def test_neighbour_vertices():
mat = np.array([[1, 1, 1, 0, 0], [1, 0, 0, 1, 0], [0, 1, 1, 0, 0],
[0, 0, 0, 1, 2]])
assert [(1, 0), (2, 1), (2, 2)] == list(graph.neighbours(mat, 0))
assert [(0, 0), (3, 3)] == list(graph.neighbours(mat, 1))
assert [(0, 1), (0, 2)] == list(graph.neighbours(mat, 2))
assert [(1, 3), (3, 4)] == list(graph.neighbours(mat, 3))
def sample_pixel(i, j, image, labels, eps, beta):
"""Sample pixel from conditional probability distribution.
Arguments:
i {int} -- row coordinate of pixel
j {int} -- column coordinate of pixel
image {numpy.ndarray} -- image
labels {list} -- list of all labels ([0, 1] for black and white images)
eps {float} -- noise parameter
beta {float} -- edge cost parameter
Returns:
int -- sampled pixel
"""
probs = []
neighbour_pxls = neighbours(image, i, j)
for label in labels:
pixel = Pixel(i, j, label)
pxl_cost = pixel_cost(pixel, image[i, j], eps)
neighbours_costs = []
for neighbour in neighbour_pxls:
neighbours_costs += [edge_cost(pixel, neighbour, beta)]
probs.append(np.exp(-pxl_cost - np.sum(neighbours_costs)))
probs = probs / np.sum(probs)
sampled_pixel = np.random.choice(labels, p=probs)
return sampled_pixel
def dijkstra(graph: Graph, start: tuple) -> Tuple[dict, dict]:
distance = {}
ancestor = {}
visited = {}
# Initialize structures
for vertex in Graph.vertices:
v_id = vertex[0]
distance[v_id] = float("inf")
ancestor[v_id] = None
visited[v_id] = False
start_v_id = start[0]
distance[start_v_id] = 0
while False in visited.values():
non_visited_distance = {
k: distance[k]
for k, v in visited.items() if v == False
}
u = min(non_visited_distance, key=non_visited_distance.get)
visited[u] = True
for vertex in neighbours(u):
v = vertex[0]
if visited[v] == False:
if distance[v] > distance[u] + weight(u, v):
distance[v] = distance[u] + weight(u, v)
ancestor[v] = u
return distance, ancestor
def prim(graph: Graph):
not_visited = [v[0] for v in graph.vertices]
r = not_visited[0]
not_visited.remove(r) # we choose the first vertex
Q = [] # priority queue
A = [] # mininum spanning tree
weight_sum = 0 # combined value of the tree's edges
while not_visited:
for neighbour in neighbours(r):
heapq.heappush(Q, (weight(neighbour[0], r), (neighbour[0], r)))
while Q:
e_weight, u = heapq.heappop(Q) # return edge with smallest weight
if u[0] in not_visited:
next_r = u[0]
break
if u[1] in not_visited:
next_r = u[1]
break
weight_sum += e_weight
A.append(u)
r = next_r
not_visited.remove(r)
return weight_sum, A
def hierholzer(graph:Graph):
edges = [edge[0] for edge in graph.edges]
# The graphs we're working with are undirected
# So an edge (v, u) is the same as an edge (u, v)
# This bit check which of the "repeated" edges are
# not present and adds them to the list
for v in graph.vertices:
for n in neighbours(v[0]):
if (v[0], n[0]) not in edges:
edges.append((v[0], n[0]))
if (n[0], v[0]) not in edges:
edges.append((n[0], v[0]))
# Initially, all edges are marked unvisited
e_visited = {edge: False for edge in edges}
# We begin the algorithm from the first vertex
vertex = graph.vertices[0]
(r, cycle) = eulerian_subcycle(graph, vertex[0], e_visited)
if not r:
return (False, None)
elif not all(e_visited):
return (False, None)
else:
return (True, cycle)
def bfs(n_vertices: int) -> Tuple[dict, dict]:
visited = {}
distance = {}
ancestor = {}
# Initialize structures
for vertex in Graph.vertices:
label = vertex[0]
visited[label] = False
distance[label] = float("inf")
ancestor[label] = None
# Add starting node
start = Graph.vertices[0]
start_label = start[0]
visited[start_label] = True
distance[start_label] = 0
# Exploration loop
queue = [start]
while queue:
current_node = queue.pop()
cnode_label = current_node[0]
for neighbour in neighbours(cnode_label):
n_label = neighbour[0]
if not visited[n_label]:
visited[n_label] = True
distance[n_label] = distance[cnode_label] + 1
ancestor[n_label] = n_label
queue.append(neighbour)
return distance, ancestor
def dfs(current: int, visited: dict, sorted_vertices: list):
visited[current] = True
for neighbour in neighbours(current):
if not visited[neighbour]:
dfs(neighbour, visited, sorted_vertices)
sorted_vertices.insert(0, current)
def graph_coloring(graph):
# Reversed sort by number of neighbours
vertices = sorted(graph.vertices, key=lambda x: len(neighbours(x)), reverse=True)
colors = []
color_map = {}
for v in vertices:
color_tmp = [True for i in vertices]
for n in neighbours(v[0]):
if n in color_map:
color = color_map[n]
color_tmp[color] = False
for color, available in enumerate(color_tmp):
if available:
color_map[v] = color
if color not in color_map:
colors.append(color)
break
return color_map
def test_neighbours(self):
"""
FUNCTION: neighbours, in graph.py.
