Minimizing Algebraic Error in Geometric Estimation Problems

This paper gives a widely applicable technique for solving many of the parameter estimation problems encountered in geometric computer vision. A commonly used approach is to minimize an algebraic error function instead of a possibly preferable geometric error function. It is claimed in this paper that minimizing algebraic error will usually give excellent results, and in fact the main problem with most algorithms minimizing algebraic distance is that they do not take account of mathematical constraints that should be imposed on the quantity being estimated. This paper gives an efficient method of minimizing algebraic distance while taking account of the constraints. This provides new algorithms for the problems of resectioning a pinhole camera, computing the fundamental matrix, and computing the tri-focal tensor. Evaluation results are given for the resectioning and tri-focal tensor estimation algorithms.