Topology-Preserving Deformations of Two-Valued Digital Pictures

✍ Scribed by Azriel Rosenfeld; T.Yung Kong; Akira Nakamura

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 236 KB
• Volume: 60
• Category: Article
• ISSN: 1077-3169
• DOI: 10.1006/gmip.1997.0459

✦ Synopsis

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 "wellcomposed," 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.