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. In this work, we focus on the parameterization of frequently used geometric primitives including points, lines, planes, ellipsoids, cylinders, and cones. We first present a unified representation based on quadrics, leading to a consistent and concise formulation. Then we further study a decomposed model of quadrics that discloses the symmetric and degenerated properties of a primitive. Based on the decomposition, we develop geometrically meaningful quadrics factors in the settings of a graph-SLAM problem. Then in simulation experiments, it is shown that the decomposed formulation has better efficiency and robustness to observation noises than baseline parameterizations. Finally, in real-world experiments, the proposed back-end framework is demonstrated to be capable of building compact and regularized maps.
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