Perceptual Completion and Saliency Computations in Areas V1 and V2 of Visual Cortex

Lance Williams

In spite of a wealth of experimental data obtained through visual psychophysics and electrophysiology, a comprehensive theory of perceptual completion and saliency computations in areas V1 and V2 of visual cortex still eludes us. It is my belief that the primary reason for the lack of progress has been the absence of a sufficiently abstract characterization of the underlying computational goal of these processes. In a series of recent papers, my colleagues and I have proposed that the goal of these processes is to compute a distribution of closed contours consistent with position and scale constraints derived by spatial filtering ( Williams and Jacobs '97a, Williams and Jacobs '97b, Thornber and Williams '96 ). The novelty of our approach follows from the use of the mathematical device of a particle moving with constant speed in a direction given by a Brownian motion to characterize the probability distribution of natural shapes. Because of the connection between Brownian motion and diffusion processes, this device has allowed us to bridge the conceptual gulf between the abstract goal and its concrete embodiment in a network of neurons. The long-term objective of my research is to develop more general neural models which can compute scale-invariant distributions of closed contours for multiple occluded objects and also account for unexplained phenomena such as orientation selectivity and observed phase correlation in neural firing patterns.