GEOMETRIC CONSTRAINTS AND STEREO DISPARITY COMPUTATION

Most stereo techniques compute disparity assuming that it varies slowl y along surfaces. We quantify and justify this assumption, using weak assumptions about surface orientation distributions in the world to de rive the density of disparity surface orientations. The small disparit y change assumption is justified by the orientation density's heavy bi as toward disparity surfaces that are nearly parallel to the image pla ne. In addition, the bias strengthens with smaller baselines, larger f ocal lengths, and as surfaces move farther from the cameras. To analyz e current stereo techniques, we derive three densities from the first density, those of the disparity gradient magnitude, the directional de rivative of disparity, and the difference in disparity between neighbo ring surface points. The latter may be used in Bayesian algorithms com puting dense disparity fields. The directional derivative density and the disparity difference density both show that feature-based algorith ms should strongly favor small disparity changes, contrary to several well-known algorithms. Finally, we use our original surface orientatio n density and the gradient magnitude density to derive two new ''surfa ces-from-stereo'' techniques, techniques combining feature-based match ing and surface reconstruction. The first uses the densities to severe ly restrict the search range for the optimum fit. The second incorpora tes the surface orientation density into the optimization criteria, pr oducing a Bayesian formulation. Both algorithms are shown to be effici ent and effective.