"""
"""Use the function to determine the neighbours of each node"""
neighbours = []
for i in range(0, self.n):
neighbours.append(graph.neighbours(self.dag, i))
"""
Assert that the function returns the expected neighbours for each node.
"""
assert neighbours[0] == [1, 2]
assert neighbours[1] == [3, 0]
assert neighbours[2] == [3, 0]
assert neighbours[3] == [1, 2]
def eulerian_subcycle(graph, v, e_visited):
cycle = [v]
t = v
while True:
v_isolated = True
for u in neighbours(v):
edge = (v, u[0])
if e_visited[edge] == False and e_visited[u[0], v] == False:
e_visited[edge] = True
e_visited[u[0], v] = True
v = u[0]
cycle.append(v)
v_isolated = False
break
if v_isolated:
return (False, None)
if v == t:
break
for x in cycle:
for w in neighbours(x):
if e_visited[(x, w[0])] == False:
(r, aux_cycle) = eulerian_subcycle(graph, x, e_visited)
if r == False:
return (False, None)
else:
# append subcycles
cycle = cycle[:cycle.index(x)] + aux_cycle + cycle[(cycle.index(x) +1):]
return (True, cycle)
def test_neighbours(self):
"""
FUNCTION: neighbours, in graph.py.
"""
"""Use the function to determine the neighbours of each node"""
neighbours = []
for i in range(0, self.n):
neighbours.append(graph.neighbours(self.dag, i))
"""
Assert that the function returns the expected neighbours for each node.
"""
assert neighbours[0] == [1, 2]
assert neighbours[1] == [3, 0]
assert neighbours[2] == [3, 0]
assert neighbours[3] == [1, 2]
def create_graph(labeling, alpha, L, S):
graph = maxflow.Graph[float]()
height, width = labeling.shape
nodeids = graph.add_grid_nodes(labeling.shape)
for i in range(height):
for j in range(width):
current_pxl = Pixel(i, j, labeling[i, j])
current_label = current_pxl.label
neighbours_list = neighbours(labeling, i, j)
for neighbour in neighbours_list:
weight = edge_cost(current_pxl, neighbour, S, L)
graph.add_edge(nodeids[i, j], nodeids[neighbour.i, neighbour.j], weight, weight)
pxl_weight_0 = pixel_cost(current_pxl, current_label)
pxl_weight_1 = pixel_cost(current_pxl, alpha)
graph.add_tedge(nodeids[i, j], pxl_weight_0, pxl_weight_1)
return graph, nodeids
def dfs_visit(self, u, adj_mat, directed):
"""
Performs a depth first serach visit on a node in a graph.
Parameters
----------
-'u': Int
The index of the node to visit.
-'adj_mat': Numpy ndarray
Adjacency matrix. If adj_mat[i, j] = 1, there exists
a directed edge from node i to node j.
-'directed': Int
Equals 1 if it is a directed graph, 0 otherwise.
"""
self.pre.append(u)
self.color[0, u] = self.gray
self.time_stamp = self.time_stamp + 1
self.d[0, u] = self.time_stamp
if directed == 1:
ns = graph.children(adj_mat, u)
else:
ns = graph.neighbours(adj_mat, u)
ns = np.unique(ns)
ns = np.setdiff1d(np.array(ns), np.array([self.pred[0, u]]))
ns = ns.tolist()
for v in ns:
if self.color[0, v] == self.white:
self.pred[0, v] = u
self.dfs_visit(v, adj_mat, directed)
elif self.color[0, v] == self.gray:
self.cycle = 1
self.color[0, u] = self.black
self.post.append(u)
self.time_stamp = self.time_stamp + 1
self.f[0, u] = self.time_stamp
def dfs_visit(self, u, adj_mat, directed):
"""
Performs a depth first serach visit on a node in a graph.
Parameters
----------
-'u': Int
The index of the node to visit.
-'adj_mat': Numpy ndarray
Adjacency matrix. If adj_mat[i, j] = 1, there exists
a directed edge from node i to node j.
-'directed': Int
Equals 1 if it is a directed graph, 0 otherwise.
"""
self.pre.append(u)
self.color[0, u] = self.gray
self.time_stamp = self.time_stamp + 1
self.d[0, u] = self.time_stamp
if directed == 1:
ns = graph.children(adj_mat, u)
else:
ns = graph.neighbours(adj_mat, u)
ns = np.unique(ns)
ns = np.setdiff1d(np.array(ns), np.array([self.pred[0, u]]))
ns = ns.tolist()
for v in ns:
if self.color[0, v] == self.white:
self.pred[0, v] = u
self.dfs_visit(v, adj_mat, directed)
elif self.color[0, v] == self.gray:
self.cycle = 1
self.color[0, u] = self.black
self.post.append(u)
self.time_stamp = self.time_stamp + 1
self.f[0, u] = self.time_stamp