Fitting Generalized Essential Matrices from Generic 6x6 Matrices and its Applications
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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 33 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 goal solution. To test the algorithm, we evaluate with both synthetic and real data. From the results with synthetic data, we conclude that the proposed method is much faster than applying general optimization techniques to the original problem with 33 constraints. To conclude and to further motivate the relevance of our method, we develop an efficient and robust algorithm for estimation of the general relative pose problem, which will be compared with the state-of-the-art techniques. It is shown, in particular, that some existing approaches to solving the relative pose estimation problem can be considerably improved, if combined with our method for estimating the closest generalized essential matrix. Real data to validate the algorithm is used as well.
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