Approximate and SQP Two View Triangulation
The two view triangulation problem with Gaussian errors, aka optimal triangulation, has an optimal solution that requires finding the roots of a 6th degree polynomial. This is computationally quite demanding for a basic building block of many reconstruction algorithms. We consider two faster triangulation methods. The first is a closed form approximate solution that comes with intuitive and tight error bounds that also describe cases where the optimal method is needed. The second is an iterative method based on local sequential quadratic programming (SQP). In simulations, triangulation errors of the approximate method are on par with the optimal method in most cases of practical interest and the triangulation errors of the SQP method are on par with the optimal method in practically all cases. The SQP method is faster of the two and about two orders of magnitude faster than the optimal method.
KeywordsApproximate Method Sequential Quadratic Programming Optimal Error Epipolar Line Sequential Quadratic Programming Method
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