def segmentation(self):
self.K = TreeModel()
self.K_to_P = defaultdict(list) # ki -> list of (i, d)'s
self.P_to_K = {} # pi -> (ki, d)
self.level_to_graph = [None for _ in range(len(self.level_sets))]
self.level_to_segment_graphs = [None for _ in
range(len(self.level_sets))]
for level, points in self.level_sets.items():
N_level_inter = self.N.subgraph(points)
segment_nodes_list = nx.connected_components(N_level_inter)
self.level_to_graph[level] = N_level_inter
self.level_to_segment_graphs[level] = \
nx.connected_component_subgraphs(N_level_inter)
for segment_nodes in segment_nodes_list:
segment_centroid = harray(mean(self.P[[segment_nodes]], axis=0))
node = self.K.add_node(pos=segment_centroid,
points=set(segment_nodes), level=level)
max_dist = float('-inf')
avg_dist = 0
for j in segment_nodes:
d = dist(segment_centroid, self.P[j])
max_dist = max(max_dist, d)
avg_dist += d
self.K_to_P[node.id].append((j, d))
assert j not in self.P_to_K
self.P_to_K[j] = (node.id, d)
# initial radius estimation (can be refined with
# volume_reconstruction)
avg_dist /= len(segment_nodes)
node.radius = avg_dist
def compute_nearest_neighbors_in_radius(self, r):
start = time.time()
kdtree1 = KDTree(self.P)
kdtree2 = KDTree(self.P)
result = kdtree1.query_ball_tree(kdtree2, r)
self.N_full = nx.Graph()
for i, i_nns in enumerate(result):
for j in i_nns:
if i == j: continue
d = dist(self.P[i], self.P[j])
self.N_full.add_edge(i, j, weight=d)
print time.time() - start
print len(self.N_full.edges())
self.find_nn_connected_components()
def compute_nearest_neighbors_in_radius(self, r):
start = time.time()
kdtree1 = KDTree(self.P)
kdtree2 = KDTree(self.P)
result = kdtree1.query_ball_tree(kdtree2, r)
self.N_full = nx.Graph()
for i, i_nns in enumerate(result):
for j in i_nns:
if i == j: continue
d = dist(self.P[i], self.P[j])
self.N_full.add_edge(i, j, weight=d)
print time.time() - start
print len(self.N_full.edges())
self.find_nn_connected_components()
def segmentation(self):
self.K = TreeModel()
self.K_to_P = defaultdict(list) # ki -> list of (i, d)'s
self.P_to_K = {} # pi -> (ki, d)
self.level_to_graph = [None for _ in range(len(self.level_sets))]
self.level_to_segment_graphs = [
None for _ in range(len(self.level_sets))
]
for level, points in self.level_sets.items():
N_level_inter = self.N.subgraph(points)
segment_nodes_list = nx.connected_components(N_level_inter)
self.level_to_graph[level] = N_level_inter
self.level_to_segment_graphs[level] = \
nx.connected_component_subgraphs(N_level_inter)
for segment_nodes in segment_nodes_list:
segment_centroid = harray(mean(self.P[[segment_nodes]],
axis=0))
node = self.K.add_node(pos=segment_centroid,
points=set(segment_nodes),
level=level)
max_dist = float('-inf')
avg_dist = 0
for j in segment_nodes:
d = dist(segment_centroid, self.P[j])
max_dist = max(max_dist, d)
avg_dist += d
self.K_to_P[node.id].append((j, d))
assert j not in self.P_to_K
self.P_to_K[j] = (node.id, d)
# initial radius estimation (can be refined with
# volume_reconstruction)
avg_dist /= len(segment_nodes)
node.radius = avg_dist
def volume_reconstruction(self):
for ki in self.K:
if not self.K[ki].children:
kj = ki
while self.K[kj].parent is not None:
