Support-theoretic subgraph preconditioners for large-scale SLAM and structure from motion
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Simultaneous localization and mapping (SLAM) and Structure from Motion (SfM) are important problems in robotics and computer vision. One of the challenges is to solve a large-scale optimization problem associated with all of the robot poses, camera parameters, landmarks and measurements. Yet neither of the two reigning paradigms, direct and iterative methods, scales well to very large and complex problems. Recently, the subgraph-preconditioned conjugate gradient method has been proposed to combine the advantages of direct and iterative methods. However, how to find a good subgraph is still an open problem. The goal of this dissertation is to address the following two questions: (1) What are good subgraph preconditioners for SLAM and SfM? (2) How to find them? To this end, I introduce support theory and support graph theory to evaluate and design subgraph preconditioners for SLAM and SfM. More specifically, I make the following contributions: First, I develop graphical and probabilistic interpretations of support theory and used them to visualize the quality of subgraph preconditioners. Second, I derive a novel support-theoretic metric for the quality of spanning tree preconditioners and design an MCMC-based algorithm to find high-quality subgraph preconditioners. I further improve the efficiency of finding good subgraph preconditioners by using heuristics and domain knowledge available in the problems. Our results show that the support-theoretic subgraph preconditioners significantly improve the efficiency of solving large SLAM problems. Third, I propose a novel Hessian factor graph representation, and use it to develop a new class of preconditioners, generalized subgraph preconditioners, that combine the advantages of subgraph preconditioners and Hessian-based preconditioners. I apply them to solve large SfM problems and obtain promising results. Fourth, I develop the incremental subgraph-preconditioned conjugate gradient method for large-scale online SLAM problems. The main idea is to combine the advantages of two state-of-the-art methods, incremental smoothing and mapping, and the subgraph-preconditioned conjugate gradient method. I also show that the new method is efficient, optimal and consistent. To sum up, preconditioning can significantly improve the efficiency of solving large-scale SLAM and SfM problems. While existing preconditioning techniques do not utilize the problem structure and have no performance guarantee, I take the first step toward a more general setting and have promising results.