二值图像中骨架上两点之间的最短路径

我有一个二进制图像，其中包含图像的一个像素宽度骨架。您可能基本上知道，在这个二值图像中，我在骨架上有 1，在其他地方有 0。 如何找到骨架上两个非零元素之间的最短距离？路径也应该在骨架本身上。 我想使用 A-star 算法的 C++ 实现。我找到了下面的代码，我需要修改它来解决我的问题。

我将非常感谢任何帮助。谢谢。

/** {{{ http://code.activestate.com/recipes/577457/ (r4) */
// Astar.cpp
// http://en.wikipedia.org/wiki/A*
// Compiler: Dev-C++ 4.9.9.2
// FB - 201012256
#include <iostream>
#include <iomanip>
#include <queue>
#include <string>
#include <math.h>
#include <ctime>
using namespace std;

const int n=60; // horizontal size of the map
const int m=60; // vertical size size of the map
static int map[n][m];
static int closed_nodes_map[n][m]; // map of closed (tried-out) nodes
static int open_nodes_map[n][m]; // map of open (not-yet-tried) nodes
static int dir_map[n][m]; // map of directions
const int dir=8; // number of possible directions to go at any position
// if dir==4
//static int dx[dir]={1, 0, -1, 0};
//static int dy[dir]={0, 1, 0, -1};
// if dir==8
static int dx[dir]={1, 1, 0, -1, -1, -1, 0, 1};
static int dy[dir]={0, 1, 1, 1, 0, -1, -1, -1};

class node
{
// current position
int xPos;
int yPos;
// total distance already travelled to reach the node
int level;
// priority=level+remaining distance estimate
int priority;  // smaller: higher priority

public:
    node(int xp, int yp, int d, int p) 
        {xPos=xp; yPos=yp; level=d; priority=p;}

    int getxPos() const {return xPos;}
    int getyPos() const {return yPos;}
    int getLevel() const {return level;}
    int getPriority() const {return priority;}

    void updatePriority(const int & xDest, const int & yDest)
    {
         priority=level+estimate(xDest, yDest)*10; //A*
    }

    // give better priority to going strait instead of diagonally
    void nextLevel(const int & i) // i: direction
    {
         level+=(dir==8?(i%2==0?10:14):10);
    }

    // Estimation function for the remaining distance to the goal.
    const int & estimate(const int & xDest, const int & yDest) const
    {
        static int xd, yd, d;
        xd=xDest-xPos;
        yd=yDest-yPos;         

        // Euclidian Distance
        d=static_cast<int>(sqrt(xd*xd+yd*yd));

        // Manhattan distance
        //d=abs(xd)+abs(yd);

        // Chebyshev distance
        //d=max(abs(xd), abs(yd));

        return(d);
    }
};

// Determine priority (in the priority queue)
bool operator<(const node & a, const node & b)
{
 return a.getPriority() > b.getPriority();
}

// A-star algorithm.
// The route returned is a string of direction digits.
string pathFind( const int & xStart, const int & yStart, 
             const int & xFinish, const int & yFinish )
{
static priority_queue<node> pq[2]; // list of open (not-yet-tried) nodes
static int pqi; // pq index
static node* n0;
static node* m0;
static int i, j, x, y, xdx, ydy;
static char c;
pqi=0;

// reset the node maps
for(y=0;y<m;y++)
{
    for(x=0;x<n;x++)
    {
        closed_nodes_map[x][y]=0;
        open_nodes_map[x][y]=0;
    }
}

// create the start node and push into list of open nodes
n0=new node(xStart, yStart, 0, 0);
n0->updatePriority(xFinish, yFinish);
pq[pqi].push(*n0);
open_nodes_map[x][y]=n0->getPriority(); // mark it on the open nodes map

// A* search
while(!pq[pqi].empty())
{
    // get the current node w/ the highest priority
    // from the list of open nodes
    n0=new node( pq[pqi].top().getxPos(), pq[pqi].top().getyPos(), 
                 pq[pqi].top().getLevel(), pq[pqi].top().getPriority());

    x=n0->getxPos(); y=n0->getyPos();

    pq[pqi].pop(); // remove the node from the open list
    open_nodes_map[x][y]=0;
    // mark it on the closed nodes map
    closed_nodes_map[x][y]=1;

    // quit searching when the goal state is reached
    //if((*n0).estimate(xFinish, yFinish) == 0)
    if(x==xFinish && y==yFinish) 
    {
        // generate the path from finish to start
        // by following the directions
        string path="";
        while(!(x==xStart && y==yStart))
        {
            j=dir_map[x][y];
            c='0'+(j+dir/2)%dir;
            path=c+path;
            x+=dx[j];
            y+=dy[j];
        }

        // garbage collection
        delete n0;
        // empty the leftover nodes
        while(!pq[pqi].empty()) pq[pqi].pop();           
        return path;
    }

