Remarks on Recognizability of Four-Dimensional Topological Components
- 10.2991/jrnal.2014.1.3.9How to use a DOI?
- digital geometry, interlocking component, one marker automaton, three-dimensional automaton, topological component, Turing machine
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.
- © 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/).
Cite this article
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 -