1980
@article{Dau1980,
vgclass = {refpap},
author = {John G. Daugman},
title = {Two-dimensional Spectral Analysis of Cortical Receptive
Field Profiles},
journal = {Vision Research},
volume = {20},
number = {10},
pages = {847--856},
year = {1980},
url = {http://dx.doi.org/10.1016/0042-6989(80)90065-6},
abstract = {Most vision research embracing the spatial frequency
paradigm has been conceptually and mathematically a one-dimensional
analysis of two-dimensional mechanisms. Spatial vision models and the
experiments sustaining them have generally treated spatial frequency as
a one-dimensional variable, even though receptive fields and retinal
images are two-dimensional and linear transform theory obliges any
frequency analysis to preserve dimension. Four models of cortical
receptive fields are introduced and studied here in 2D form, in order
to illustrate the relationship between their excitatory/inhibitory
spatial structure and their resulting 2D spectral properties. It
emerges that only a very special analytic class of receptive fields
possess independent tuning functions for spatial frequency and
orientation; namely, those profiles whose two-dimensional Fourier
Transforms are expressible as the separable product of a radial
function and an angular function. Furthermore, only such receptive
fields would have the same orientation tuning curve for single bars as
for gratings. All classes lacking this property would describe cells
responsive to different orientations for different spatial frequencies
and vice versa; this is shown to be the case, for example, for the
Hubel \& Wiesel model of cortical orientation-tuned simple cells
receiving inputs from an aligned row of center/surround LGN cells. When
these results are considered in conjunction with psychophysical
evidence for nonseparability of spatial frequency and orientation
tuning properties within a "channel", it becomes mandatory that future
spatial vision research of the Fourier genre take on an explicitly
two-dimensional character.},
}