    // generate moves (child nodes) in all possible directions
    for(i=0;i<dir;i++)
    {
        xdx=x+dx[i]; ydy=y+dy[i];

        if(!(xdx<0 || xdx>n-1 || ydy<0 || ydy>m-1 || map[xdx][ydy]==1 
            || closed_nodes_map[xdx][ydy]==1))
        {
            // generate a child node
            m0=new node( xdx, ydy, n0->getLevel(), 
                         n0->getPriority());
            m0->nextLevel(i);
            m0->updatePriority(xFinish, yFinish);

            // if it is not in the open list then add into that
            if(open_nodes_map[xdx][ydy]==0)
            {
                open_nodes_map[xdx][ydy]=m0->getPriority();
                pq[pqi].push(*m0);
                // mark its parent node direction
                dir_map[xdx][ydy]=(i+dir/2)%dir;
            }
            else if(open_nodes_map[xdx][ydy]>m0->getPriority())
            {
                // update the priority info
                open_nodes_map[xdx][ydy]=m0->getPriority();
                // update the parent direction info
                dir_map[xdx][ydy]=(i+dir/2)%dir;

                // replace the node
                // by emptying one pq to the other one
                // except the node to be replaced will be ignored
                // and the new node will be pushed in instead
                while(!(pq[pqi].top().getxPos()==xdx && 
                       pq[pqi].top().getyPos()==ydy))
                {                
                    pq[1-pqi].push(pq[pqi].top());
                    pq[pqi].pop();       
                }
                pq[pqi].pop(); // remove the wanted node

                // empty the larger size pq to the smaller one
                if(pq[pqi].size()>pq[1-pqi].size()) pqi=1-pqi;
                while(!pq[pqi].empty())
                {                
                    pq[1-pqi].push(pq[pqi].top());
                    pq[pqi].pop();       
                }
                pqi=1-pqi;
                pq[pqi].push(*m0); // add the better node instead
            }
            else delete m0; // garbage collection
        }
    }
    delete n0; // garbage collection
}
return ""; // no route found
}

int main()
{
srand(time(NULL));

// create empty map
for(int y=0;y<m;y++)
{
    for(int x=0;x<n;x++) map[x][y]=0;
}

// fillout the map matrix with a '+' pattern
for(int x=n/8;x<n*7/8;x++)
{
    map[x][m/2]=1;
}
for(int y=m/8;y<m*7/8;y++)
{
    map[n/2][y]=1;
}

// randomly select start and finish locations
int xA, yA, xB, yB;
switch(rand()%8)
{
    case 0: xA=0;yA=0;xB=n-1;yB=m-1; break;
    case 1: xA=0;yA=m-1;xB=n-1;yB=0; break;
    case 2: xA=n/2-1;yA=m/2-1;xB=n/2+1;yB=m/2+1; break;
    case 3: xA=n/2-1;yA=m/2+1;xB=n/2+1;yB=m/2-1; break;
    case 4: xA=n/2-1;yA=0;xB=n/2+1;yB=m-1; break;
    case 5: xA=n/2+1;yA=m-1;xB=n/2-1;yB=0; break;
    case 6: xA=0;yA=m/2-1;xB=n-1;yB=m/2+1; break;
    case 7: xA=n-1;yA=m/2+1;xB=0;yB=m/2-1; break;
}

cout<<"Map Size (X,Y): "<<n<<","<<m<<endl;
cout<<"Start: "<<xA<<","<<yA<<endl;
cout<<"Finish: "<<xB<<","<<yB<<endl;
// get the route
clock_t start = clock();
string route=pathFind(xA, yA, xB, yB);
if(route=="") cout<<"An empty route generated!"<<endl;
clock_t end = clock();
double time_elapsed = double(end - start);
cout<<"Time to calculate the route (ms): "<<time_elapsed<<endl;
cout<<"Route:"<<endl;
cout<<route<<endl<<endl;

// follow the route on the map and display it 
if(route.length()>0)
{
    int j; char c;
    int x=xA;
    int y=yA;
    map[x][y]=2;
    for(int i=0;i<route.length();i++)
    {
        c =route.at(i);
        j=atoi(&c); 
        x=x+dx[j];
        y=y+dy[j];
        map[x][y]=3;
    }
    map[x][y]=4;

    // display the map with the route
    for(int y=0;y<m;y++)
    {
        for(int x=0;x<n;x++)
            if(map[x][y]==0)
                cout<<".";
            else if(map[x][y]==1)
                cout<<"O"; //obstacle
            else if(map[x][y]==2)
                cout<<"S"; //start
            else if(map[x][y]==3)
                cout<<"R"; //route
            else if(map[x][y]==4)
                cout<<"F"; //finish
        cout<<endl;
    }
}
getchar(); // wait for a (Enter) keypress  
return(0);
}
/** end of http://code.activestate.com/recipes/577457/ }}} */