Repairing Binary Images Through the 2D Diamond Grid

A 2D binary image is well-composed if it does not contain a 2×2 configuration of two diagonal black and two diagonal white squares. We propose a simple repairing algorithm to construct two well-composed images I4 and I8 starting from an image I, and we prove that I4 and I8 are homotopy equivalent to I with 4- and 8-adjacency, respectively. This is achieved by passing from the original square grid to another one, rotated by π/4, whose pixels correspond to the original pixels and to their vertices. The images I4 and I8 are double in size with respect to the image I. Experimental comparisons and applications are also shown.