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Vicky Froyen, Jacob Feldman, Manish Singh; Bayesian Hierarchical Grouping: perceptual grouping as mixture estimation. Journal of Vision 2014;14(10):591. doi: 10.1167/14.10.591.
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© ARVO (1962-2015); The Authors (2016-present)
We propose a novel Bayesian framework for perceptual grouping based on the idea of mixture models, called Bayesian Hierarchical Grouping (BHG). In BHG we assume that the observed configuration of visual elements was generated by a set of distinct mixture components ("objects"), each of which generates image elements stochastically under some probabilistic assumptions (which define an object class). Grouping, in this framework, means estimating the number and the parameters of the mixture components that generated the image, including estimating which image elements are "owned" by which components. BHG encompasses as special cases a number of classical perceptual grouping problems, including dot clustering, contour integration, and part decomposition. Moreover, unlike some competing models, BHG allows us to quantify the degree of belief for each competing grouping hypothesis. We present an algorithmic implementation of the framework, based on the hierarchical clustering approach of Heller & Gharamani (2005), illustrating it with examples drawn from each of the above problems. Although in principle there is an exponential number of competing grouping hypotheses, this framework allows a tractable approximation of the posterior. The output is an intuitive hierarchical representation of image elements, which gives an explicit decomposition of the image into mixture components, along with estimates of the probability of various candidate decompositions. Moreover the framework can generate predictive estimates of missing data, which provides intuitive predictions of amodally completed shapes. We show that the BHG accounts well for human grouping judgments, and gives good fits for our own human data as well as data drawn from the literature. Because BHG provides a principled quantification of the plausibility of grouping interpretations over a wide range of grouping problems, we argue that it provides an appealing, and unifying, formalization of the elusive Gestalt notion of Prägnanz.
Meeting abstract presented at VSS 2014
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