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JACIII Vol.11 No.10 pp. 1262-1273
doi: 10.20965/jaciii.2007.p1262
(2007)

Paper:

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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
Published:
December 20, 2007
Creative Commons License
Keywords:
graph theory, knot theory, impossible figure, computer vision, visual psychology
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.
Cite this article as:
K. Tarui, F. Dong, Y. Hatakeyama, and K. Hirota, “Graph/Knot Theoretical Analysis and Generation for Impossible Figures,” J. Adv. Comput. Intell. Intell. Inform., Vol.11 No.10, pp. 1262-1273, 2007.
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References
  1. [1] C. C. Adams, “The Knot Book,” Freeman, pp. 1-30, 2001.
  2. [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. [3] T. M. Cowan, “Organizing the properties of impossible figures, Perception,” Vol.6, pp. 41-56, 1977.
  4. [4] B. Mohar and C. Thomassen, “Graphs on Surfaces,” Johns Hopkins University Press, pp. 3-98, 2001.
  5. [5] D. A. Huffman, “Impossible objects as nonsense sentences,” Machine Intelligence, Vol.6, pp. 295-323, 1971.
  6. [6] K. Sugihara, “Three-dimensional realization of anomalous pictures – An application of picture interpretation theory to toy design,” Pattern Recognition, Vol.30, No.7, pp. 1061-1067, 1997.
  7. [7] K. Sugihara, “Studies on mathematical structures of line drawings of polyhedral and their applications to scene analysis,” Researches of the Electrotechnical Laboratory, No.800, pp. 1-22, 1979 (in Japanese).
  8. [8] K. Sugihara, “Classification of impossible objects,” Perception, Vol.11, pp. 65-74, 1982.
  9. [9] L. Ros and F. Thomas, “Overcoming superstrictness in line drawing interpretation,” IEEE Trans. Pattern Analysis and Machine Intelligence, Vol.24, pp. 456-466, 2002.
  10. [10] J. Liu and Y. T. Lee, “A graph-based method for face identification from a single 2D line drawing,” IEEE Trans. Pattern Analysis and Machine Intelligence, Vol.23, pp. 1106-1119, 2001.
  11. [11] J. Liu and X. T. Tang, “Evolutionary search for faces from line drawings,” IEEE Trans. Pattern Analysis and Machine Intelligence, Vol.27, pp. 861-872, 2005.
  12. [12] Y. Sun and Y. T. Lee, “Topological analysis of a single line drawing for 3D shape recovery,” Proc. Graphite, pp. 167-172, 2004.

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