Minimizing absolute parallax in a stereo image
David F. McAllister · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1992
We assume a left handed coordinate system with interocular distance e and viewer distance to the stereo window d < 0. Using the standard off-axis perspective projection to compute homologous points, the horizontal parallax of a point with coordinates (x, y, z) becomes ez/(z - d). Given a finite set of points D equals {(xj, yj, zj), 1 j in a z-buffer after applying hidden surface elimination. In the first case the solution is based on the root of a quadratic equation. In the second case we approximate the translated parallax function zj + v)/(zj + v - d) by the first term in its series expansion, (zj + v)/d , and use it to analyze the behavior of the sum near the minimum. If we suitably restrict the distance between the closet point and furthest point from the viewer, we argue that the minimum occurs to the right of max {d-zi} and at a root -zj of a parallax function. The root can be located by determining the index i where the function changes sign and evaluating the absolute parallax sum at values -zj where j is close to i.