Efficient Implementation for Block Matrix Operations Nonlinear Least Squares Problems for Robotic Applications

A large number of robotic, computer vision and computer graphics applications rely on efficiently solving the associated sparse linear system. Simultaneous localization and mapping (SLAM), structure from motion (SFM), non-rigid shape recovery, elastodynamic simulations, are only few examples in this direction. In general, those problems are non-linear and the solution can be approximated by incrementally solving a series of linearized problems. In some applications, the size of the systems might considerable affect the performance, especially when the sparsity is low. This paper exploits the block structure of such problems and offers efficient solutions to manipulate block matrices. In particular, we focus on testing the method on SLAM applications, but the applicability of the technique remains general.