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Computational Geometry in the Human Brain

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8845))

Abstract

Geometric information processing in the human brain is very different from that in a computer: it is slow, local, and imprecise. However, humans are able to manage a huge amount of visual data, can understand the scenes in front of them, and thus can survive in their daily lives. We use visual illusions to investigate how the human brain treats geometric data, and we point out the similarities between the robustness of human geometric processing and the topology-oriented principle, which we have proposed for use in the design of robust geometric algorithms for computers by presenting a new algorithm for straight skeletons.

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References

  1. Aho, A.V., Hopcroft, J.E., Ullmann, J.D.: The Design and Analysis of Computer Algorithms. Addison Wesley, Reading (1974)

    MATH  Google Scholar 

  2. Aichholzer, O., Aurenhammer, F.: Straight skeletons for general polygonal figures in the plane. In: Cai, J.-Y., Wong, C.K. (eds.) COCOON 1996. LNCS, vol. 1090, pp. 117–126. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  3. Ballard, D.H., Brown, C.M.: Computer Vision. Prentice Hall, Englewood Cliffs (1982)

    Google Scholar 

  4. Cheng, S.-W., Vigneron, A.: Motorcycle graphs and straight skeletons. In: Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 156–165 (2002)

    Google Scholar 

  5. de Berg, M., Cheong, O., van Kreveld, M., Overmars, M.: Computational Geometry: Algorithms and Applications. Springer, Heidelberg (2008)

    Book  Google Scholar 

  6. Demaine, E.D., Demaine, M.L., Lubiw, A.: Folding and cutting paper. In: Akiyama, J., Kano, M., Urabe, M. (eds.) JCDCG 1998. LNCS, vol. 1763, pp. 104–118. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  7. Edelsbrunner, H.: Algorithm in Combinatorial Geometry. Springer, Berlin (1987)

    Book  Google Scholar 

  8. Fermüller, C., Pless, R., Aloimonos, Y.: The Ouchi illusion as an artifact of biased flow estimation. Vis. Res. 40, 77–96 (2000)

    Article  Google Scholar 

  9. Fermüller, C., Malm, H.: Uncertainty in visual processes predicts geometric optical illusions. Vis. Res. 44, 727–749 (2004)

    Article  Google Scholar 

  10. Fogaras, D., Sugihara, K.: Topology-oriented construction of line arrangements. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. E85-A, 930–937 (2002)

    Google Scholar 

  11. Goto, T., Tanaka, H.: Handbook of the Science of Illusion. University of Tokyo Press, Tokyo (2005)

    Google Scholar 

  12. Huber, S., Held, M.: A fast straight-skeleton algorithm based on generalized motorcycle graphs. Int. J. Comput. Geom. Appl. 22, 471–498 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  13. Marr, D.: Vision. W. H. Freeman, New York (1982)

    Google Scholar 

  14. Ninio, J.: The Science of Illusions. Cornell University Press, Ithaca (2001)

    Google Scholar 

  15. Minakawa, T., Sugihara, K.: Topology-oriented construction of three-dimensional convex hulls. Optim. Methods Softw. 10, 357–371 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  16. Ouchi, H.: Japanese Optical and Geometrical Art. Dover, New York (1977)

    Google Scholar 

  17. Preparata, F., Shamos, M.I.: Computational Geometry–An Introduction. Springer-Verlag, New York (1985)

    Google Scholar 

  18. Sugihara, K.: Classification of impossible objects. Perception 11, 65–74 (1982)

    Article  Google Scholar 

  19. Sugihara, K.: Machine Interpretation of Line Drawings. The MIT Press, Cambridge (1986)

    Google Scholar 

  20. Sugihara, K.: A robust and consistent algorithm for intersecting convex polyhedra. Comput. Graph. Forum 13(Conference Issue), C-45–C-54 (1994). (EUROGRAPHICS’94, September 12–16, 1994, Oslo, Norway)

    Google Scholar 

  21. Sugihara, K.: A characterization of a class of anomalous solids. Interdisc. Inf. Sci. 11, 149–156 (2005)

    MathSciNet  Google Scholar 

  22. Sugihara, K.: Robust geometric computation based on the principle of independence. Nonlinear Theory Appl. IEICE 2, 32–42 (2011)

    Article  Google Scholar 

  23. Sugihara, K.: Design of pop-up cards based on weighted straight skeleton. In: 10th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2013), pp. 23–28 (2013)

    Google Scholar 

  24. Sugihara, K., Iri, M.: Two design principles of geometric algorithms in finite-precision arithmetic. Appl. Math. Lett. 2, 203–206 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  25. Sugihara, K., Iri, M.: A robust topology-oriented incremental algorithm for Voronoi diagrams. Int. J. Comput. Geom. Appl. 4, 179–228 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  26. Sugihara, K., Iri, M., Inagaki, H., Imai, T.: Topology-oriented implementation–an approach to robust geometric algorithms. Algorithmica 27, 5–20 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  27. Tomoeda, A., Sugihara, K.: Computational creation of a new illusionary solid sign. In: 9th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2012), pp. 144–147 (2012)

    Google Scholar 

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Acknowledgment

This research is supported by the Grant-in-Aid for Challenging Exploratory Research No. 24650015 and Scientific Research (B) No. 24360039 of MEXT.

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Correspondence to Kokichi Sugihara .

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© 2014 Springer International Publishing Switzerland

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Sugihara, K. (2014). Computational Geometry in the Human Brain. In: Akiyama, J., Ito, H., Sakai, T. (eds) Discrete and Computational Geometry and Graphs. JCDCGG 2013. Lecture Notes in Computer Science(), vol 8845. Springer, Cham. https://doi.org/10.1007/978-3-319-13287-7_13

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  • DOI: https://doi.org/10.1007/978-3-319-13287-7_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-13286-0

  • Online ISBN: 978-3-319-13287-7

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