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

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Meghana Dinesh
Meghana Dinesh 2018-1-19
评论： Meghana Dinesh 2018-1-22
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.

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回答（1 个）

Image Analyst
Image Analyst 2018-1-19
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.

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