Distance regression by Gauss-Newton-type methods and iteratively re-weighted least-squares (Q1034749)

A generalized problem of fitting a curve or surface to given measurement data is presented. The solution is focused on the situations when the usual least-squares approach is not suitable. The generalization of the fitting problem lies in minimizing the sum of the so called norm-like functions applied to the residual vectors that connect the measured points with associated points on the fitted curve or surface. This approach represents an extension of the iteratively re-weighted least-squares method (Gauss-Newton-type method) for minimizing a sum of norm-like functions of scalar residuals. The obtained results can be used in various applications of computational geometry -- reconstruction of geometric models from point cloud data, regression analysis, image segmentation, pattern recognition, etc.