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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 30, Iss. 5 — May. 1, 2013
  • pp: 1002–1012

Analysis of multidimensional difference-of-Gaussians filters in terms of directly observable parameters

Davis Cope, Barbara Blakeslee, and Mark E. McCourt  »View Author Affiliations


JOSA A, Vol. 30, Issue 5, pp. 1002-1012 (2013)
http://dx.doi.org/10.1364/JOSAA.30.001002


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Abstract

The difference-of-Gaussians (DOG) filter is a widely used model for the receptive field of neurons in the retina and lateral geniculate nucleus (LGN) and is a potential model in general for responses modulated by an excitatory center with an inhibitory surrounding region. A DOG filter is defined by three standard parameters: the center and surround sigmas (which define the variance of the radially symmetric Gaussians) and the balance (which defines the linear combination of the two Gaussians). These parameters are not directly observable and are typically determined by nonlinear parameter estimation methods applied to the frequency response function. DOG filters show both low-pass (optimal response at zero frequency) and bandpass (optimal response at a nonzero frequency) behavior. This paper reformulates the DOG filter in terms of a directly observable parameter, the zero-crossing radius, and two new (but not directly observable) parameters. In the two-dimensional parameter space, the exact region corresponding to bandpass behavior is determined. A detailed description of the frequency response characteristics of the DOG filter is obtained. It is also found that the directly observable optimal frequency and optimal gain (the ratio of the response at optimal frequency to the response at zero frequency) provide an alternate coordinate system for the bandpass region. Altogether, the DOG filter and its three standard implicit parameters can be determined by three directly observable values. The two-dimensional bandpass region is a potential tool for the analysis of populations of DOG filters (for example, populations of neurons in the retina or LGN), because the clustering of points in this parameter space may indicate an underlying organizational principle. This paper concentrates on circular Gaussians, but the results generalize to multidimensional radially symmetric Gaussians and are given as an appendix.

© 2013 Optical Society of America

OCIS Codes
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(070.6110) Fourier optics and signal processing : Spatial filtering
(330.0330) Vision, color, and visual optics : Vision, color, and visual optics
(330.4060) Vision, color, and visual optics : Vision modeling
(330.6110) Vision, color, and visual optics : Spatial filtering
(070.2615) Fourier optics and signal processing : Frequency filtering

ToC Category:
Fourier Optics and Signal Processing

History
Original Manuscript: September 14, 2012
Revised Manuscript: March 28, 2013
Manuscript Accepted: March 28, 2013
Published: April 29, 2013

Virtual Issues
Vol. 8, Iss. 6 Virtual Journal for Biomedical Optics

Citation
Davis Cope, Barbara Blakeslee, and Mark E. McCourt, "Analysis of multidimensional difference-of-Gaussians filters in terms of directly observable parameters," J. Opt. Soc. Am. A 30, 1002-1012 (2013)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-30-5-1002


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