Decomposability and Indecomposability of Binary Shapes: A Theory of Shape Arithmetics

Abstract

We observe that the resemblance between the integer number system with multiplication & division and the system of convex objects with Minkowski addition & decomposition is really striking. We present an idea of the shape decomposition into prime shapes, which are analogue of the prime numbers and indecomposable ones. Here, we concentrate the discussion on binary images, and present some propositions on the indecomposability problem.