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Davis Cope, Barbara Blakeslee, Mark E. McCourt; Spatial filter efficiency and implications for center-surround receptive field parameters. Journal of Vision 2014;14(15):74. doi: https://doi.org/10.1167/14.15.74.
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© ARVO (1962-2015); The Authors (2016-present)
The receptive field associated with a neuron acts as a spatial filter. We define a conversion efficiency factor (CEF) for spatial filters as the product of a spatial domain term and a frequency domain term where the respective terms involve standard deviations associated with the filter and its Fourier transform. The CEF has properties which provide an absolute scale for evaluating spatial filters: 1) CEFs are dimensionless and invariant under translation and rotation; 2) CEFs have a simple intuitive interpretation as an index of the trading relations between specificity in the spatial- versus frequency-domains (specifically, smaller CEF values imply that a given change in the frequency domain can be achieved by smaller changes in the space domain receptive field, and vice versa); and 3) CEFs have an absolute smallest value determined by the Uncertainty Principle. This theorem of Fourier analysis is named for its original application in quantum mechanics and was introduced in its one-dimensional form as a fundamental principle in signal processing by Gabor (1946). We discuss two CEFs, one based on a weak form of the two-dimensional Uncertainty Principle (Daugman, 1985), and one based on a strong form which is introduced here. A CEF provides a means for comparing spatial filters and thus for making testable predictions of observable filter parameters. We apply this approach to difference-of-circular-gaussians spatial filters, the standard receptive field model for center-surround neurons, using published parameter values spanning some thirty years.
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