A Generic Grouping Algorithm and Its Quantitative Analysis

This paper presents a generic method for perceptual grouping, and an analysis of its expected grouping quality. The grouping method is fairly general: it may be used for the grouping of various types of data features, and to incorporate diierent grouping cues, operating over feature sets of diierent sizes. The proposed method is divided into two parts: Constructing a graph representation of the available perceptual grouping evidence, and then nding the \best" partition of the graph into groups. The rst stage includes a cue enhancement procedure, which integrates the information available from multi-feature cues into very reliable bi-feature cues. Both stages are implemented using known statistical tools such as Wald's SPRT algorithm and the Maximum Likelihood criterion. The accompanying theoretical analysis of this grouping criterion quantiies intuitive expectations and predicts that the expected grouping quality increases with cue reliability. It also shows that investing more computational eeort in the grouping algorithm leads to better grouping results. This analysis, which quantiies the grouping power of the Maximum Likelihood criterion, is independent of the grouping domain. To our best knowledge, such an analysis of a grouping process is given here for the rst time. Three grouping algorithms, in three diierent domains, are synthesized as instances of the generic method, They demonstrate the applicability and generality of this grouping method.