A triangulation method based on minmaxKKT

Triangulation is one of important issues in machine vision. Although L ₂ norm based least square method is reasonably fast, the globally optimal solution cannot be obtained theoretically due to its non-convexity of the objective function. Even if some optimization strategies, such as branch and bound, are adopted, the result is locally optimal in most cases. In theoretical, L _∞ norm based approach can produce global optimal solution, however, its computational cost increases rapidly according to the size of measurement data. In this paper, we proposed a minmaxKKT based triangulation method. The minmaxKTT condition is first utilized to verify whether the solution by L ₂ norm is globally optimal. If the decision is negative, we apply hybrid steepest decent algorithm to pursuit global optimum. The proposed method can not only achieve global optimum but also raise the computational speed greatly compared to L _∞ based approach. Experimental results on benchmark data and real world scene have proven the feasibility and merit of the proposed method.