Abstract

Given a pair of matched stereo images how is it possible to recover the stereo viewing parameters as well as the 3-D scene geometry? This problem has received considerable attention in both the vision and photogrammetric literature. Typically, solutions have been iterative in nature and/or numerically unstable. Here a new analysis is presented which leads to numerically stable closed-form solutions. The analysis begins by considering stereo disparity and its gradient. It is shown that the unknown viewing parameters and 3-D world geometry can be related in terms of horizontal and orientational disparities. (Orientational disparities are defined as the difference in imaged orientation of world surface detail.) This first part of the analysis is similar in spirit to Koenderink and van Doorn.¹ The variables are further related by invoking a simple constraint: For stereo viewing the two eyes should be focused on the same world point. With this analysis in place, it is shown that the unknown quantities (viewing parameters and world geometry) can be recovered in terms of measurable quantities (horizontal and orientational disparities) via a quasilinear system of equations.

© 1988 Optical Society of America