Nonlinear attractive force model for perceptual clustering and geometrical illusions

Hiroyuki Matsunaga, Kiichi Urahama

Research output: Contribution to journalArticlepeer-review


A mathematical model based on an optimization formulation is presented for perceptual clustering of dot patterns. The features in the present model are its nonlinearity enabling the model to reveal hysteresis phenomena and its scale invariance. The clustering of dots is given by the mutual linking of dots by virtual lines. Every dot is assumed to be perceived at locations displaced from their original places. It is exemplified with simulations that the model can produce a hierarchical clustering of dots by variation in thresholds for the wiring of virtual lines and also the model can additionally reproduce some geometrical illusions semiquantitatively. This model is further extended for perceptual grouping in line segment patterns and geometrical illusions observed in those patterns are reproduced by the extended model.

Original languageEnglish
Pages (from-to)1587-1594
Number of pages8
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Issue number10
Publication statusPublished - 1996
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Applied Mathematics
  • Electrical and Electronic Engineering
  • Computer Graphics and Computer-Aided Design


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