Repairing Binary Images Through the 2D Diamond Grid - Čomić, Lidija; Magillo, Paola (Combinatorial Image Analysis, 2020)
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 $$I_4$$ 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 $$π /4$$ , 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.