Outlier feature matches and loop-closures that survived front-end data association can lead to catastrophic failures in the back-end optimization of large-scale point cloud based 3D reconstruction. To alleviate this problem, we propose a probabilistic approach for robust back-end optimization in the presence of outliers. More specifically, we model the problem as a Bayesian network and solve it using the Expectation-Maximization algorithm. Our approach leverages on a long-tail Cauchy distribution to suppress outlier feature matches in the odometry constraints, and a Cauchy-Uniform mixture model with a set of binary latent variables to simultaneously suppress outlier loop-closure constraints and outlier feature matches in the inlier loop-closure constraints. Furthermore, we show that by using a Gaussian-Uniform mixture model, our approach degenerates to the formulation of a state-of-the-art approach for robust indoor reconstruction. Experimental results demonstrate that our approach has comparable performance with the state-of-the-art on a benchmark indoor dataset, and outperforms it on a large-scale outdoor dataset. Our source code can be found on the project website.
In this paper, we model the robust loop-closure pose-graph SLAM problem as a Bayesian network and show that it can be solved with the Classification Expectation-Maximization (EM) algorithm. In particular, we express our robust pose-graph SLAM as a Bayesian network where the robot poses and constraints are latent and observed variables. An additional set of latent variables is introduced as weights for the loop-constraints. We show that the weights can be chosen as the Cauchy function, which are iteratively computed from the errors between the predicted robot poses and observed loop-closure constraints in the Expectation step, and used to weigh the cost functions from the pose-graph loop-closure constraints in the Maximization step. As a result, outlier loop-closure constraints are assigned low weights and exert less influences in the pose-graph optimization within the EM iterations. To prevent the EM algorithm from getting stuck at local minima, we perform the EM algorithm multiple times where the loop constraints with very low weights are removed after each EM process. This is repeated until there are no more changes to the weights. We show proofs of the conceptual similarity between our EM algorithm and the M-Estimator. Specifically, we show that the weight function in our EM algorithm is equivalent to the robust residual function in the M-Estimator. We verify our proposed algorithm with experimental results from multiple simulated and real-world datasets, and comparisons with other existing works. The modeling of spatial discontinuities for problems such as surface recovery, segmentation, image reconstruction, and optical flow has been intensely studied in computer vision. While “line-process” models of discontinuities have received a great deal of attention, there has been recent interest in the use of robust statistical techniques to account for discontinuities. This paper unifies the two approaches. To achieve this we generalize the notion of a “line process” to that of an analog “outlier process” and show how a problem formulated in terms of outlier processes can be viewed in terms of robust statistics. We also characterize a class of robust statistical problems for which an equivalent outlier-process formulation exists and give a straightforward method for converting a robust estimation problem into an outlier-process formulation. We show how prior assumptions about the spatial structure of outliers can be expressed as constraints on the recovered analog outlier processes and how traditional continuation methods can be extended to the explicit outlier-process formulation. These results indicate that the outlier-process approach provides a general framework which subsumes the traditional line-process approaches as well as a wide class of robust estimation problems. Examples in surface reconstruction, image segmentation, and optical flow are presented to illustrate the use of outlier processes and to show how the relationship between outlier processes and robust statistics can be exploited. An appendix provides a catalog of common robust error norms and their equivalent outlier-process formulations. We present an approach to indoor scene reconstruction from RGB-D video. The key idea is to combine geometric registration of scene fragments with robust global optimization based on line processes. Geometric registration is error-prone due to sensor noise, which leads to aliasing of geometric detail and inability to disambiguate different surfaces in the scene. The presented optimization approach disables erroneous geometric alignments even when they significantly outnumber correct ones. Experimental results demonstrate that the presented approach substantially increases the accuracy of reconstructed scene models. Current SLAM back-ends are based on least squares optimization and thus are not robust against outliers like data association errors and false positive loop closure detections. Our paper presents and evaluates a robust back-end formulation for SLAM using switchable constraints. Instead of proposing yet another appearance-based data association technique, our system is able to recognize and reject outliers during the optimization. This is achieved by making the topology of the underlying factor graph representation subject to the optimization instead of keeping it fixed. The evaluation shows that the approach can deal with up to 1000 false positive loop closure constraints on various datasets. This largely increases the robustness of the overall SLAM system and closes a gap between the sensor-driven front-end and the back-end optimizers.