Perceptual grouping as bayesian estimation of mixture models
We propose a Bayesian approach to perceptual grouping in which the goal of the computation is to estimate the organization that best explains an observed configuration of image elements. We formalize the problem as a mixture estimation problem, where it is assumed that the configuration of elements is generated by a set of distinct components ("objects" or "clusters"), whose underlying parameters we seek to estimate (including location and "ownership" of image elements). Among other parameters, we can estimate the number of components in the image, given a set of assumptions about the underlying generative model. We illustrate our approach, and compare it to human perception, in the context of one such generative class: Gaussian dot-clusters. We find that numerical estimates derived from our model closely match subjects' perceptual estimates of number of clusters. Thus our Bayesian approach to perceptual grouping, as one side-effect, effectively models the perception of cluster numerosity.