Remarks on Recognizability of Four-Dimensional Topological Components

DOI

10.2991/jrnal.2014.1.3.9How to use a DOI?

Keywords

digital geometry, interlocking component, one marker automaton, three-dimensional automaton, topological component, Turing machine

Abstract

The study of four-dimensional automata as the computational model of four-dimensional pattern processing has been meaningful. However, it is conjectured that the three-dimensional pattern processing has its our difficulties not arising in two- or three-dimensional case. One of these difficulties occurs in recognizing topological properties of four-dimensional patterns because the four-dimensional neighborhood is more complicated than two- or three-dimensional case. Generally speaking, a property or relationship is topological only if it is preserved when an arbitrary ’ rubber-sheet ’ distortion is applied to the pictures . For example, adjacency and connectedness are topological ; area, elongatedness, convexity, straightness, etc. are not. In recent years, there have been many interesting papers on digital topological properties. For example, an interlocking component was defined as a new topological property in multi-dimensional digital pictures, and it was proved that no one marker automaton can recognize interlocking components in a three-dimensional digital picture. In this paper, we deal with recognizability of topological components by four-dimensional Turing machines, and investigate some properties.

Copyright

© 2013, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Makoto Nagatomo
AU  - Makoto Sakamoto
AU  - Tatsuma Kurogi
AU  - Satoshi Ikeda
AU  - Masahiro Yokomichi
AU  - Hiroshi Furutani
AU  - Takao Ito
AU  - Yasuo Uchida
AU  - Tsunehiro Yoshinaga
PY  - 2014
DA  - 2014/12/15
TI  - Remarks on Recognizability of Four-Dimensional Topological Components
JO  - Journal of Robotics, Networking and Artificial Life
SP  - 212
EP  - 215
VL  - 1
IS  - 3
SN  - 2352-6386
UR  - https://doi.org/10.2991/jrnal.2014.1.3.9
DO  - 10.2991/jrnal.2014.1.3.9
ID  - Nagatomo2014
ER  -