我正在尝试使用boost :: boykov_kolmogorov_max_flow进行前景/背景图像分割。我想出了这个：
#include <iostream>
#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/graph_traits.hpp>
#include <boost/property_map/property_map.hpp>
#include <boost/graph/boykov_kolmogorov_max_flow.hpp>
typedef boost::adjacency_list<boost::vecS, boost::vecS, boost::directedS,
boost::no_property,
boost::property<boost::edge_index_t, std::size_t> > GraphType;
typedef boost::graph_traits<GraphType>::vertex_descriptor VertexDescriptor;
typedef boost::graph_traits<GraphType>::edge_descriptor EdgeDescriptor;
typedef boost::graph_traits<GraphType>::vertices_size_type VertexIndex;
typedef boost::graph_traits<GraphType>::edges_size_type EdgeIndex;
void AddBidirectionalEdge(GraphType& graph, unsigned int source, unsigned int target, float weight,
std::vector<EdgeDescriptor>& reverseEdges, std::vector<float>& capacity)
{
// Add edges between grid vertices. We have to create the edge and the reverse edge,
// then add the reverseEdge as the corresponding reverse edge to 'edge', and then add 'edge'
// as the corresponding reverse edge to 'reverseEdge'
int nextEdgeId = num_edges(graph);
EdgeDescriptor edge;
bool inserted;
boost::tie(edge,inserted) = add_edge(source, target, nextEdgeId, graph);
if(!inserted)
{
std::cerr << "Not inserted!" << std::endl;
}
EdgeDescriptor reverseEdge = add_edge(target, source, nextEdgeId + 1, graph).first;
reverseEdges.push_back(reverseEdge);
reverseEdges.push_back(edge);
capacity.push_back(weight);
capacity.push_back(weight);
}
int main()
{
GraphType graph;
unsigned int numberOfVertices = 3*3 + 2; // a 3x3 grid plus the source and sink terminals
std::vector<int> groups(numberOfVertices);
std::vector<EdgeDescriptor> reverseEdges;
std::vector<float> capacity;
/*
0 - 1 = 2
| || |
3 - 4 - 5
| || |
6 = 7 - 8
*/
float smallWeight = 1;
float largeWeight = 1000;
// Horizontal edges
AddBidirectionalEdge(graph, 0, 1, smallWeight, reverseEdges, capacity);
AddBidirectionalEdge(graph, 1, 2, largeWeight, reverseEdges, capacity);
AddBidirectionalEdge(graph, 3, 4, smallWeight, reverseEdges, capacity);
AddBidirectionalEdge(graph, 4, 5, smallWeight, reverseEdges, capacity);
AddBidirectionalEdge(graph, 6, 7, largeWeight, reverseEdges, capacity);
AddBidirectionalEdge(graph, 7, 8, smallWeight, reverseEdges, capacity);
// Vertical edges
AddBidirectionalEdge(graph, 0, 3, smallWeight, reverseEdges, capacity);
AddBidirectionalEdge(graph, 3, 6, smallWeight, reverseEdges, capacity);
AddBidirectionalEdge(graph, 1, 4, largeWeight, reverseEdges, capacity);
AddBidirectionalEdge(graph, 4, 7, largeWeight, reverseEdges, capacity);
AddBidirectionalEdge(graph, 2, 5, smallWeight, reverseEdges, capacity);
AddBidirectionalEdge(graph, 5, 8, smallWeight, reverseEdges, capacity);
int sourceId = 9;
int sinkId = 10;
// Add links to terminals for uncertain nodes
std::vector<unsigned int> uncertainNodes = {{2, 4, 7, 6}};
for(size_t i = 0; i < uncertainNodes.size(); ++i)
{
AddBidirectionalEdge(graph, uncertainNodes[i], sourceId, 1, reverseEdges, capacity);
AddBidirectionalEdge(graph, uncertainNodes[i], sinkId, 1, reverseEdges, capacity);
}
// Add links to terminals for "definitely source"
std::vector<unsigned int> sourceNodes = {{0, 3}};
for(size_t i = 0; i < sourceNodes.size(); ++i)
{
AddBidirectionalEdge(graph, sourceNodes[i], sourceId, largeWeight, reverseEdges, capacity);
