The Role of Propagation and Medial Geometry in Human Vision

A key challenge underlying theories of vision is how the spatially restricted, retinotopically represented feature computations can be integrated to form abstract, coordinate-free object models. A resolution likely depends on the use of intermediate-level representations which can on the one hand be populated by local features and on the other hand be used as atomic units underlying the formation of, and interaction with, object hypotheses. The precise structure of this intermediate representation derives from the varied requirements of a range of visual tasks, which motivate a significant role for incorporating a geometry of visual form. The need to integrate input from features capturing surface properties such as texture, shading, motion, color, etc., as well as from features capturing surface discontinuities such as silhouettes, T-junctions, etc., implies a geometry which captures both regional and boundary aspects. Curves, as a geometric model of boundaries, have been extensively and explicitly used as an intermediate representation in computational, perceptual, and physiological studies. However, the medial axis which has been popular in computer vision as a geometric regionbased model of the interior of closed boundaries, has not been explicitly used as an intermediate representation. We present a unified theory of perceptual grouping and object recognition where the intermediate representation is a visual fragment which itself is based on the medial axis. Through various sequences of transformations of the medial axis representation, visual fragments are grouped in various configurations to form object hypotheses, and are related to stored models. The mechanisms underlying both the computation and the transformation of the medial axis is a lateral wave propagation model. Recent psychophysical experiments depicting contrast sensitivity map peaks at the medial axes of stimuli, and experiments on perceptual filling-in, and brightness induction and modulation, are consistent with both the use of a medial axis representation and a propagationbased scheme. Also, recent neurophysiological recordings in V1 correlate with the medial axis hypothesis and a horizontal propagation scheme. This evidence supports a geometric computational paradigm for processing sensory data where both dynamic in-plane propagation and feedforward-feedback connections play an integral role.