May 2008
Volume 8, Issue 6
Free
Vision Sciences Society Annual Meeting Abstract  |   May 2008
Structural theorems for simple cell receptive fields
Author Affiliations
  • Davis Cope
    Department of Mathematics, North Dakota State University, Fargo, ND
  • Barbara Blakeslee
    Department of Psychology, North Dakota State University, Fargo, ND, and Center for Visual Neuroscience, North Dakota State University, Fargo, ND
  • Mark McCourt
    Department of Psychology, North Dakota State University, Fargo, ND, and Center for Visual Neuroscience, North Dakota State University, Fargo, ND
Journal of Vision May 2008, Vol.8, 802. doi:10.1167/8.6.802
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      Davis Cope, Barbara Blakeslee, Mark McCourt; Structural theorems for simple cell receptive fields. Journal of Vision 2008;8(6):802. doi: 10.1167/8.6.802.

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Abstract

Theorists interested in developing mathematical descriptions and computational models of human spatial vision frequently employ Gabor filters as basis functions. Due to some undesirable features of the Gabor function, in particular the fact that it does not integrate to zero for all spatial phases of the carrier wave, a variety of competing mathematical formulations has been proposed, which include the difference-of-Gaussians, the Laplacian-of-a-Gaussian, the log-Gabor and the Cauchy function, to name a few. Here, we mathematically derive a class of functions based on three cardinal response properties of simple cells. Specifically, receptive field models must satisfy the following criteria: 1) Their response to a spatially homogeneous stimulus must be zero; 2) There must exist a direction (orientation) which produces zero response to sinusoidal grating stimuli; and 3) The response to sinusoidal grating stimuli must be a monotonic function of orientation, increasing from zero to a maximum as orientation changes from the zero response direction. The class of receptive field functions satisfying these criteria includes, as its most representative case, a novel variation of the Gabor filter - the balanced-Gabor - which integrates to zero for all spatial phases of the carrier wave. The balanced Gabor filter possesses all of the desirable features of the standard Gabor model of simple cells and, by virtue of integrating to zero, obviates its chief deficiency.

Cope, D. Blakeslee, B. McCourt, M. (2008). Structural theorems for simple cell receptive fields [Abstract]. Journal of Vision, 8(6):802, 802a, http://journalofvision.org/8/6/802/, doi:10.1167/8.6.802. [CrossRef]
Footnotes
 Supported by R01 EY014015 and P20 RR020151.
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