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Arvind Iyer, Johannes Burge; Optimal binocular disparity estimation in the presence of natural depth variation. Journal of Vision 2018;18(10):627. doi: https://doi.org/10.1167/18.10.627.
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© ARVO (1962-2015); The Authors (2016-present)
Reliable estimation of binocular disparity is fundamental to our ability to estimate the relative depth of objects in natural scenes. Classical laboratory stimuli are not representative of the stimuli that disparity-processing mechanisms encounter in natural scenes. Here, we examine the impact of natural disparity variation (arising from natural depth variation) on optimal disparity estimation. First, we obtained a database of calibrated natural stereo-images with precisely co-registered laser measurements of groundtruth distance at each pixel. Next, we developed a procedure for sampling binocular stereo-pairs from the dataset with arcsec precision and created a ground-truth labeled training set for a range of disparities (1deg/patch; 1000patch/disparity). Then, using Accuracy Maximization Analysis, we learned a small population of model neurons having linear receptive-fields (RFs) optimized for disparity estimation. The population responses were obtained by projecting the contrast-normalized stereo-pairs onto the RFs with multiplicative neural noise. These population responses optimally encode the disparity information in the natural stimuli, and also specify the optimal non-linear (quadratic) pooling rules for decoding disparity. Finally, we measured disparity estimation performance with an optimal Bayesian decoder. To isolate the effect of natural depth variation on estimation performance, we repeated the analyses with 'flat' stimuli i.e. stereo-pairs sampled from a single eye's image thus preserving natural luminance variation but excluding natural depth variation. For both natural and flat stimuli, the precision of disparity estimation decreases consistent with Weber's Law. Estimate precision is approximately tenfold lower for stimuli with natural depth variation than for flat stimuli. Natural stimuli vary in the amount of local depth variation they exhibit, which we quantify by a measure called disparity contrast. In future work, we will systematically study the effect of disparity contrast on population responses of the optimal encoders, and on overall estimation performance.
Meeting abstract presented at VSS 2018
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