Sparse Non-Linear Least Squares Optimization for Geometric Vision

Abstract

Several estimation problems in vision involve the minimization of cumulative geometric error using non-linear least-squares fitting. Typically, this error is characterized by the lack of interdependence among certain subgroups of the parameters to be estimated, which leads to minimization problems possessing a sparse structure. Taking advantage of this sparseness during minimization is known to achieve enormous computational savings. Nevertheless, since the underlying sparsity pattern is problem-dependent, its exploitation for a particular estimation problem requires non-trivial implementation effort, which often discourages its pursuance in practice. Based on recent developments in sparse linear solvers, this paper provides an overview of sparseLM , a general-purpose software package for sparse non-linear least squares that can exhibit arbitrary sparseness and presents results from its application to important sparse estimation problems in geometric vision.