Fitting Generalized Essential Matrices from Generic 6x6 Matrices with Applications to Pose Problems

This paper addresses the problem of finding the closest generalized essential matrix from a given 6x6 matrix, with respect to the Frobenius norm. To the best of our knowledge, this nonlinear constrained optimization problem has not been addressed in the literature yet. Although it can be solved directly, it involves a large amount of constraints, and any optimization method to solve it will require much computational time. Then, we start by converting the original problem into a new one, involving only orthogonal constraints, and propose an efficient algorithm of steepest descent-type to find the solution. To test our algorithm, we start by evaluating our method with synthetic data, and conclude that the proposed method is much faster than applying general optimization techniques to the original problem with 33 constraints. To further motivate the relevance of our method, we apply our technique in two pose problems (relative and absolute) using synthetic and real data.