Qualitative depth from vertical and horizontal binocular disparities, in agreement with psychophysical evidence

The author concentrates on the problem of obtaining depth information from binocular disparities. It is motivated by the fact that implementing registration algorithms and using the results for depth computations is hard in practice with real images due to noise and quantization errors. It is shown that qualitative depth information can be obtained from stereo disparities with almost no computations, and with no prior knowledge (or computation) of camera parameters. The only constraint is that the epipolar plane of the fixation point includes the X-axes of both cameras. Two expressions are derived that order all matched points in the images in two distinct depth-consistent ways from image coordinates only. One is a tilt-related order λ, which depends only on the polar angles of the matched points, the other is a depth-related order χ. Using λ for tilt estimation and point separation (in depth) demonstrates some anomalies and unusual characteristics that have been observed in psychophysical experiments, most notably the induced size effect