Unified Representation of Geometric Primitives for Graph-SLAM Optimization Using Decomposed Quadrics

In Simultaneous Localization And Mapping (SLAM) problems, high-level landmarks have the potential to build compact and informative maps compared to traditional point-based landmarks. This work is focused on the parameterization problem of high-level geometric primitives that are most frequently used, including points, lines, planes, ellipsoids, cylinders, and cones. We first present a unified representation of those geometric primitives using \emph{quadrics} which yields a consistent and concise formulation. Then we further study a decomposed model of quadrics that discloses the symmetric and degenerated nature of quadrics. Based on the decomposition, we develop physically meaningful quadrics factors in the settings of the graph-SLAM problem. Finally, in simulation experiments, it is shown that the decomposed formulation has better efficiency and robustness to observation noises than baseline parameterizations. And in real-world experiments, the proposed back-end framework is demonstrated to be capable of building compact and regularized maps.