Directed diffusion and orientational harmonics: Neural network models of long-range boundary completion through short-range interactions

This dissertation presents neural network models of boundary completion for visual scenes. The dissertation first models a variant of the Boundary Contour System/Feature Contour System (BCS/FCS) model of visual perception. Large scale cooperative cells of the BCS/FCS are replaced by directed diffusion of oriented information between small orientation-specific cells. Such a model can complete either straight or smoothly curved boundaries between spatially disparate inducers. Long-range boundary completion hereby emerges via parallel action of multiple local elements, in the spirit of the perceptual grouping principles proposed by Gestalt psychologists. Model 1-D and 2-D computer simulations are in qualitative agreement with psychophysical data on the perception of straight and curved illusory boundaries when the configuration of inducing visual stimuli is varied.;The directed diffusion model is then extended to include a closed ring of orientation-specific cells at each point in space. These cells can complete boundaries from vertices defined by multiple combinations of intersecting oriented edges. Neural connections within the ring of cells create a harmonic resonance among the orientation-specific cells. The resonance emphasizes combinations of oriented inputs corresponding to the natural harmonics of the ring of cells, and leads to cooperative and competitive interactions between different harmonics. These interactions are described in terms of Fourier analysis of the orientational signal. They lead to specific predictions of the perceived grouping of visual stimuli in various configurations. In this fashion, the model emulates Gestalt rules for visual grouping, such as proximity, good continuation, and symmetry. The periodicity of the orientational harmonic system generates a compressed and rotation-invariant representation of the vertex input pattern.;The final part of the dissertation shows how the orientational harmonic model can be embedded within a neural architecture that is capable of both bottom-up abstraction, or information compression, as well as top-down priming, or figural completion.