{ In this paper we present a method for optimally estimating the rotation and translation between a camera and a 3-D object from point and/or line correspondences. First we devise an error function and second we s h o w h o w to minimize this error function. The quadratic nature of this function is made possible by representing rotation and translation with a dual number quaternion. We p r o vide a detailed account of the computational aspects of a trust-region optimization method. This method compares favourably with Newton's method which has extensively been used to solve the problem at hand, with Faugeras-Toscani's linear method 6] for calibrating a camera, and with the Levenberg-Marquardt non-linear optimization method. Finally we present some experimental results which demonstrate the robustness of our method with respect to image noise and matching errors.

We are dealing with a numerical method for solving the problem of minimizing a difference of two convex functions (a d.c. function) over a closed convex set in R". This algorithm combines a new prismatic branch and bound technique with polyhedral outer approximation in such a way that only linear programming problems have to be solved.

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