Document Type





Stereoscopic depth, correspondence problem, false matches, symmetry




Behavior and Behavior Mechanisms | Neurosciences | Vision Science


Veridical stereoscopic depth depends on matching corresponding image points. This requires solving the stereo correspondence problem: how are true matches distinguished from false ones? Conventional algorithms select true matches on the basis of feature detection [what do you mean by ‘feature detection’ here? Is there some more specific term?] and adherence to natural statistics. They reject false matches as noise. We propose here an alternative that uses the signals present in false matches to delineate the true solution. When visualized in a Keplerian array, binocular matches are symmetrically reflected about an axis that is a potential solution. Properties such as extent and curvature of the solution are encoded the transformation that describes how one-half of the matches reflects onto the other.

To implement this strategy, left and right images were convolved with Gaussian kernels of various standard deviations (spatial frequencies). Keplerian arrays comparing filter responses across left and right spatial-frequency combinations were then constructed. Responses that are minimally different across the eyes give rise to regions of high symmetry; position within the Keplerian array indicates the location of a solution in space. Solutions that possess natural surface regularities consistently showed minimal differences for one left : right spatial frequency ratio, which is correlated with local surface slant. As a result, combining responses within particular ratio families can distinguish true matches from false ones. True matches tend to be long and smoothly contoured, and symmetry would be preserved across all members of a ratio family from low to high spatial-frequency combinations.

This approach is efficient; preprocessing is minimal since no feature extraction is involved. It can be implemented in machine vision to solve the correspondence problem for depth sensing algorithms. It is robust when tested against perfectly camouflaged surfaces in random dot stereograms and consistent with physiological data showing that false match signals are propagated to higher cortical areas along the dorsal pathway.