AddBidirectionalEdge(graph, sourceNodes[i], sinkId, smallWeight, reverseEdges, capacity);
}
// Add links to terminals for "definitely sink"
std::vector<unsigned int> sinkNodes = {{5, 8}};
for(size_t i = 0; i < sinkNodes.size(); ++i)
{
AddBidirectionalEdge(graph, sinkNodes[i], sourceId, smallWeight, reverseEdges, capacity);
AddBidirectionalEdge(graph, sinkNodes[i], sinkId, largeWeight, reverseEdges, capacity);
}
std::vector<float> residual_capacity(num_edges(graph), 0);
VertexDescriptor sourceVertex = vertex(sourceId,graph);
VertexDescriptor sinkVertex = vertex(sinkId,graph);
// There should be 3*3 + 2 = 11 nodes
std::cout << "Number of vertices " << num_vertices(graph) << std::endl;
// There should be 2*(12) + 2*2*9 = 60 edges
std::cout << "Number of edges " << num_edges(graph) << std::endl;
boost::boykov_kolmogorov_max_flow(graph,
boost::make_iterator_property_map(&capacity[0], get(boost::edge_index, graph)),
boost::make_iterator_property_map(&residual_capacity[0], get(boost::edge_index, graph)),
boost::make_iterator_property_map(&reverseEdges[0], get(boost::edge_index, graph)),
boost::make_iterator_property_map(&groups[0], get(boost::vertex_index, graph)),
get(boost::vertex_index, graph),
sourceVertex,
sinkVertex);
// Display the segmentation
// for(size_t index=0; index < groups.size(); ++index)
// {
// std::cout << "Vertex " << index << " is in group " << groups[index] << std::endl;
// }
std::cout << "Source group " << groups[sourceVertex] << std::endl;
std::cout << "Sink group " << groups[sinkVertex] << std::endl;
for(size_t index=0; index < numberOfVertices - 2; ++index)
{
if(groups[index] == groups[sourceVertex])
{
std::cout << "Vertex " << index << " is attached to the source. (group " << groups[index] << ")" << std::endl;
}
else if(groups[index] == groups[sinkVertex])
{
std::cout << "Vertex " << index << " is attached to the sink. (group " << groups[index] << ")" << std::endl;
}
else
{
std::cerr << "Vertex " << index << " is not attached to the source or sink! (group " << groups[index] << ")" << std::endl;
}
}
return EXIT_SUCCESS;
}
构建并运行没有错误。然而，即使在这个简单的小例子中，输出也很奇怪。以下是上述代码的输出：
Number of vertices 11
Number of edges 56
Source group label 4
Sink group label 0
Vertex 0 is attached to the source. (group 4)
Vertex 3 is attached to the source. (group 4)
Vertex 5 is attached to the sink. (group 0)
Vertex 8 is attached to the sink. (group 0)
Vertex 1 is not attached to the source or sink! (group 1)
Vertex 2 is not attached to the source or sink! (group 1)
Vertex 4 is not attached to the source or sink! (group 1)
Vertex 6 is not attached to the source or sink! (group 1)
Vertex 7 is not attached to the source or sink! (group 1)
如您所见，输出中有三个组，称为＆＃34; 0＆＃34;，＆＃34; 1＆＃34;和＆＃34; 4＆＃34;。
任何人都可以解释标签的含义，以及为什么分段输出中有超过2个组？
-----编辑-----
我制作了一个略大的图形（3x5），我知道顶点5应该连接到源，顶点9应该连接到接收器，而2,7和12可以连接到任何一个终端同等的惩罚，但他们都应该是一样的。在这种情况下，它似乎按预期工作：
#include <iostream>
#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/graph_traits.hpp>
#include <boost/property_map/property_map.hpp>
#include <boost/graph/boykov_kolmogorov_max_flow.hpp>
/*
F F x B B F F F B B
x F x B x -> F F F B B
F F x B B F F F B B
*/
typedef boost::adjacency_list<boost::vecS, boost::vecS, boost::directedS,
boost::no_property,
boost::property<boost::edge_index_t, std::size_t> > GraphType;
typedef boost::graph_traits<GraphType>::vertex_descriptor VertexDescriptor;
typedef boost::graph_traits<GraphType>::edge_descriptor EdgeDescriptor;
