A new quantitative analysis of simple cell space-time receptive fields

Abstract

Many spatial aspects of simple cell receptive fields can be explained by models which assume that simple cells efficiently encode statistical structure in static natural images (Olshausen et al. 1996). We extend these results to the time domain by assuming primary visual cortex treats dynamic imagery locally as static natural image patches translating at constant velocity. We developed a unified model of linear spatiotemporal aspects of simple cell receptive fields based on these assumptions, and fit it to published data from 291 cat simple cells (DeAngelis et al. 1993, 1999). Highlights:

1. Spatial frequency bandwidth obeys the simple relation sigma_k=a*(k+k0), which for preferred spatial frequency k>>k0 yields a scale invariant representation. Our analysis of the cat data gives a=0.39 +/− 0.03 and k0=0.20 +/− 0.03 cycles per degree. Rough estimates derived from published monkey data (DeValois et al. 1982) give a=0.39 and k0=0.6. The identical scaling factor for cat and monkey implies identical asymptotic shape for simple cell filters across species, supporting the image statistics hypothesis.

2. Spatially filtering a uniformly translating image at a velocity v with a spatial frequency bandwidth sigma_k produces a signal with temporal bandwidth sigma_k*v. A cell with preferred spatial and temporal frequencies k and w is optimally tuned to a velocity v=w/k. To avoid discarding signal energy, the cell's temporal bandwidth must be greater than sigma_k*w/k. This is found to be true for the vast majority of cells, supporting our model of image dynamics.

3. The space-time profiles of the cells are well fit by a weighted sum of two Gabors tuned to motion in opposite directions. The histogram of the directional weights is broad, but bimodal. One peak corresponds to equal weight in the preferred and nonpreferred directions, the second to a 2.5/1 ratio. In contrast, most current models utilize pure unidirectional tuning.