[SOLVED] Efficient algorithm for looping over all neighbor pairs (2 point cliques) in 2-D array

Efficient algorithm for looping over all neighbor pairs (2 point cliques) in 2-D array

I need to loop over all (unordered) pairs of pixels in an image that are neighbors of each other without repetition. I am using an 8 point neighborhood. For example:

  x,y| 0   1   2   3   4
  ---+---+---+---+---+---+
   0 |   |   |   |   |   |
     +---+---+---+---+---+
   1 | a | b | c | d |   |
     +---+---+---+---+---+
   2 | e | f | g | h |   |
     +---+---+---+---+---+
   3 | i | j | k | l |   |
     +---+---+---+---+---+
   4 |   |   |   |   |   |
     +---+---+---+---+---+

The neighbors of pixel f are in the 3x3 square around it. Thus, g, for example, forms a 2 point clique with f. If I were to loop over all the rows and columns of the image, this clique would be counted twice, once when f is the center pixel and once when g is the center pixel. Similar inefficiencies would occur with the rest of the cliques.

So what I would like to do, is loop over all the cliques, rather than each pixel. If I were familiar with graph theory, I think some of the answers already given to similar questions would suffice, but as I am not, I would really appreciate any help that you can give with an efficient algorithm in layman's terms. Thanks in advance!

Solution

Loop the first point over all points. Inner loop the second point over the right, lower-left, lower, and lower-right neighbors (if they exist).