typedef boost::graph_traits<GraphType>::vertices_size_type VertexIndex;
typedef boost::graph_traits<GraphType>::edges_size_type EdgeIndex;
void AddBidirectionalEdge(GraphType& graph, unsigned int source, unsigned int target, float weight,
std::vector<EdgeDescriptor>& reverseEdges, std::vector<float>& capacity)
{
// Add edges between grid vertices. We have to create the edge and the reverse edge,
// then add the reverseEdge as the corresponding reverse edge to 'edge', and then add 'edge'
// as the corresponding reverse edge to 'reverseEdge'
int nextEdgeId = num_edges(graph);
EdgeDescriptor edge;
bool inserted;
boost::tie(edge,inserted) = add_edge(source, target, nextEdgeId, graph);
if(!inserted)
{
std::cerr << "Not inserted!" << std::endl;
}
EdgeDescriptor reverseEdge = add_edge(target, source, nextEdgeId + 1, graph).first;
reverseEdges.push_back(reverseEdge);
reverseEdges.push_back(edge);
capacity.push_back(weight);
// Not sure what to do about reverse edge weights
capacity.push_back(weight);
// capacity.push_back(0);
}
int main()
{
GraphType graph;
unsigned int numberOfVertices = 3*5 + 2; // a 3x5 grid plus the source and sink terminals
std::vector<int> groups(numberOfVertices);
std::vector<EdgeDescriptor> reverseEdges;
std::vector<float> capacity;
float smallWeight = 1;
float largeWeight = 1000;
// Horizontal edges
AddBidirectionalEdge(graph, 0, 1, smallWeight, reverseEdges, capacity);
AddBidirectionalEdge(graph, 1, 2, largeWeight, reverseEdges, capacity);
AddBidirectionalEdge(graph, 2, 3, smallWeight, reverseEdges, capacity);
AddBidirectionalEdge(graph, 3, 4, smallWeight, reverseEdges, capacity);
AddBidirectionalEdge(graph, 5, 6, largeWeight, reverseEdges, capacity);
AddBidirectionalEdge(graph, 6, 7, smallWeight, reverseEdges, capacity);
AddBidirectionalEdge(graph, 7, 8, smallWeight, reverseEdges, capacity);
AddBidirectionalEdge(graph, 8, 9, smallWeight, reverseEdges, capacity);
AddBidirectionalEdge(graph, 10, 11, smallWeight, reverseEdges, capacity);
AddBidirectionalEdge(graph, 11, 12, smallWeight, reverseEdges, capacity);
AddBidirectionalEdge(graph, 12, 13, smallWeight, reverseEdges, capacity);
AddBidirectionalEdge(graph, 13, 14, smallWeight, reverseEdges, capacity);
// Vertical edges
AddBidirectionalEdge(graph, 0, 5, smallWeight, reverseEdges, capacity);
AddBidirectionalEdge(graph, 1, 6, smallWeight, reverseEdges, capacity);
AddBidirectionalEdge(graph, 2, 7, largeWeight, reverseEdges, capacity);
AddBidirectionalEdge(graph, 3, 8, largeWeight, reverseEdges, capacity);
AddBidirectionalEdge(graph, 4, 9, smallWeight, reverseEdges, capacity);
AddBidirectionalEdge(graph, 5, 10, smallWeight, reverseEdges, capacity);
AddBidirectionalEdge(graph, 6, 11, smallWeight, reverseEdges, capacity);
AddBidirectionalEdge(graph, 7, 12, smallWeight, reverseEdges, capacity);
AddBidirectionalEdge(graph, 8, 13, smallWeight, reverseEdges, capacity);
AddBidirectionalEdge(graph, 9, 14, smallWeight, reverseEdges, capacity);
int sourceId = 15;
int sinkId = 16;
// Add links to terminals for uncertain nodes
std::vector<unsigned int> uncertainNodes = {{2, 5, 7, 9, 12}};
for(size_t i = 0; i < uncertainNodes.size(); ++i)
{
AddBidirectionalEdge(graph, uncertainNodes[i], sourceId, 1, reverseEdges, capacity);
AddBidirectionalEdge(graph, uncertainNodes[i], sinkId, 1, reverseEdges, capacity);
}
// Add links to terminals for "definitely source"
