Authors
Makoto Nagatomo, Makoto Sakamoto, Tatsuma Kurogi, Satoshi Ikeda, Masahiro
Yokomichi, Hiroshi Furutani, Takao Ito, Yasuo Uchida, Tsunehiro Yoshinaga
Corresponding Author
Makoto Sakamoto
Available Online 15 December 2014.
DOI
https://doi.org/10.2991/jrnal.2014.1.3.9
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 ALife Robotics Corp. Ltd..
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).