Three-dimensional motion and dense-structure estimation using convex projections

We propose a novel method for estimating the 3D motion and dense structure of an object form its two 2D images. The proposed method is an iterative algorithm based on the theory of projections onto convex sets (POCS) that involves successive projections onto closed convex constraint sets. We seek a solution for the 3D motion and structure information that satisfies the following constraints: (i) rigid motion - the 3D motion parameters are the same for each point on the object. (ii) Smoothness of the structure - depth values of the neighboring points on the object vary smoothly. (iii) Temporal correspondence - the intensities in the given 2D images match under the 3D motion and structure parameters. We mathematically derive the projection operators onto these sets and discuss the convergence properties of successive projections. Experimental results show that the proposed method significantly improves the initial motion and structure estimates.