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Three-D motion and dense structure estimation using convex

Alatan, Abdullah Aydın
Erdem, AT
Onural, L
We propose a novel method for estimating the 3-D motion and dense structure (depth) of an object from its two 2-D 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 3-D motion and structure information that satisfies the following constraints: (i) Rigid motion - the 3-D motion (rotation and translation) parameters are the same for each point on the object. (ii) Smoothness of the structure - the depth values of the neighboring points on the object vary smoothly. (iii) Temporal correspondence - the intensities in the given 2-D images match under the 3-D 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.