.bool)
mask[inds] = True
timings['create_mask'] = time.time() - start_time
start_time = time.time()
# create a masked version of the mesh
mask_mesh = mesh.apply_mask(mask)
timings['apply_mask'] = time.time() - start_time
start_time = time.time()
ccs, labels = sparse.csgraph.connected_components(mask_mesh.csgraph,
return_labels=True)
# map the original indices into this masked space
mask_inds = mask_mesh.filter_unmasked_indices(
np.array([vert_ind_a, vert_ind_b]))
timings['masked_ccs'] = time.time() - start_time
start_time = time.time()
# find all the multually closest edges between the linked components
new_edges = find_close_edges_sym(mask_mesh.vertices, labels,
labels[mask_inds[0]],
labels[mask_inds[1]])
timings['find_close_edges_sym'] = time.time() - start_time
start_time = time.time()
# if there is now way to do this, fall back to adding all
# edges that are close
if len(new_edges) == 0:
if verbose:
print('finding all close edges')
new_edges = find_all_close_edges(mask_mesh.vertices, labels, ccs)
if verbose:
print(f'new_edges shape {new_edges.shape}')
# if there are still not edges we have a problem
if len(new_edges) == 0:
raise Exception('no close edges found')
# create a new mesh that has these added edges
#new_mesh = make_new_mesh_with_added_edges(mask_mesh, new_edges)
total_edges = np.vstack([mask_mesh.graph_edges, new_edges])
graph = utils.create_csgraph(mask_mesh.vertices, total_edges)
timings['make_new_mesh'] = time.time() - start_time
start_time = time.time()
# find the shortest path to one of the linking spots in this new mesh
d_ais_to_all, pred = sparse.csgraph.dijkstra(graph,
indices=mask_inds[0],
unweighted=False,
directed=False,
return_predecessors=True)
timings['find_close_edges_sym'] = time.time() - start_time
start_time = time.time()
# make sure we found a good path
if np.isinf(d_ais_to_all[mask_inds[1]]):
raise Exception(
f"cannot find link between {vert_ind_a} and {vert_ind_b}")
# turn this path back into a original mesh index edge list
path = utils.get_path(mask_inds[0], mask_inds[1], pred)
path_as_edges = utils.paths_to_edges([path])
good_edges = np_shared_rows(path_as_edges, new_edges)
good_edges = np.sort(path_as_edges[good_edges], axis=1)
timings['remap answers'] = time.time() - start_time
if verbose:
print(timings)
return mask_mesh.map_indices_to_unmasked(good_edges)
def mesh_teasar(mesh,
root=None,
valid=None,
root_ds=None,
root_pred=None,
soma_pt=None,
soma_thresh=7500,
invalidation_d=10000,
return_timing=False,
return_map=False):
"""core skeletonization function used to skeletonize a single component of a mesh"""
# if no root passed, then calculation one
if root is None:
root, root_ds, root_pred, valid = setup_root(mesh,
soma_pt=soma_pt,
soma_thresh=soma_thresh)
# if root_ds have not be precalculated do so
if root_ds is None:
root_ds, root_pred = sparse.csgraph.dijkstra(mesh.csgraph,
False,
root,
return_predecessors=True)
# if certain vertices haven't been pre-invalidated start with just
# the root vertex invalidated
if valid is None:
valid = np.ones(len(mesh.vertices), np.bool)
valid[root] = False
else:
if (len(valid) != len(mesh.vertices)):
raise Exception("valid must be length of vertices")
if return_map == True:
mesh_to_skeleton_dist = np.full(len(mesh.vertices), np.inf)
mesh_to_skeleton_map = np.full(len(mesh.vertices), np.nan)
total_to_visit = np.sum(valid)
if np.sum(np.isinf(root_ds) & valid) != 0:
print(np.where(np.isinf(root_ds) & valid))
raise Exception("all valid vertices should be reachable from root")
# vector to store each branch result
paths = []
# vector to store each path's total length
path_lengths = []
# keep track of the nodes that have been visited
visited_nodes = [root]
# counter to track how many branches have been counted
k = 0
# arrays to track timing
start = time.time()
time_arrays = [[], [], [], [], []]
with tqdm(total=total_to_visit) as pbar:
# keep looping till all vertices have been invalidated
while (np.sum(valid) > 0):
k += 1
t = time.time()
# find the next target, farthest vertex from root
# that has not been invalidated
target = np.nanargmax(root_ds * valid)
if (np.isinf(root_ds[target])):
raise Exception('target cannot be reached')
time_arrays[0].append(time.time() - t)
t = time.time()
# figure out the longest this branch could be
# by following the route from target to the root
# and finding the first already visited node (max_branch)
# The dist(root->target) - dist(root->max_branch)
# is the maximum distance the shortest route to a branch
# point from the target could possibly be,
# use this bound to reduce the djisktra search radius for this target
max_branch = target
while max_branch not in visited_nodes:
max_branch = root_pred[max_branch]
max_path_length = root_ds[target] - root_ds[max_branch]
# calculate the shortest path to that vertex
# from all other vertices
# up till the distance to the root
ds, pred_t = sparse.csgraph.dijkstra(mesh.csgraph,
False,
target,
limit=max_path_length,
return_predecessors=True)
# pick out the vertex that has already been visited
# which has the shortest path to target
min_node = np.argmin(ds[visited_nodes])
# reindex to get its absolute index
branch = visited_nodes[min_node]
# this is in the index of the point on the skeleton
# we want this branch to connect to
time_arrays[1].append(time.time() - t)
t = time.time()
# get the path from the target to branch point
path = utils.get_path(target, branch, pred_t)
visited_nodes += path[0:-1]
# record its length
assert (~np.isinf(ds[branch]))
path_lengths.append(ds[branch])
# record the path
paths.append(path)
time_arrays[2].append(time.time() - t)
t = time.time()
# get the distance to all points along the new path
# within the invalidation distance
dm, _, sources = sparse.csgraph.dijkstra(mesh.csgraph,
False,
path,
limit=invalidation_d,
min_only=True,
return_predecessors=True)
time_arrays[3].append(time.time() - t)
t = time.time()
# all such non infinite distances are within the invalidation
# zone and should be marked invalid
nodes_to_update = ~np.isinf(dm)
marked = np.sum(valid & ~np.isinf(dm))
if return_map == True:
new_sources_closer = dm[
nodes_to_update] < mesh_to_skeleton_dist[nodes_to_update]
mesh_to_skeleton_map[nodes_to_update] = np.where(
new_sources_closer, sources[nodes_to_update],
mesh_to_skeleton_map[nodes_to_update])
mesh_to_skeleton_dist[nodes_to_update] = np.where(
new_sources_closer, dm[nodes_to_update],
mesh_to_skeleton_dist[nodes_to_update])
valid[~np.isinf(dm)] = False
# print out how many vertices are still valid
pbar.update(marked)
time_arrays[4].append(time.time() - t)
# record the total time
dt = time.time() - start
out_tuple = (paths, path_lengths)
if return_map:
out_tuple = out_tuple + (mesh_to_skeleton_map, )
if return_timing:
out_tuple = out_tuple + (time_arrays, dt)
return out_tuple