A Probabilistic Approach to Perceptual Grouping

distributions over the space of possible image feature groupings. for higher level processing [17, 34]. The framework can be used to find several of the most probable Less progress has been made in determining how feapartitions of image features into groupings, rather than just tures should be organized into more abstract structures to returning a single partition of the features as do most feature be used by higher level visual processes. Much of the work grouping techniques. In addition to the groupings themselves, in this area has been driven by the early work of the Gestalt the probability of each partition is computed, providing inforpsychologists, who claimed that humans group features mation on the relative probability of multiple partitions that based on several principles, including proximity, symmetry, few grouping techniques offer. In determining the probability continuation, closure, and familiarity [21, 44]. The work distribution of groupings, no parameters are estimated, thus of the Gestalt psychologists has inspired a number of comeliminating problems that occur with small data sets and outliputer vision approaches to perceptual grouping [2, 6, 19, ers such as the compounding of errors that can occur when 26, 23, 34, 38]. Typically, these computational approaches parameters are estimated and the estimated parameters are rely on thresholds (e.g., a threshold on the difference beused in the next grouping step. We have instantiated our framework for the two special cases of grouping line segments into tween orientation of line segments [26], or on the linking straight lines and for grouping bilateral symmetries with paralradius described in [6]), or on certainty measures that are lel axes, where bilateral symmetries are formed by pairs of derived in an ad hoc fashion (e.g., basing the certainty edges. Results are presented for these cases on several real of grouping two line segments on the proximity of their images.  1996 Academic Press, Inc. endpoints [23], or using a decaying exponential to define