Abstract
Three-dimensional visual perception requires correct matching of images projected to the left and right eyes. The matching process is faced with an ambiguity: part of one eye's image can be matched to multiple parts of the other eye's image. This stereo correspondence problem is complicated for random-dot stereograms (RDSs), because dots with an identical appearance produce numerous potential matches. Despite such complexity, human subjects can perceive a coherent depth structure. A coherent solution to the correspondence problem does not exist for anticorrelated RDSs (aRDSs), in which luminance contrast is reversed in one eye. Neurons in the visual cortex reduce disparity selectivity for aRDSs progressively along the visual processing hierarchy. A disparity-energy model followed by threshold nonlinearity (threshold energy model) can account for this reduction, providing a possible mechanism for the neural matching process. However, the essential computation underlying the threshold energy model is not clear. Here, we propose that a nonlinear modification of cross-correlation, which we term “cross-matching,” represents the essence of the threshold energy model. We placed half-wave rectification within the cross-correlation of the left-eye and right-eye images. The disparity tuning derived from cross-matching was attenuated for aRDSs. We simulated a psychometric curve as a function of graded anticorrelation (graded mixture of aRDS and normal RDS); this simulated curve reproduced the match-based psychometric function observed in human near/far discrimination. The dot density was 25% for both simulation and observation. We predicted that as the dot density increased, the performance for aRDSs should decrease below chance (i.e., reversed depth), and the level of anticorrelation that nullifies depth perception should also decrease. We suggest that cross-matching serves as a simple computation underlying the match-based disparity signals in stereoscopic depth perception.
Highlights
The stereoscopic system gives rise to three-dimensional visual perception by combining the images from the left and right eyes
We explored a more general version of cross-matching, in which signals are spatially averaged with various window sizes prior to the threshold. We showed that both versions of cross-matching reproduced a nearly flat disparity-tuning function to anticorrelated random-dot stereograms (RDSs)
We showed that cross-matching produced disparity tunings nearly insensitive to anticorrelated RDSs but sensitive to correlated and half-matched RDSs (Figure 3, right) when the dot density was low (e.g., 25%)
Summary
The stereoscopic system gives rise to three-dimensional visual perception by combining the images from the left and right eyes. The matching process is often confronted with the stereo correspondence problem, in which locally correct but globally incoherent matches (i.e., false matches) result in ambiguous solutions to the problem. The correspondence problem is complex for random-dot stereograms (RDSs; Figure 1; Julesz, 1971), in which identical black and white dots yield numerous false matches (Figure 2). Despite this complexity, human subjects can perceive a coherent three-dimensional structure embedded in RDSs, suggesting that the stereoscopic system is capable of selecting a globally consistent solution to the correspondence problem (red rounded box, Figure 2)
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