Graph/Knot Theoretical Analysis and Generation for Impossible Figures

Author:

Tarui Kento, ,Dong Fangyan,Hatakeyama Yutaka,Hirota Kaoru,

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.

Publisher

Fuji Technology Press Ltd.

Subject

Artificial Intelligence,Computer Vision and Pattern Recognition,Human-Computer Interaction

Reference12 articles.

1. C. C. Adams, “The Knot Book,” Freeman, pp. 1-30, 2001.

2. T. M. Cowan, “The theory of braids and the analysis of impossible figures, Journal of Mathematical Psychology,” Vol.11, pp. 190-212, 1974.

3. T. M. Cowan, “Organizing the properties of impossible figures, Perception,” Vol.6, pp. 41-56, 1977.

4. B. Mohar and C. Thomassen, “Graphs on Surfaces,” Johns Hopkins University Press, pp. 3-98, 2001.

5. D. A. Huffman, “Impossible objects as nonsense sentences,” Machine Intelligence, Vol.6, pp. 295-323, 1971.

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Torus Figure Generating System Based on Graph Theoretical Representation and Topological Analysis;Journal of Japan Society for Fuzzy Theory and Intelligent Informatics;2008

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