Analytic solution of stochastic completion fields (original) (raw)
Abstract.
We use generalized particle trajectories to derive an analytic expression characterizing the probability distribution of boundary-completion shape. This is essential to the understanding of the perceptual phenomenon of illusory (subjective) contours. The particles' dynamics include Poisson-distributed ensembles of driving forces as well as particle decay. The resulting field, representing completed surface boundaries, is characterized by the fraction of particles at \(\vec{x}\) with velocity \(\dot{\vec{x}}\). The distributions are projectively covariant in the sense that fields calculated in any lower-dimensional projection correspond to the projections of fields calculated in any higher dimension. Being analytic, the relationship between velocity, diffusivity, and decay can be made readily apparent.
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Authors and Affiliations
- NEC Research Institute, 4 Independence Way, Princeton, NJ 08540, USA, , , , , , US
K.K. Thornber & L.R. Williams
Authors
- K.K. Thornber
- L.R. Williams
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Received: 13 September 1995 / Accepted in revised form: 16 April 1996
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Thornber, K., Williams, L. Analytic solution of stochastic completion fields .Biol Cybern 75, 141–151 (1996). https://doi.org/10.1007/s004220050282
- Issue date: August 1996
- DOI: https://doi.org/10.1007/s004220050282