Optimal Computing of Structure from Motion Using Point Correspondences in Two Frames

Abstract

One of the problems associated with any approach to the structure from motion problem using point correspondence, i.e. recovering the structure of a moving object from its successive images, is the use of least squares on dependent variables. We formulate the problem as a quadratic minimization problem with a non-linear constraint. Then we derive the condition for i, he solution to be optimal under the assumption of Gaussian noise in the input, in the Maximum Likelihood Principle sense. This constraint minimization reduces to the solution of a nonlinear system which in the presence of modest noise is easy to approximate. We present two efficient ways to approximate it and we discuss some inherent limitations of the structure from motion problem when two frames are used that should be taken into account in robotics applications that involve dynamic imagery. In addition, our formulation introduces a framework in which previous works on the subject become special cases.