Analytic solution of stochastic completion fields

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.