A Decomposition Approach to Geometric Fitting

Many geometric fitting problems encountered in computer vision are of non-linear nature and have a large number of parameters. Typically, iterative techniques such as the Levenberg-Marquardt algorithm are used to compute the optimum of highly complex optimization functions. Here we are faced with problems of good initial estimates and high risk of getting in local optimums. In this paper we propose a decomposition approach to alleviating these problems by reducing the number of optimization parameters. This way not only the optimization process itself is simplified, it tends also easier to investigate low-dimensional optimization spaces. We apply the decomposition approach to solving various fitting problems from both 2D and 3D domain. Particularly for cylinder fitting, we are able to reduce the number of parameters from five or six of earlier methods to only two. Experiments have demonstrated the advantages of our approach.