Tectonic smoothing and mapping
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Large-scale mapping has become the key to numerous applications, e.g. simultaneous localization and mapping (SLAM) for autonomous robots. Despite of the success of many SLAM projects, there are still some challenging scenarios in which most of the current algorithms are not able to deliver an exact solution fast enough. One of these challenges is the size of SLAM problems, which has increased by several magnitudes over the last decade. Another challenge for SLAM problems is the large amount of noise baked in the measurements, which often yields poor initializations and slows or even fails the optimization. Urban 3D reconstruction is another popular application for large-scale mapping and has received considerable attention recently from the computer vision community. High-quality 3D models are useful in various successful cartographic and architectural applications, such as Google Earth or Microsoft Live Local. At the heart of urban reconstruction problems is structure from motion (SfM). Due to the wide availability of cameras, especially on handhold devices, SfM is becoming a more and more crucial technique to handle a large amount of images. In the thesis, I present a novel batch algorithm, namely Tectonic Smoothing and Mapping (TSAM). I will show that the original SLAM graph can be recursively partitioned into multiple-level submaps using the nested dissection algorithm, which leads to the cluster tree, a powerful graph representation. By employing the nested dissection algorithm, the algorithm greatly minimizes the dependencies between two subtrees, and the optimization of the original graph can be done using a bottom-up inference along the corresponding cluster tree. To speed up the computation, a base node is introduced for each submap and is used to represent the rigid transformation of the submap in the global coordinate frame. As a result, the optimization moves the base nodes rather than the actual submap variables. I will also show that TSAM can be successfully applied to the SfM problem as well, in which a hypergraph representation is employed to capture the pairwise constraints between cameras. The hierarchical partitioning based on the hypergraph not only yields a cluster tree as in the SLAM problem but also forces resulting submaps to be nonsingular. I will demonstrate the TSAM algorithm using various simulation and real-world data sets.