Perceptual Grouping by Selection of a Logically Minimal Model

This paper presents a logic-based approach to grouping and perceptual organization, called Minimal Model theory, and presents efficient methods for computing interpretations in this framework. Grouping interpretations are first defined as logical structures, built out of atomic qualitative scene descriptors (“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 logical depth). 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 depth. This maximum-depth interpretation, also called the minimal model or minimal interpretation, is in a sense the “simplest” (algebraically minimal) interpretation available of the image configuration. As a side-effect, the “most salient” or most structured part of the scene can be identified, as the maximum-depth subtree of the minimal model. An efficient (O(n2)) method for computing the minimal interpretation is presented, along with examples. Computational experiments show that the algorithm performs well under a wide range of parameter settings.