How to find minimum number of largest square of 1 in an 2D bool matrix

I have a 2D bool image (dimension 81x65) with several irregular regions black(mainly in the middle) and other pixes white(mainly in the outer part).

Is there a way to split the white region into square pieces as large as possible, and get the position and size for each square?

Thanks.

[Walter Roberson]

Do the letters need to be taken into account in the actual images?

[raym]

sorry the image is from google just for demo. I will draw a new one.

[Walter Roberson]

What would be the desired output in the above case? And should all of the square be the same size?

[raym]

The square can be any size and with different sizes. The key is to split white pixels into less squares, so some of the square should have large area.

Answer 1

[Walter Roberson]

D = bwdistgeodesic(logical(YourImage), ~YourImage);

Now iterate. if there are no finite values in D, break the loop. Find the largest value in D. It is at the corner of a square of white pixels of that dimension, but you will need to do a little work to figure out which corner it is. When you have figured out which corner it is, record that square location and then set all the D locations inside that square to be inf or nan. Now return back to the beginning of the loop (looking for the largest remaining value)

This is a "greedy" algorithm. It makes no attempt at all to be consistent in block sizes. If there were a situation in which two squares of equal size plus one small square would cover a section, then the algorithm would instead take the larger square leaving the rest to be broken up into a number of smaller squares.