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The quantized geometry of visual space: The coherent computation of depth, form, and lightness

Published online by Cambridge University Press:  04 February 2010

Stephen Grossberg
Center for Adaptive Systems, Department of Mathematics, Boston University, Boston, Mass. 02215


A theory is presented of how global visual interactions between depth, length, lightness, and form percepts can occur. The theory suggests how quantized activity patterns which reflect these visual properties can coherently fill-in, or complete, visually ambiguous regions starting with visually informative data features. Phenomena such as the Cornsweet and Craik–O'Brien effects, phantoms and subjective contours, binocular brightness summation, the equidistance tendency, Emmert's law, allelotropia, multiple spatial frequency scaling and edge detection, figure-ground completion, coexistence of depth and binocular rivalry, reflectance rivalry, Fechner's paradox, decrease of threshold contrast with increased number of cycles in a grating pattern, hysteresis, adaptation level tuning, Weber law modulation, shift of sensitivity with background luminance, and the finite capacity of visual short term memory are discussed in terms of a small set of concepts and mechanisms. Limitations of alternative visual theories which depend upon Fourier analysis, Laplacians, zero-crossings, and cooperative depth planes are described. Relationships between monocular and binocular processing of the same visual patterns are noted, and a shift in emphasis from edge and disparity computations toward the characterization of resonant activity-scaling correlations across multiple spatial scales is recommended. This recommendation follows from the theory's distinction between the concept of a structural spatial scale, which is determined by local receptive field properties, and a functional spatial scale, which is defined by the interaction between global properties of a visual scene and the network as a whole. Functional spatial scales, but not structural spatial scales, embody the quantization of network activity that reflects a scene's global visual representation. A functional scale is generated by a filling-in resonant exchange, or FIRE, which can be ignited by an exchange of feedback signals among the binocular cells where monocular patterns are binocularly matched.

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Copyright © Cambridge University Press 1983

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