CAREER: The Logic of Grouping and Perceptual Organization

This project will investigate one of the most basic aspects of human perceptual intelligence, the ability to organize the visual world. Perceptual organization---the process whereby individual bits of the visual image are aggregated into coherent, meaningful wholes---is a fundamental process that is known to influence many other aspects of visual processing. Yet no mathematically well-defined theory of it exists. The key stumbling block is the pervasive but slippery notion known as ``goodness of form,'' which has resisted attempts to define it rigorously. The approach taken in this proposal is a modern, mathematically-motivated version of the idea that for any visual image, human observers see the simplest interpretation possible. In most previous renditions of this idea, the term ``simplest'' is only very vaguely or subjectively defined. The lack of concrete definitions or algorithms in turn makes it impossible to determine empirically whether the interpretation that human subjects see is, in fact, the simplest. Minimal Model (MM) theory builds on ideas from modern computational logic, with which which the term ``interpretation'' and ``simple'' can be given extremely precise definitions. Under these definitions, it turns out that human judgments---for example, the way line drawings are grouped and organized---correspond closely to the formally minimal interpretation in a well-defined logical language. This minimal interpretation is in a sense the least ``coincidental'' interpretation possible of a given scene; that is, the one that explains the image best. An efficient algorithm exists for rapidly computing the minimal interpretation. Moreover predictions derived from this theory have already been used to answer some long-standing empirical questions about human perceptual grouping. The experiments to be conducted in this project investigate many of the most difficult and important problems in perceptual organization: the perception of occluded figures, the detection of figures amid complex and cluttered scenes, the interpretation of three-dimensional structure, and the representation and categorization of shape. For each of these visual tasks, MM theory makes definite and concrete predictions what people will see under various conditions, and about the limits of the visual system's ability to recover the true structure of the visual world. Educational activities in connection with this project include the creation of new courses at the undergraduate and graduate levels. The proposed undergraduate course (Topics in Cognitive Research) and graduate course (Mathematical Methods in Cognitive Science) emphasize an interdisciplinary approach to research in which both behavioral and computational studies are emphasized.