Computational Geometry in the Human Brain - Discrete and Computational Geometry and Graphs - page 144

Computational Geometry in the Human Brain

B

Kokichi Sugihara (

)

Graduate School of Advanced Mathematical Sciences,
Meiji University, 4-21-1 Nakano, Nakano-ku, Tokyo 164-8525, Japan
[e-mail]
http://home.mims.meiji.ac.jp/~sugihara

Abstract. Geometric information processing in the human brain is very
different from that in a computer: it is slow, local, and imprecise. How-
ever, 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 geomet-
ric algorithms for computers by presenting a new algorithm for straight
skeletons.

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Keywords: Visual illusion Human vision Robust geometric algo-

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rithm Topology-oriented approach Brain computing Zollner illusion

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Ouchi illusion Impossible motion Straight skeleton

1 Introduction

Computational geometry is the field in which geometric algorithms are designed
for computers [ 5 , 7 , 17 ]. Computers are much more precise than human brains,
and hence the main concern is to make these algorithms as ecient as possible
[ 1 ]. Indeed, a huge number of very ecient algorithms have been established, and
sometimes these are the most ecient, i.e., optimal, in terms of the order of the
computational time with respect to the problem size. In this sense, computational
geometry is one of the most successful areas of computer science.
However, we note that computational geometry mainly treats well-defined
problems, while in the real world, we encounter many geometric problems that
are not well defined and cannot be solved easily by the current techniques of
computational geometry. Such problems include, for example, image pattern
recognition and scene understanding [ 3 ].
The human brain, on the other hand, seems to be able to solve those problems
relatively easily. We receive geometric information about the world around us in
the form of projected images on the retina, and our brains process those images
and understand the scenes in front of us without any major diculties. This
ability is surprising when we recall that the computations of the human brain
are slow and imprecise, compared to electronic computers. If we can understand
c