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.