This paper addresses the problem of assessing trajectory quality in conditions when no ground truth poses are available or when their accuracy is not enough for the specific task - for example, small-scale mapping in outdoor scenes. In our work, we propose a no-reference metric, Mutually Orthogonal Metric (MOM), that estimates the quality of the map from registered point clouds via the trajectory poses. MOM strongly correlates with full-reference trajectory metric Relative Pose Error, making it a trajectory benchmarking tool on setups where 3D sensing technologies are employed. We provide a mathematical foundation for such correlation and confirm it statistically in synthetic environments. Furthermore, since our metric uses a subset of points from mutually orthogonal surfaces, we provide an algorithm for the extraction of such subset and evaluate its performance in synthetic CARLA environment and on KITTI dataset.
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