An implementation of the partitioned Levenberg-Marquardt algorithm for applications in computer vision

At several applications of computer vision is necessary to estimate parameters for a specific model which best fits an experimental data set. For these cases, a minimization algorithm might be used and one of the most popular is the Levenberg-Marquardt algorithm. Although several free applies from this algorithm are available, any of them has great features when the resolution of problem has a sparse Jacobian matrix . In this case, it is possible to have a great reduce in the algorithm's complexity. This work presents a Levenberg-Marquardt algorithm implemented in cases which has a sparse Jacobian matrix. To illustrate this algorithm application, the camera calibration with 1D pattern is applied to solve the problem. Empirical results show that this method is able to figure out satisfactorily with few iterations, even with noise presence.