Find closest 8-connected chessboard distance between multiple pairs of points: shortest m-path

I am working on binary images. I have two sets of points: PNodes and FNodes. I want to find the closest PNode to each of the FNodes (shortest m-path); closest in terms of 8-connected chessboard distance.

In the example below, suppose PNodes (donated by *) are: (6,1), (6,5) and (5,8). (indexing starts from 0, first element is row number). FNodes (denoted by #) are: (0,1), (0,9), (1,6), (2,5) and (4,3).

 In = 
      [0,  1#, 0,  0,  0,  0,  0,  0,  0,  1#, 0;
       1,  0,  0,  0,  0,  0,  1#, 0,  1,  0,  0;
       0,  1,  0,  0,  0,  1#, 0,  0,  1,  0,  0;
       0,  0,  1,  0,  0,  0,  1,  0,  0,  1,  0;
       0,  1,  1,  1#, 0,  1,  0,  0,  1,  0,  0;
       0,  1,  0,  0,  0,  1,  0,  0,  1*, 0,  0;
       0,  1*, 0,  0,  0,  1*, 0,  0,  1,  0,  0;
       0,  1,  0,  0,  1,  0,  1,  1,  0,  0,  0;
       0,  0,  1,  1,  0,  0,  0,  1,  0,  0,  0]

 Distance Matrix =  
      [0,  6#, 0,  0,  0,  0,  0,  0,  0,  5#, 0;
       5,  0,  0,  0,  0,  0,  5#, 0,  4,  0,  0;
       0,  4,  0,  0,  0,  4#, 0,  0,  3,  0,  0;
       0,  0,  3,  0,  0,  0,  3,  0,  0,  2,  0;
       0,  2,  2,  3#, 0,  2,  0,  0,  1,  0,  0;
       0,  1,  0,  0,  0,  1,  0,  0,  **, 0,  0;
       0, **,  0,  0,  0,  **, 0,  0,  1,  0,  0;
       0,  1,  0,  0,  1,  0,  1,  1,  0,  0,  0;
       0,  0,  1,  1,  0,  0,  0,  1,  0,  0,  0]

I want to find out the distance of closest path from each FNode to reach closest PNode. Something like this: FNode at (0,1) is closest to PNode at (6,1). FNode at (4,3) is closest to PNode at (6,1). All distances are in terms of 8-connected chessboard distance.

Ultimate requirement from this entire process: I just want to make sure all PNodes have atleast 1 FNode which lie within a given distance range (along the path of 1s);

Suppose PNode (PN_1) has a FNode (FN_1) which lies within the required distance range, I also make sure that PN_1 is closest to FN_1, and not any other PNode.

For a better understanding, I have attached an image below; FNodes are rectangular and PNodes are circular.

I don't care about other elements in the matrix, apart from those of PNodes and FNodes, as depicted.

Answer 1

[Image Analyst]

See Steve's 5-part blog series on shortest path distances in images: http://blogs.mathworks.com/steve/2011/11/01/exploring-shortest-paths-part-1/ It goes into a lot of detail that should help you if you make an effort to follow along.

[Meghana Dinesh]

Thanks! I'll have a look and try to implement it.