Topology-Preserving Deformations of Two-Valued Digital Pictures

Abstract

In a two-valued digital picture (in brief: “image”), it is well known that changing a “simple” pixel from 1 to 0 or vice versa preserves the topology of the image—specifically, it preserves the adjacency/surroundedness relations between the connected components of 0's and 1's. We prove here that the converse is also true: Any two topologically equivalent images can be transformed into one another by changes in the values of simple pixels. As a preliminary, we show how an image can be magnified by an arbitrary integer factor, or translated along an arbitrary path, or rendered “well-composed,” by repeatedly changing the values of simple pixels. The relationship between the simple pixel method and other types of “topology-preserving” deformations of images is also briefly discussed.