Efficient regularity-based grouping

This paper summarizes a novel logic-based approach to grouping and perceptual organization, and presents novel efficient methods for computing interpretations in this framework. Grouping interpretations are first defined as logical structures, built out of atomic premises ("regularities") that are derived from considerations of non-accidentalness. These interpretations can then be partially ordered by their degree of regularity or constraint (measured numerically by their codimension). The genericity constraint-the principle that interpretations should minimize coincidences in the observed configuration-dictates that the preferred interpretation will be the minimum in this partial order, i.e. the interpretation with maximum codimension. The preferred interpretation, called the qualitative parse, corresponds neatly to the interpretation intuitively preferred by human observers. As a side-effect, the "most salient" or most structured part of the scene can be identified, as the highest-codimension subtree of the qualitative parse. An efficient (O(n/sup 2/)) method for computing the maximum codimension interpretation is presented, along with examples.