Least-Squares Algorithms for Motion and Shape Recovery Under Perspective Projection
Chiou-Shann Fuh and Petros Maragos* Department of Computer Science and Information Engineering National Taiwan University Taipei, Taiwan, R.O.C. *School of Electrical Engineering Georgia Institute of Technology Atlanta, GA 30332, USA
This paper presents an algorithm for 3-D motion and shape recovery using two perspective views and their relative 2-D displacement field. The 2-D displacement vectors are estimated as parameters of a 2-D affine model that generalizes standard block matching by allowing affine shape deformations of image blocks and affine intensity transformations. The matching block size is effectively found via morphological size histograms. The parameters of the rigid body motion are estimated using a least-squares algorithm that requires solving a system of linear equations with rank three. Some stabilization of the recovered motion parameters under noise is achieved through a simple form of maximum a posteriori estimation. A multi-scale search in the parameter space is also used to improve accuracy without high computational cost. Experiments on applying this algorithm to various real world image sequences demonstrate that it can estimate dense displacement fields and recover motion parameters and object shape with relatively small errors.