std::vector<unsigned int> sourceNodes = {{0, 1, 6, 10, 11}};
for(size_t i = 0; i < sourceNodes.size(); ++i)
{
AddBidirectionalEdge(graph, sourceNodes[i], sourceId, largeWeight, reverseEdges, capacity);
AddBidirectionalEdge(graph, sourceNodes[i], sinkId, smallWeight, reverseEdges, capacity);
}
// Add links to terminals for "definitely sink"
std::vector<unsigned int> sinkNodes = {{3, 4, 8, 13, 14}};
for(size_t i = 0; i < sinkNodes.size(); ++i)
{
AddBidirectionalEdge(graph, sinkNodes[i], sourceId, smallWeight, reverseEdges, capacity);
AddBidirectionalEdge(graph, sinkNodes[i], sinkId, largeWeight, reverseEdges, capacity);
}
std::vector<float> residual_capacity(num_edges(graph), 0);
VertexDescriptor sourceVertex = vertex(sourceId,graph);
VertexDescriptor sinkVertex = vertex(sinkId,graph);
// There should be 3*5 + 2 = 17 nodes
std::cout << "Number of vertices " << num_vertices(graph) << std::endl;
// There should be 2*2*(15) + 2* ((5-1)*3 + 5*(3-1)) = 60 + 2(12 + 10) = 104 edges
std::cout << "Number of edges " << num_edges(graph) << std::endl;
boost::boykov_kolmogorov_max_flow(graph,
boost::make_iterator_property_map(&capacity[0], get(boost::edge_index, graph)),
boost::make_iterator_property_map(&residual_capacity[0], get(boost::edge_index, graph)),
boost::make_iterator_property_map(&reverseEdges[0], get(boost::edge_index, graph)),
boost::make_iterator_property_map(&groups[0], get(boost::vertex_index, graph)),
get(boost::vertex_index, graph),
sourceVertex,
sinkVertex);
// Display the segmentation
// for(size_t index=0; index < groups.size(); ++index)
// {
// std::cout << "Vertex " << index << " is in group " << groups[index] << std::endl;
// }
std::cout << "Source group label " << groups[sourceVertex] << std::endl;
std::cout << "Sink group label " << groups[sinkVertex] << std::endl;
//for(size_t index=0; index < numberOfVertices - 2; ++index)
for(size_t index=0; index < numberOfVertices; ++index)
{
if(groups[index] == groups[sourceVertex])
{
std::cout << "Vertex " << index << " is attached to the source. (group " << groups[index] << ")" << std::endl;
}
else if(groups[index] == groups[sinkVertex])
{
std::cout << "Vertex " << index << " is attached to the sink. (group " << groups[index] << ")" << std::endl;
}
else
{
std::cerr << "Vertex " << index << " is not attached to the source or sink! (group " << groups[index] << ")" << std::endl;
}
}
return EXIT_SUCCESS;
}
输出：
Number of vertices 17
Number of edges 104
Source group label 4
Sink group label 0
Vertex 0 is attached to the source. (group 4)
Vertex 1 is attached to the source. (group 4)
Vertex 2 is attached to the source. (group 4)
Vertex 3 is attached to the sink. (group 0)
Vertex 4 is attached to the sink. (group 0)
Vertex 5 is attached to the source. (group 4)
Vertex 6 is attached to the source. (group 4)
Vertex 7 is attached to the source. (group 4)
Vertex 8 is attached to the sink. (group 0)
Vertex 9 is attached to the sink. (group 0)
Vertex 10 is attached to the source. (group 4)
Vertex 11 is attached to the source. (group 4)
Vertex 12 is attached to the source. (group 4)
Vertex 13 is attached to the sink. (group 0)
Vertex 14 is attached to the sink. (group 0)
Vertex 15 is attached to the source. (group 4)
Vertex 16 is attached to the sink. (group 0)
答案 0 :(得分：0)
来自增强文档：
＆＃34;如果运行算法后顶点的颜色为黑色，则顶点属于源树 else ，它属于sink树（用于最小切割）。＆＃34;（ boykov_kolmogorov_max_flow）
我猜你应该将其他值作为接收树集的一部分计算。