Local Patterns and Connectivity Indexes in a Three Dimensional Digital Picture

Junichiro Toriwaki¹* and Tatsuhiro Yonekura²

¹Department of Information Engineering, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan
²Department of Computer and Information Sciences, School of Engineering, Ibaraki University, 4-12-1, Nakanarusawa-cho, Hitachi, Ibaraki 316-8511, Japan
*E-mail address: toriwaki@nuie.nagoya-u.ac.jp

(Received October 5, 2002; Accepted November 5, 2002)

Keywords: Digital Picture Processing, Local Patterns, Connectivity Index, Digital Topology, Discrete Geometry, Three Dimensional Picture

Abstract. In this paper we present the basic data of the local pattern on the area of the size of 3 3 3 voxels denoted as N₃₃₃(x) on a three dimensional digital binary picture. Topological features called the connectivity index are studied by calculating them for all possible patterns. Main results are summarized as follows.
(1)List of all possible values of the connectivity index
(2)Examples of local patterns on N₃₃₃(x) which take specific values of the connectivity index.
(3)Numbers of different patterns on N₃₃₃(x) for all possible values of the connectivity index.
All arrangements of 0 and 1 on N₃₃₃(x) (local patterns) were systematically generated by computer, and feature values were calculated.