Paper:
Language: English:

Graph/Knot Theoretical Analysis and Generation for Impossible Figures

Kento Tarui^, Fangyan Dong^, Yutaka Hatakeyama^**,
and Kaoru Hirota^*

^*Hirota Laboratory, Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama 226-8502, Japan
^**Center of Medical Information Science, Medical School, Kochi University, Kohasu Oko-cho Nankoku-city Kochi

Received: July 13, 2007

Accepted: August 27, 2007

Keywords: graph theory, knot theory, impossible figure, computer vision, visual psychology

Journal ref: Journal of Advanced Computational Intelligence and Intelligent Informatics, Vol.11, No.10 pp. 1262-1273, 2007

Abstract

An algorithm to represent impossible multibar figures and their subclass of torus figures is proposed based on graph and knot theory. A multibar type graph, which is an abstract concept of multibar figures, is defined by the junction graph that represents the connections of the lines. It is shown that the junction graph is able to characterize multibar figures where this characterization is realized according to the type of the multibar type graph. An automatic drawing system of torus figures is also presented by analyzing junction graphs that construct the shapes of corners of torus figures. The proposed method aims a basic tool for experiments in visual psychology and possible/impossible figures generation.

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