Analysis Of Three-Dimensional Time Varying Scene

We present some of the highlights of the recent advancements in the uniqueness and estimation of 3-D motion parameters and object surface structure from perspective views, a key issue in the analysis of 3-D time varying scene. For estimating planar patch motion from two views, there are two solutions in general, unless the 3 x 3 matrix containing the canonical coordinates of a Lie group has multiple singular values. Closed form solutions are derived analytically. The solutions would be unique if three views are given. For curved surface motion, two theorems, one lemma and a collection of corollaries on the conditions of uniqueness of solution are given. Closed form solutions for the nonlinear motion equations are derived. Results of simulation and real experiments are discussed.