kj_start_points = self.level_start_points[self.K[kj].level] \
& self.K[kj].points
# if not, will use initial radius estimation (not good!)
if kj_start_points:
kj_to_parent_midpoint = mean(
(self.K[kj].pos, self.K[self.K[kj].parent].pos),
axis=0)
radius = 0
for pi in kj_start_points:
radius += dist(self.P[pi], kj_to_parent_midpoint)
radius /= len(kj_start_points)
self.K[kj].radius = radius
kj = self.K[kj].parent
# segment radius smoothing
roots = set()
for ki in self.K:
if not self.K[ki].children:
segment = {} # kj -> radius
kj = ki
while self.K[kj].parent is not None:
segment[kj] = self.K[kj].radius
if len(self.K[kj].children) > 1 or \
self.K[self.K[kj].parent].parent is None:
# flush segment
avg_segment_radius = sum(
segment.values()) / len(segment)
for kk in segment:
self.K[kk].radius = avg_segment_radius
segment = {}
kj = self.K[kj].parent
if self.K[ki].parent is None:
roots.add(ki)
# roots radius
#print 'roots: %s' % roots
for ki in roots:
#assert self.K[ki].get('radius', None) is None
rad = 0
for kj in self.K[ki].children:
rad += self.K[kj].radius
rad /= len(self.K[ki].children)
self.K[ki].radius = rad
# decreasing radius smoothing
need_smoothing = True
while need_smoothing:
need_smoothing = False
for ki in self.K:
if not self.K[ki].children:
kj = ki
prev_radius = None
while self.K[kj].parent is not None:
curr_radius = self.K[kj].radius
next_radius = self.K[self.K[kj].parent].radius
if curr_radius > next_radius:
need_smoothing = True
if prev_radius:
curr_radius = (prev_radius + next_radius) / 2
else:
curr_radius = next_radius
curr_radius -= (0.01 * curr_radius)
self.K[kj].radius = curr_radius
prev_radius = curr_radius
kj = self.K[kj].parent
def skeleton_reconstruction(self,
use_greedy_search=True,
extend_end_segments=True):
for k in self.K:
if self.K[k].level == 0: continue
potential_k_parents = [] # list of (dist, potential_k_parent)'s
found_k_parent = False
for i, dist_ki in self.K_to_P[k]:
# travel from k toward source, via one of its belonging paths
for j in self.shortest_paths[i][::-1]:
if j not in self.P_to_K: continue
l, dist_lj = self.P_to_K[j]
if self.K[l].level >= self.K[k].level: continue
dist_kl = dist(self.K[k].pos, self.K[l].pos)
cost = dist_ki + dist_kl + dist_lj
potential_k_parents.append((cost, l))
if use_greedy_search:
# for full search (takes really longer),
# comment out these two lines (not sure it
# makes sense though!)
found_k_parent = True
break
if found_k_parent:
break
#assert potential_k_parents
if not potential_k_parents:
print "warning: couldn't find a parent for skeleton node %s" % k
continue
k_parent = sorted(potential_k_parents)[0][1]
self.K[k].parent = k_parent
self.K[k_parent].children.add(k)
self.K.remove_orphan_nodes()
if extend_end_segments:
# more precise method, derived from:
# http://mathworld.wolfram.com/Point-LineDistance3-Dimensional.html
for k, node in self.K.items():
if not node.children:
# find point with max dist from source
p_max_dist = [float('-inf'), None]
for i in node.points:
if self.P_dist[i] > p_max_dist[0]:
p_max_dist[0] = self.P_dist[i]
p_max_dist[1] = i
p_max_dist = self.P[p_max_dist[1]]
x1 = self.K[node.parent].pos
x2 = node.pos
x0 = p_max_dist
s = -dot((x1 - x0), (x2 - x1)) / (linalg.norm(x2 - x1)**2)
v = x1 + (x2 - x1) * s
self.K[k].pos = v
if node.parent is None:
p_min_dist = [float('inf'),
None] # should be the src point?
for i in node.points:
if self.P_dist[i] < p_min_dist[0]:
p_min_dist[0] = self.P_dist[i]
p_min_dist[1] = i
p_min_dist = self.P[p_min_dist[1]]
first_child_k = list(node.children)[0]
x1 = self.K[first_child_k].pos
x2 = node.pos
x0 = p_min_dist
s = -dot((x1 - x0), (x2 - x1)) / (linalg.norm(x2 - x1)**2)
v = x1 + (x2 - x1) * s
self.K[k].pos = v
def volume_reconstruction(self):
for ki in self.K:
if not self.K[ki].children:
kj = ki
while self.K[kj].parent is not None:
