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Summary: In Third IEEE-CS Workshop on Perceptual Organization in Computer Vision at
International Conference of Computer Vision, Vancouver, July 2001.
A Field Model for Contour Organization
and Partial Di erential Equations
Jonas August and Steven W. Zucker Yale University
From its earliest roots in Gestalt psychology, thinking about perceptual organization has
been predominantly discrete in nature. For example, in one standard grouping demonstra-
tion, a subject is presented with a stimulus consisting of perhaps a dozen dots, and the
theoretical task is to explain why the subject chose one particular partitioning of the dots
among the nite set of possibilities. In illusory contour perception as well, the stimulus is
a number of inducing endpoints, where one seek to understand the (perceptual) selection
of one of a nite set of arrangements. The \units" of perceptual organization here (dots,
endpoints) are discrete, and typically few in number. Arti cial intelligence has reinforced
this view, where the units of perceptual organization become the \atoms" of LISP programs
and symbol manipulation. Modern graph theoretic models of perceptual organization in
computer vision have entrenched this discrete thinking, even to the extent that the formal
task of perceptual organization has become identi ed with the grouping of a nite set of
( xed) entities.
Unfortunately, natural images are ambiguous, and not only in terms of the groupings of
discrete units: even the existence or absence of these units is uncertain. In contour perception
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