Using the symmetry of false matches to solve the correspondence problem.
Correspondence problem, Binocular correspondence, stereeoscopic vision
Cognition and Perception | Cognitive Neuroscience
Sensing stereoscopic depth requires that image points be binocularly matched. Therein lies the correspondence problem: how are true matches distinguished from false ones? Conventional algorithms select true matches on the basis of correlated features and adherence to natural statistics, while rejecting 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 represents a potential solution. Surface properties such as slant and curvature are encoded the transformation that describes how one-half of the matches reflects across the symmetry axis onto the other. To implement this strategy, we convolved left and right images with Gaussian kernels of various standard deviations (spatial frequencies). We then produced Keplerian arrays by comparing filter responses across left and right spatial-frequency combinations. Responses that are minimally different across the eyes gave rise to regions of high symmetry; response position within the Keplerian array gave the location of a solution in space. Solutions possessing natural surface regularities consistently showed minimal differences for one left : right spatial frequency ratio, which is correlated with the local surface slant. As a result, combining responses within particular ratio families can distinguish true matches from false ones. True matches tend to be elongated and smoothly contoured, with symmetry 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.
Ng, C. J. & Farell, B. (2015). Using the symmetry of false matches to solve the correspondence problem. Journal of Vision, 15, 269. doi:10.1167/15.12.269