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, 120, 108-20

Encoding and Estimation of First- And Second-Order Binocular Disparity in Natural Images

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Encoding and Estimation of First- And Second-Order Binocular Disparity in Natural Images

Paul B Hibbard et al. Vision Res.

Abstract

The first stage of processing of binocular information in the visual cortex is performed by mechanisms that are bandpass-tuned for spatial frequency and orientation. Psychophysical and physiological evidence have also demonstrated the existence of second-order mechanisms in binocular processing, which can encode disparities that are not directly accessible to first-order mechanisms. We compared the responses of first- and second-order binocular filters to natural images. We found that the responses of the second-order mechanisms are to some extent correlated with the responses of the first-order mechanisms, and that they can contribute to increasing both the accuracy, and depth range, of binocular stereopsis.

Keywords: Binocular disparity; Binocular energy model; Depth perception; Natural images; Second-order stereopsis.

Figures

Fig. 1
Fig. 1
Outline of the binocular energy model. (a) Images are filtered with quadrature pairs of Gabor receptive fields. The white areas represent excitatory regions of the receptive fields, and the dark areas inhibitory regions. Responses are summed across the two eyes for corresponding filters, then squared. Finally, these squared outputs are summed across the two halves of the quadrature pair. (b) Positional disparity tuning is achieved if the two eyes’ receptive fields are in different locations. Here, the vertical red line shows the centre of the left eye’s receptive field; the right eye’s receptive field is identical in shape but shifted to the right. (c) Phase disparity tuning is achieved if the two eyes’ receptive fields have a different shape. Here, the two receptive fields are in the same location, but the left eye’s is odd-symmetric while the right eye’s is even symmetric.
Fig. 2
Fig. 2
An example stimulus containing second-order disparity. The two eyes’ images consist of identical white noise samples that have been contrast modulated by a sinusoid. The phase of the sinusoid differs across the two images, creating a second-order disparity. The disparity in this stimulus is crossed, resulting in the perception of near depth. The left and centre images are arranged for crossed fusion, the centre and right images for uncrossed fusion. The graph shows the responses of first- and second-order mechanisms to this stimulus, as a function of the disparity in the contrast envelope. The blue line shows the response for a second-order mechanism tuned to a vertical orientation, and the same spatial frequency as the contrast envelope. The red and black lines show the responses of vertical first-order filters tuned to the same spatial frequency as the first- and second-stage filters of the second-order mechanism. Results are averaged over 500 sample images.
Fig. 3
Fig. 3
A second-order binocular energy model. Energy responses are first calculated separately for each eye. These monocular energy responses form the input to second-order filters, at a lower spatial frequency. These are then used to calculate a second-order binocular energy response in the same way as the standard first-order energy response.
Fig. 4
Fig. 4
An example of the binocular stimuli used. The left and centre images are arranged for crossed fusion, then centre and right images for uncrossed fusion.
Fig. 5
Fig. 5
(a and b) Distributions of phase disparities in the responses of first- and second-order mechanisms for spatial frequency tunings of (a) 0.2 cpd and (b) 0.4 cpd. The first-order results are for a vertically-oriented filter. The second-order results are for a mechanism with a vertical second-stage filter, and are pooled over all 12 combinations of frequency ratio and orientation in the first-stage filters. (c) These distributions are replotted as a function of the equivalent positional disparity, for the two frequencies of first-order filters. (d) Results plotted in the same way for the second-order mechanisms.
Fig. 6
Fig. 6
(a) The correlation between the disparities in the first- and second-order channels, for the lower frequency (0.2 cpd) filters. Results show the mean, over all images, of the correlation, calculated separately for each of the 12 combinations of first-stage filter frequency and orientation tuning. (b) The correlations, plotted in the same way, for the higher frequency (0.4 cpd) filters. (c) The mean correlations, over all images and spatial frequencies, as a function of orientation. The correlation was lower when the first-stage filters were horizontal. Error bars show ±1 standard error of the mean.
Fig. 7
Fig. 7
Distributions of winner-takes-all disparity estimates for first- and second-order mechanisms. The first-order results are for filters with the same frequency tuning as the first-stage filters of the second-order mechanism. The results for the first-order mechanisms are in blue; the results for the second-order mechanisms in red. The dotted vertical line shows the stimulus disparity. Each row shows the results for a particular stimulus disparity, with the three columns showing results for the three ratios of spatial frequency tuning of the first- and second-stage filters. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 8
Fig. 8
Distributions of winner-takes-all disparity estimates for first- and second-order mechanisms. The first-order results are for filters with the same frequency tuning as the second-stage filters of the second-order mechanism. The results for the first-order mechanisms are in blue; the results for the second-order mechanisms in red. The solid black line shows the results after pooling across the two. The dotted black vertical line marks the stimulus disparity (0 arc min). Each column shows the results for a single orientation (indicated in the plots) and each row the results for a single spatial frequency. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 9
Fig. 9
Distributions of winner-takes-all disparity estimates for first-and second-order mechanisms, in which results are pooled over all first-stage filter orientations and frequencies for the second-stage mechanisms. The results for the first-order mechanisms are in blue; the results for the second-order mechanisms in red. The solid black line shows the results after pooling across the two. The dotted black vertical line marks the stimulus disparity. The four plots show results for four stimulus disparities, as labelled. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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References

    1. Allenmark F., Read J. Spatial stereoresolution for depth corrugations may be set in primary visual cortex. PLoS Computational Biology. 2011;7(8):e1002142. - PMC - PubMed
    1. Anzai A., Chowdhury S.A., De Angelis G.C. Coding of stereoscopic depth information in visual areas V3 and V3A. Journal of Neuroscience. 2011;31:10270–10282. - PMC - PubMed
    1. Badcock R., Schor C. Depth-increment detection function for individual spatial channels. Journal of the Optical Society of America A. 1985;2:1211–1216. - PubMed
    1. Banks M.S., Gepshtein S., Landy M.S. Why is spatial stereo-resolution so low? Journal of Neuroscience. 2004;24(9):2077–2089. - PMC - PubMed
    1. Barlow H.B., Blakemore C., Pettigrew J.D. The neural mechanisms of binocular depth discrimination. Journal of Physiology. 1967;193:327–342. - PMC - PubMed

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