Algorithm to group sets of points together that follow a direction

Question

Note: I am placing this question in both the MATLAB and Python tags as I am the most proficient in these languages. However, I welcome solutions in any language.

Answer 1

While I can not suggest a better approach to group any given list of centroid points than the one you already tried, I hope the following idea might help you out:

Since you are very specific about the content of your image (containing a field of squares) I was wondering if you in fact need to group the centroid points from the data given in your problem setup, or if you can use the data described in Background to the problem as well. Since you already determined the corners of each detected square as well as their position in that given square it seems to me like it would be very accurate to determine a neighbour of a given square by comparing the corner-coordinates.

So for finding any candidate for a right neighbour of any square, i would suggest you compare the upper right and lower right corner of that square with the upper left and lower left corner of any other square (or any square within a certain distance). Allowing for only small vertical differences and slightly greater horizontal differences, you can "match" two squares, if both their corresponding corner-points are close enough together.

By using an upper limit to the allowed vertical/horizontal difference between corners, you might even be able to just assign the best matching square within these boundaries as neighbour

A problem might be that you don't detect all the squares, so there is a rather large space between square 30 and 32. Since you said you need 'at least' 3 squares per row, it might be viable for you to simply ignore square 32 in that horizontal line. If that is not an option for you, you could try to match as many squares as possible and afterwards assign the "missing" squares to a point in your grid by using the previously calculated data:

In the example about square 32 you would've detected that it has upper and lower neighbours 27 and 37. Also you should've been able to determine that square 27 lies within row 1 and 37 lies within row 3, so you can assign square 32 to the "best matching" row in between, which is obviously 2 in this case.

This general approach is basically the approach you have tried already, but should hopefully be a lot more accurate since you are now comparing orientation and distance of two lines instead of simply comparing the location of two points in a grid.

Also as a sidenode on your previous attempts - can you use the black cornerlines to correct the initial rotation of your image a bit? This might make further distortion algorithms (like the ones that you discussed with knedlsepp in the comments) a lot more accurate. (EDIT: I did read the comments of Parag just now - comparing the points by the angle of the lines is of course basically the same as rotating the Image beforehand)