An important property of natural images contributing to a retinal ganglion cell's (RGC) responses is the temporal modulation of mean intensity (contrast) in the receptive field (RF) center. However, these responses exhibit a significant amount of variability. This variability could arise in part from responses to the spatial intensity variation of the natural images in the RF center, i.e., their local intensity distribution or their local visual texture. We tested five predictions derived from this hypothesis: First, responses tend to increase with the variance of the local visual texture of natural images. Second, the skewed distribution of intensities in natural images leads to asymmetric responses to their onset and offset to and from a gray background of the same mean intensity. Third, repeating this experiment with the negative of natural images inverts the asymmetry. Fourth, performing an intensity histogram equalization of the images eliminates the asymmetry. Fifth, RGCs' responses increase with the spatial contrast of artificial plaids. The hypothesis passed all five tests, which indicate that responses to natural images increase with the variance of their visual texture. To account for this texture sensitivity, we propose a model in which the RFs of most RGCs of the rabbit have multiple nonlinear subunits.

^{2}on the retina). Images were presented in a random sequence, each for 1000 ms. When the natural image was removed, the display was held at a spatially uniform gray for 1000 ms before the next image was presented. The mean intensities of the gray and natural images were the same (9.10 cd/m

^{2}) to remove luminance adaptation. The long periods of presentation of gray and natural images allowed us to distinguish clearly between responses to onset and offset of the images (Smyth, Willmore, Baker, Thompson, & Tolhurst, 2003). We presented from 1,000 to 12,000 images in different experiments.

*S*and their corresponding responses

*R,*the cell's linear RF from STA is calculated by:

*S*

^{ T }

*S*is the mean autocorrelation matrix for the stimuli,

*I*is the identity matrix, and

*α*(usually 0.5–10) is the regularization parameter. The good choice of

*α*is dependent on the noise of the data (Calvetti & Reichel, 2004). An optimal

*α*was not necessary in this paper, since we did not apply STA to quantify the true linear RF. Rather, we used STA as a tool to study the asymmetry between onset and offset of natural images. This asymmetry held for a large range of

*α*.

*M*

_{ Center }was the mean intensity of the natural image in the RF center and

*M*

_{ Gray }was the mean intensity of the full-field gray background. The center of the RF can be roughly measured by using either a moving edge (Chatterjee et al., 2007) or the linear RF (STA—Willmore & Smyth, 2003). Although a precisely estimated RF center size from the natural images is preferred, it is not required in this study. For example, compared to the true RF center, the center size estimated from an artificial moving edge might be a little smaller, and that estimated from STA might be a little larger. However, the conclusions obtained in this study hold for both estimations of RF.

*R*

_{ C }) was sigmoidal and modeled well by a cumulative Gaussian function. This function was defined by (Chichilnisky, 2001):

*R*

_{max}was the maximal firing rate,

*C*

_{ maxs }was the contrast value yielding maximal slope,

*σ*was the standard deviation of the Gaussian, and

*erf*is the Gauss error function. A criterion of minimum mean-squared error was applied to obtain the optimal fitting of this function.

*R*

_{ Total }) in two parts. The first part is the response contribution of the change in the local mean intensity of the image, or the local temporal contrast (

*R*

_{ C }, see Equation 2). The second part is the contribution of the local intensity variation (

*R*

_{ V }), shown in Figure 1. The local intensity variation is represented by the histogram of relative intensities in the RF center for each image. To define these histograms, let the intensity of a pixel be

*I,*the mean in the RF center be

*M*

_{ Center }, and the intensity of the preceding gray image be

*M*

_{ Gray }. Then, the relative intensity of this pixel is

*I*

_{ Rel }= (

*I*−

*M*

_{ Center })/

*M*

_{ Gray }and we denote the histogram of relative intensities in an image as

*H*. Next, we weigh the relative-intensity histogram (

*H*(

*k*)) for each image

*k*with its elicited relative response (

*R*

_{ V }(

*k*)). This relative response is calculated by

*R*

_{ V }=

*R*

_{ Total }−

*R*

_{ C }. Finally, we sum all the response-weighed histograms from all

*N*images and perform a normalization as follows to obtain the

*RIV*:

*R*

_{ Total }−

*R*

_{ C }and thus, the RIV function, should be close to zero. If instead an intensity variation were more likely to yield a larger response than predicted by the local temporal contrast, then we would get a positive RIV. By the same token, if an intensity variation were more likely to yield a small response, then the corresponding RIV would be negative. Consequently, the RIV reveals the effects of intensity variations and thus, one can use it to probe visual texture. By comparing the RIV function at small intensity variations with those at large variations, one may be able to tell whether visual texture contributes to the response.

*I*

_{ Origin }) with

*I*

_{max}is the maximum intensity in the image,

*N*

_{ All }is its number of pixels, and

*N*

_{ j }is the number of pixels with the

*j*

^{ th }brightest intensity.

*RIV*

_{ L }and

*RIV*

_{ H }, shown in Figure 2B). We then plotted RIV

_{H}as a function of RIV

_{L}for all cells in Figure 2D. For almost all cells, the

*RIV*

_{ H }and

*RIV*

_{ L }were positive and negative respectively. In other words, the RIV structure observed in Figure 2C was generally applicable to almost all cells. In addition, RIV

_{H}and RIV

_{L}were negatively correlated (Figure 2D). Therefore, although the gain of the responses varied strongly across different types of RGCs, their dependence on texture did not.

*μ*m

^{2}.

*μ*m

^{2}. However, when we reduced the size of the squares elements of the plaid to 50 × 50

*μ*m

^{2}(Figure 6C), the RGC showed no responses to visual textures (Figure 6E). We will address the implications of this size dependence in the Discussion.

_{T}) in data like those in Figure 6D. Then, we performed linear regression on the data and measured the residual variance (V

_{R}) from the best linear fit. The percentage of variance explained by the texture was then 100%× (V

_{T}− V

_{R})/V

_{T}. For the data in Figure 6, about 75% of the variance was explained by the dependence of the responses on visual texture. For a sample of 13 RGCs, the percentage of the variance explained by visual-texture dependence was 50% ± 20%.

*μ*m

^{2}but not at around 100 × 100

*μ*m

^{2}(Figure 6E). Therefore, the spatial integration of individual subunits should be between 50 and 100

*μ*m. Such integration may be consistent with bipolar-cell RFs (Dacheux & Miller, 1981; Ghosh, Bujan, Haverkamp, Feigenspan, & Wassle, 2004; Jeon & Masland, 1995; MacNeil, Heussy, Dacheux, Raviola, & Masland, 2004; Mills & Massey, 1992).