Spatial Structure of Complex Cell Receptive Fields Measured with Natural Images

Abstract

Neuronal receptive fields (RFs) play crucial roles in visual processing. While the linear RFs of early neurons have been well studied, RFs of cortical complex cells are nonlinear and therefore difficult to characterize, especially in the context of natural stimuli. In this study, we used a nonlinear technique to compute the RFs of complex cells from their responses to natural images. We found that each RF is well described by a small number of subunits, which are oriented, localized, and bandpass. These subunits contribute to neuronal responses in a contrast-dependent, polarity-invariant manner, and they can largely predict the orientation and spatial frequency tuning of the cell. Although the RF structures measured with natural images were similar to those measured with random stimuli, natural images were more effective for driving complex cells, thus facilitating rapid identification of the subunits. The subunit RF model provides a useful basis for understanding cortical processing of natural stimuli.

Complex-Valued Independent Component Analysis of Natural Images

“…Real and imaginary part are Gabor-like filters that are in quadrature-phase. This statistical result is in line with measurements in V1 [12,11] and related empirical models [13].…”

“…In this example the magnitude and the phase in the Fourier domain of two images were exchanged, and the images which were perceptually more similar to the originals were the ones that carried the phase information. Moreover there is experimental evidence of phase coupled Gabor-like filters in V1 [12,11]. For this reason, Daugman [13] suggested that the receptive field in the first stage could be seen as Gabor sensors defined in the complex domain: the real and the imaginary part are essentially the same Gabor filter but with phases in quadrature.…”

Predicting neuronal responses during natural vision

“…Luminance at a point in space may be either excitatory or inhibitory to a phase invariant neuron, depending on the luminance at nearby locations. The image domain model requires consistent excitation or inhibition at each retinotopic position and cannot be used to estimate the STRFs of phase invariant complex cells (DeAngelis et al 1995;Touryan et al 2005).…”

Analysis and interpretation of quadratic models of receptive fields

“…(B) In physiological experiments (i) In physiological experiments, random quadratic forms can be generated by bootstrapping. The spikes can be shuffled 6,10 or the entire spike train can be shifted relative to the stimulus sequence 9,12 (this second possibility is to be preferred if the input stimuli have a temporal structure, i.e., a non-zero autocorrelation) and the same RF estimation procedure used to generate the units under consideration can be applied to the resulting data. The new randomly generated quadratic forms are compatible with the distribution of the input data and with the total number of spikes elicited in the neuron under consideration.…”

“…Quadratic forms are used in experimental studies as quadratic approximations to the input-output function of neurons and can be derived from neural data as Volterra/Wiener approximations up to the second order [3][4][5][6][7][8][9][10][11][12][13] . In addition, several theoretical studies have defined quadratic models of neuronal RFs either explicitly 2,14,15 or implicitly as neural networks [16][17][18] .…”