Space-time spectra of complex cell filters in the macaque monkey: A comparison of results obtained with pseudowhite noise and grating stimuli

Abstract

White noise stimuli were used to estimate second-order kernels for complex cells in cortical area VI of the macaque monkey, and drifting grating stimuli were presented to the same sample of neurons to obtain orientation and spatial-frequency tuning curves. Using these data, we quantified how well second-order kernels predict the normalized tuning of the average response of complex cells to drifting gratings.The estimated second-order kernel of each complex cell was transformed into an interaction function defined over all spatial and temporal lags without regard to absolute position or delay. The Fourier transform of each interaction function was then computed to obtain an interaction spectrum. For a cell that is well modeled by a second-order system, the cell’s interaction spectrum is proportional to the tuning of its average spike rate to drifting gratings. This result was used to obtain spatial-frequency and orientation tuning predictions for each cell based on its second-order kernel. From the spatial-frequency and orientation tuning curves, we computed peaks and bandwidths, and an index for directional selectivity.We found that the predictions derived from second-order kernels provide an accurate description of the change in the average spike rate of complex cells to single drifting sine–wave gratings. These findings are consistent with a model for complex cells that has a quadratic spectral energy operator at its core but are inconsistent with a spectral amplitude model.

Internal Spatial Organization of Receptive Fields of Complex Cells in the Early Visual Cortex

“…When at least one member of a pair of stimuli is a gray dot, no vote is presented. This calculation is thus essentially identical to one used for sparse noise stimuli in previous studies (Gaska et al 1994;Livingstone and Conway 2003).…”

“…In previous studies, the second-order interaction maps were often averaged across all reference positions within the receptive field of a complex cell to enhance signal-to-noise ratios for a single final map (Emerson et al 1987;Gaska et al 1994;Livingstone and Conway 2003). This means that the six-dimensional interaction maps, h 2 (x 1 , x 1 ϩ dx, y 1 , y 1 ϩ dy, 1 , 1 ϩ d), were reduced to just three dimensions of dx, dy, and d. In this approach, the original maps were assumed to be spatially homogeneous.…”

“…occupy the largest spatial extent between simultaneously presented stimuli in general (Anzai et al 2001;Gaska et al 1994), the temporal offset d was always set to 0 ms to evaluate the spatial structure and extent of second-order interaction maps. Accumulation of votes for all spikes produced the second-order interaction map for the reference (x 1 , y 1 , 1 ).…”

“…It is now possible to predict most simple cell responses from their receptive field properties. For complex cell receptive fields, pairs of bars and dots have been used intensively to elucidate the functional internal structure, called subunits, which are responsible for producing tuning for orientation, direction, spatial, and temporal frequencies (Emerson et al 1987;Gaska et al 1994;Livingstone and Conway 2003;Movshon et al 1978b). More sophisticated techniques have been developed recently to estimate key internal structures for complex cells from responses to dynamic dense noise, or overwhelmingly multidimensional, stimuli (Rust et al 2005;Touryan et al 2002).…”

Computation of motion direction by quail retinal ganglion cells that have a nonconcentric receptive field

“…In order to examine this possibility, careful measurements of local directional preferences must be performed. RF structures of DS neurons have been extensively studied in the mammalian primary visual cortex (see Emerson et al, 1987;Shapley et al, 1991;Gaska et al, 1994;DeAngelis et al, 1995). The 2nd order kernel measurement used for monkey V1 complex cells (Gaska et al, 1994) would more precisely describe spatiotemporal structures of RFs of the quail DS RGCs.…”