kj_start_points = self.level_start_points[self.K[kj].level] \
& self.K[kj].points
# if not, will use initial radius estimation (not good!)
if kj_start_points:
kj_to_parent_midpoint = mean((self.K[kj].pos,
self.K[self.K[kj].parent].pos), axis=0)
radius = 0
for pi in kj_start_points:
radius += dist(self.P[pi], kj_to_parent_midpoint)
radius /= len(kj_start_points)
self.K[kj].radius = radius
kj = self.K[kj].parent
# segment radius smoothing
roots = set()
for ki in self.K:
if not self.K[ki].children:
segment = {} # kj -> radius
kj = ki
while self.K[kj].parent is not None:
segment[kj] = self.K[kj].radius
if len(self.K[kj].children) > 1 or \
self.K[self.K[kj].parent].parent is None:
# flush segment
avg_segment_radius = sum(segment.values()) / len(segment)
for kk in segment:
self.K[kk].radius = avg_segment_radius
segment = {}
kj = self.K[kj].parent
if self.K[ki].parent is None:
roots.add(ki)
# roots radius
#print 'roots: %s' % roots
for ki in roots:
#assert self.K[ki].get('radius', None) is None
rad = 0
for kj in self.K[ki].children:
rad += self.K[kj].radius
rad /= len(self.K[ki].children)
self.K[ki].radius = rad
# decreasing radius smoothing
need_smoothing = True
while need_smoothing:
need_smoothing = False
for ki in self.K:
if not self.K[ki].children:
kj = ki
prev_radius = None
while self.K[kj].parent is not None:
curr_radius = self.K[kj].radius
next_radius = self.K[self.K[kj].parent].radius
if curr_radius > next_radius:
need_smoothing = True
if prev_radius:
curr_radius = (prev_radius + next_radius) / 2
else:
curr_radius = next_radius
curr_radius -= (0.01 * curr_radius)
self.K[kj].radius = curr_radius
prev_radius = curr_radius
kj = self.K[kj].parent
def skeleton_reconstruction(self, use_greedy_search=True,
extend_end_segments=True):
for k in self.K:
if self.K[k].level == 0: continue
potential_k_parents = [] # list of (dist, potential_k_parent)'s
found_k_parent = False
for i, dist_ki in self.K_to_P[k]:
# travel from k toward source, via one of its belonging paths
for j in self.shortest_paths[i][::-1]:
if j not in self.P_to_K: continue
l, dist_lj = self.P_to_K[j]
if self.K[l].level >= self.K[k].level: continue
dist_kl = dist(self.K[k].pos, self.K[l].pos)
cost = dist_ki + dist_kl + dist_lj
potential_k_parents.append((cost, l))
if use_greedy_search:
# for full search (takes really longer),
# comment out these two lines (not sure it
# makes sense though!)
found_k_parent = True
break
if found_k_parent:
break
#assert potential_k_parents
if not potential_k_parents:
print "warning: couldn't find a parent for skeleton node %s" % k
continue
k_parent = sorted(potential_k_parents)[0][1]
self.K[k].parent = k_parent
self.K[k_parent].children.add(k)
self.K.remove_orphan_nodes()
if extend_end_segments:
# more precise method, derived from:
# http://mathworld.wolfram.com/Point-LineDistance3-Dimensional.html
for k, node in self.K.items():
if not node.children:
# find point with max dist from source
p_max_dist = [float('-inf'), None]
for i in node.points:
if self.P_dist[i] > p_max_dist[0]:
p_max_dist[0] = self.P_dist[i]
p_max_dist[1] = i
p_max_dist = self.P[p_max_dist[1]]
x1 = self.K[node.parent].pos
x2 = node.pos
x0 = p_max_dist
s = -dot((x1 - x0), (x2 - x1)) / (linalg.norm(x2 - x1) ** 2)
v = x1 + (x2 - x1) * s
self.K[k].pos = v
if node.parent is None:
p_min_dist = [float('inf'), None] # should be the src point?
for i in node.points:
if self.P_dist[i] < p_min_dist[0]:
p_min_dist[0] = self.P_dist[i]
p_min_dist[1] = i
p_min_dist = self.P[p_min_dist[1]]
first_child_k = list(node.children)[0]
x1 = self.K[first_child_k].pos
x2 = node.pos
x0 = p_min_dist
s = -dot((x1 - x0), (x2 - x1)) / (linalg.norm(x2 - x1) ** 2)
v = x1 + (x2 - x1) * s
self.K[k].pos = v