Remarks on Recognizability of Four-Dimensional Topological Components

Makoto Nagatomo, Makoto Sakamoto, Tatsuma Kurogi, Satoshi Ikeda, Masahiro Yokomichi, Hiroshi Furutani, Takao Ito, Yasuo Uchida, Tsunehiro Yoshinaga
2014 Journal of Robotics, Networking and Artificial Life (JRNAL)  
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
more » ... eaking, 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.
doi:10.2991/jrnal.2014.1.3.9 fatcat:b65vx3udrreyrgukw753x5tg5m