Organization of simple cell responses in the three-dimensional (3-D) frequency domain

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Abstract
The amplitude spectra of simple cells in areas 17 and 18 were estimated in two and three dimensions (2–D and 3–D) using drifting sinusoidal gratings. In 2–D, responses were sampled with 16 x 16 resolution in spatial and temporal frequency at the optimal orientation. In 3–D, responses were sampled with 12 x 12 x 10 resolution in spatial frequency, orientation, and temporal frequency. For 45/50 cells studied, the spatial attributes of the receptive fields (RFs) were independent of temporal frequency except for a scale factor. The five exceptions to this general finding could be described as follows: For four area 17 cells, responses in the null direction increased with temporal frequency, reducing direction selectivity. For one area 18 cell, the optimal spatial frequency increased with temporal frequency and vice versa. The 2–D discrete Fourier transform was applied to all of the estimated amplitude spectra assuming zero spatial and temporal phase. These transforms were compared with the results of first-order reverse correlations as described in the previous paper (McLean et al., 1994). Direction selective cells exhibited excitatory subregions that were obliquely oriented in space-time in both the raw correlation data and inverse transforms of the spectral data. The slopes of the subregions found in these two measures were highly correlated. Direction indices obtained from space and frequency domain measures were comparable. We demonstrate that the spectral response profiles of most simple cells are aligned with the coordinate axes in frequency domain. That is, they may be considered one-quadrant separable, suggesting that these cells are not velocity tuned per se, but are tuned for spatiotemporal frequency. The spectral bandwidth establishes the range of velocities to which these cells will respond. These findings are consistent with the one-quadrant separability constraint of linear quadrature models. We conclude that most simple cells perform as roughly linear filters in two dimensions of space and time.