Decomposition of binary images - A survey and comparison

We present an overview of the most important methods that decompose an arbitrary binary object into a union of rectangles. We describe a run-length encoding and its generalization, decompositions based on quadtrees, on mathematical morphology, on the distance transform, and a theoretically optimal decomposition based on a maximal matching in bipartite graphs. We compare their performance in image compression, in moment computation and in linear filtering. We show that the choice is always a compromise between the complexity and time/memory consumption. We give advice how to select an appropriate method in particular cases.