Testing Quantitative Models of Binocular Disparity Selectivity in Primary Visual Cortex

Abstract

Read, Jenny C. A. and Bruce G. Cumming. Testing quantitative models of binocular disparity selectivity in primary visual cortex. J Neurophysiol 90: 2795-2817, 2003. First published July 16, 2003 10.1152/jn.01110.2002. Disparity-selective neurons in striate cortex (V1) probably implement the initial processing that supports binocular vision. Recently, much progress has been made in understanding the computations that these neurons perform on retinal inputs. The binocular energy model has been highly successful in providing a simple theory of these computations. A key feature of the energy model is that it is linear until after inputs from the two eyes are combined. Recently, however, a modified version of the energy model, incorporating threshold nonlinearities before binocular combination, has been proposed to account for the weaker disparity tuning observed with anticorrelated stimuli. In this study, we present new data needed for a critical assessment of these two models. We compare two key predictions of the models with responses of disparity-selective neurons recorded from V1 of awake fixating monkeys. We find that the original energy model, and a family of generalizations retaining linear binocular combination, are quantitatively inconsistent with the response of V1 neurons. In contrast, the modified version incorporating threshold nonlinearities can explain both sets of observations. We conclude that the energy model can be reconciled with experimental observations by adding a threshold before binocular combination. This gives us the clearest picture yet of the computation being carried out by disparity-selective V1 neurons. I N T R O D U C T I O NThe separation of the two eyes introduces disparities between the images received by the left and right eyes. The visual system is somehow able to fuse the images so as to produce a unified percept of the visual world, while using the stereoscopic disparities to extract information about how far away viewed objects are. The neural circuits specific to this ability begin in primary visual cortex (V1), the first place in the visual system where inputs from the two eyes converge on individual cells. Many V1 cells modulate their firing rate according to the stereoscopic disparity of the stimulus (Barlow et al. 1967;Nikara et al. 1968). These disparity-tuned cells are believed to perform the initial processing of retinal inputs that eventually, in higher visual areas, gives rise to stereoscopic depth perception and to binocular fusion (single vision). Thus, a detailed understanding of the computations carried out by these cells represents the first step toward a complete description of stereoscopic vision.The current best description of the operation of these cells is provided by the energy model (Adelson and Bergen 1985;Fleet et al. 1996;Ohzawa 1998;Ohzawa et al. 1990;Qian 1994), sketched in Fig. 1A and described more fully below. This elegant model has been extremely successful in explaining qualitatively the properties of disparity-tuned neurons in V1, for example...

Early computational processing in binocular vision and depth perception

“…It can be shown that the energy model requires such cells to have oscillatory disparity tuning curves, containing several peaks and troughs. In reality, disparity tuning curves are usually dominated by a single peak or trough; they may have side-lobes, but these are usually less than required to fulfill the energy model predictions Prince et al, 2002b;Read and Cumming, 2003c). Adding thresholds prior to binocular combination produces model units with less extreme side-lobes, in better agreement with experiment (Read and Cumming, 2003c).…”

“…In reality, disparity tuning curves are usually dominated by a single peak or trough; they may have side-lobes, but these are usually less than required to fulfill the energy model predictions Prince et al, 2002b;Read and Cumming, 2003c). Adding thresholds prior to binocular combination produces model units with less extreme side-lobes, in better agreement with experiment (Read and Cumming, 2003c). Another problem for the energy model is that it predicts a correlation between ocular dominance and strength of disparity tuning which is not observed.…”

“…This expectation arises because, in the energy model and its variants, two-dimensional disparity tuning is tightly coupled to orientation tuning. Neurons are sensitive to the orientation of stimuli such as bars and gratings because their receptive fields are elongated along an axis corresponding to the preferred orientation (Hubel and Wiesel, 1962); the preferred orientation is generally the same in both eyes (Bridge and Cumming, 2001;Read and Cumming, 2003c). This means that the cell is expected to respond to changes in disparity over smaller scales when these disparities are applied orthogonal to its preferred orientation than when they are parallel to it; Fig.…”

Disparity processing in primary visual cortex

“…These changes in preferred disparity of the subunits lead to changes in the spatial scale of the disparity tuning curve, without changing the monocular spatial frequency tuning. Thus, in principle, the extended BEM might account for the observed neuronal properties [38,39]. Two recent studies suggest that this explanation is correct: the observed mismatch is largely explained by the effects of summing across the inferred set of LN subunits.…”

“…For example, the preferred spatial frequency measured monocularly determines the spatial scale (distance between preferred and null disparities) of the disparity tuning to RDS. 5 It has been recognized for many years that this is not true in real neurons [38,39], but this mismatch remained unresolved. One hallmark of a mechanism that combines BEM subunits is that these simple relationships need no longer hold.…”