Computational Geometry in the Human Brain - Discrete and Computational Geometry and Graphs - page 158

The strategy we followed for designing Algorithm 2 can be considered to be
a topology-oriented approach, which we have proposed as a basic principle for
designing robust geometric algorithms [ 22 , 25 ]. Indeed, in this approach, the basic
part of the algorithm is described in only topological terms, and the numerical
data are used only for selecting the most promising branch of the processing.
Thus we can say that the idea behind simulating the persistency of the human
brain is very similar to the topological approach for robust geometric algorithms.
6 Concluding Remarks
We observed how the human brain processed computations by looking at three
visual illusions: the Zollner illusion, the Ouchi illusion, and the impossible motion
illusion, and we then composed a new algorithm for computing straight skeletons.
Based on our observations, we pointed out that designing algorithms based on
how the human brain computes is very similar to the topology-oriented approach,
which we have developed for a long time. Thus, the topology-oriented approach
can be used if we want to mimic the processing of the human brain.
Acknowledgment. This research is supported by the Grant-in-Aid for Challeng-
ing Exploratory Research No. 24650015 and Scientific Research (B) No. 24360039 of
MEXT.
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