Repairing Binary Images Through the 2D Diamond Grid

A 2D binary image is well-composed if it does not contain a \(2\times 2\) configuration of two diagonal black and two diagonal white squares. We propose a simple repairing algorithm to construct two well-composed images \(I_4\) and \(I_8\) starting from an image I, and we prove that \(I_4\) and \(I_8\) 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 \(\pi /4\), whose pixels correspond to the original pixels and to their vertices. The images \(I_4\) and \(I_8\) are double in size with respect to the image I. Experimental comparisons and applications are also shown.