Improvement to the Minimization of Hybrid Error Functions for Pose Alignment

Many problems in computer vision such as pose recovery and structure estimation are formulated as a minimization process. These problems vary in the use of image measurements directly or using them to extract 3D cues in the minimization process. Hybrid methods have the advantage of combining the 2D and 3D visual information to improve the performance over the above two methods. In this paper, we present a new formulation for minimizing a class of hybrid error functions. This is done by using 2D information from the image space and 3D information from the Cartesian space in one error function. Applications to visual servoing and image alignment problems are presented. The positioning task of a robot arm has been formulated as a minimization problem. Gradient descent as a first order approximation and Gauss-Newton as a second order approximation are considered in this paper. Simulation results show, comparing with 2frac12 D hybrid method, that these two methods provide an efficient solution to the features visibility problems and the camera trajectory in the Cartesian space