TOPOLOGY-PRESERVING DEFORMATIONS OF 2-VALUED DIGITAL PICTURES

In a two-valued digital picture (in brief: ''image''), it is well know n that changing a ''simple'' pixel from 1 to 0 or vice versa preserves the topology of the image-specifically, it preserves the adjacency/su rroundedness relations between the connected components of 0's and l's . We prove here that the converse is also true: Any two topologically equivalent images can be transformed into one another by changes in th e values of simple pixels. As a preliminary, we show how an image can be magnified by an arbitrary integer factor, or translated along an ar bitrary path, or rendered ''well-composed,'' by repeatedly changing th e values of simple pixels. The relationship between the simple pixel m ethod and other types of ''topology-preserving'' deformations of image s is also briefly discussed. (C) 1998 Academic Press.