A bayesian approach to simultaneously recover camera pose and non-rigid shape from monocular images

© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/In this paper we bring the tools of the Simultaneous Localization and Map Building (SLAM) problem from a rigid to a deformable domain and use them to simultaneously recover the 3D shape of non-rigid surfaces and the sequence of poses of a moving camera. Under the assumption that the surface shape may be represented as a weighted sum of deformation modes, we show that the problem of estimating the modal weights along with the camera poses, can be probabilistically formulated as a maximum a posteriori estimate and solved using an iterative least squares optimization. In addition, the probabilistic formulation we propose is very general and allows introducing different constraints without requiring any extra complexity. As a proof of concept, we show that local inextensibility constraints that prevent the surface from stretching can be easily integrated. An extensive evaluation on synthetic and real data, demonstrates that our method has several advantages over current non-rigid shape from motion approaches. In particular, we show that our solution is robust to large amounts of noise and outliers and that it does not need to track points over the whole sequence nor to use an initialization close from the ground truth.Peer ReviewedPostprint (author's final draft

Benchmarking Particle Filter Algorithms for Efficient Velodyne-Based Vehicle Localization

Keeping a vehicle well-localized within a prebuilt-map is at the core of any autonomous vehicle navigation system. In this work, we show that both standard SIR sampling and rejection-based optimal sampling are suitable for efficient (10 to 20 ms) real-time pose tracking without feature detection that is using raw point clouds from a 3D LiDAR. Motivated by the large amount of information captured by these sensors, we perform a systematic statistical analysis of how many points are actually required to reach an optimal ratio between efficiency and positioning accuracy. Furthermore, initialization from adverse conditions, e.g., poor GPS signal in urban canyons, we also identify the optimal particle filter settings required to ensure convergence. Our findings include that a decimation factor between 100 and 200 on incoming point clouds provides a large savings in computational cost with a negligible loss in localization accuracy for a VLP-16 scanner. Furthermore, an initial density of ∼2 particles/m 2 is required to achieve 100% convergence success for large-scale (∼100,000 m 2 ), outdoor global localization without any additional hint from GPS or magnetic field sensors. All implementations have been released as open-source software

Lagrangian Duality in 3D SLAM: Verification Techniques and Optimal Solutions

State-of-the-art techniques for simultaneous localization and mapping (SLAM) employ iterative nonlinear optimization methods to compute an estimate for robot poses. While these techniques often work well in practice, they do not provide guarantees on the quality of the estimate. This paper shows that Lagrangian duality is a powerful tool to assess the quality of a given candidate solution. Our contribution is threefold. First, we discuss a revised formulation of the SLAM inference problem. We show that this formulation is probabilistically grounded and has the advantage of leading to an optimization problem with quadratic objective. The second contribution is the derivation of the corresponding Lagrangian dual problem. The SLAM dual problem is a (convex) semidefinite program, which can be solved reliably and globally by off-the-shelf solvers. The third contribution is to discuss the relation between the original SLAM problem and its dual. We show that from the dual problem, one can evaluate the quality (i.e., the suboptimality gap) of a candidate SLAM solution, and ultimately provide a certificate of optimality. Moreover, when the duality gap is zero, one can compute a guaranteed optimal SLAM solution from the dual problem, circumventing non-convex optimization. We present extensive (real and simulated) experiments supporting our claims and discuss practical relevance and open problems.Comment: 10 pages, 4 figure