Accelerating Globally Optimal Consensus Maximization in Geometric Vision

Branch-and-bound-based consensus maximization stands out due to its important ability of retrieving the globally optimal solution to outlier-affected geometric problems. However, while the discovery of such solutions caries high scientific value, its application in practical scenarios is often prohibited by its computational complexity growing exponentially as a function of the dimensionality of the problem at hand. In this work, we convey a novel, general technique that allows us to branch over an $n-1$ dimensional space for an n-dimensional problem. The remaining degree of freedom can be solved globally optimally within each bound calculation by applying the efficient interval stabbing technique. While each individual bound derivation is harder to compute owing to the additional need for solving a sorting problem, the reduced number of intervals and tighter bounds in practice lead to a significant reduction in the overall number of required iterations. Besides an abstract introduction of the approach, we present applications to three fundamental geometric computer vision problems: camera resectioning, relative camera pose estimation, and point set registration. Through our exhaustive tests, we demonstrate significant speed-up factors at times exceeding two orders of magnitude, thereby increasing the viability of globally optimal consensus maximizers in online application scenarios

Intuitive 3D Maps for MAV Terrain Exploration and Obstacle Avoidance

Recent development showed that Micro Aerial Vehicles (MAVs) are nowadays capable of autonomously take off at one point and land at another using only one single camera as exteroceptive sensor. During the flight and landing phase the MAV and user have, however, little knowledge about the whole terrain and potential obstacles. In this paper we show a new solution for a real-time dense 3D terrain reconstruction. This can be used for efficient unmanned MAV terrain exploration and yields a solid base for standard autonomous obstacle avoidance algorithms and path planners. Our approach is based on a textured 3D mesh on sparse 3D point features of the scene. We use the same feature points to localize and control the vehicle in the 3D space as we do for building the 3D terrain reconstruction mesh. This enables us to reconstruct the terrain without significant additional cost and thus in real-time. Experiments show that the MAV is easily guided through an unknown, GPS denied environment. Obstacles are recognized in the iteratively built 3D terrain reconstruction and are thus well avoide

Scale jump-aware pose graph relaxation for monocular SLAM with re-initializations

Pose graph relaxation has become an indispensable addition to SLAM enabling efficient global registration of sensor reference frames under the objective of satisfying pair-wise relative transformation constraints. The latter may be given by incremental motion estimation or global place recognition. While the latter case enables loop closures and drift compensation, care has to be taken in the monocular case in which local estimates of structure and displacements can differ from reality not just in terms of noise, but also in terms of a scale factor. Owing to the accumulation of scale propagation errors, this scale factor is drifting over time, hence scale-drift aware pose graph relaxation has been introduced. We extend this idea to cases in which the relative scale between subsequent sensor frames is unknown, a situation that can easily occur if monocular SLAM enters re-initialization and no reliable overlap between successive local maps can be identified. The approach is realized by a hybrid pose graph formulation that combines the regular similarity consistency terms with novel, scale-blind constraints. We apply the technique to the practically relevant case of small indoor service robots capable of effectuating purely rotational displacements, a condition that can easily cause tracking failures. We demonstrate that globally consistent trajectories can be recovered even if multiple re-initializations occur along the loop, and present an in-depth study of success and failure cases.Comment: 8 pages, 23 figures, International Conference on Intelligent Robots and Systems 202

The generalized relative pose and scale problem: View-graph fusion via 2D-2D registration

It is well-known that the relative pose problem can be generalized to non-central cameras. We present a further generalization, denoted the generalized relative pose and scale problem. It has surprising importance for classical problems such as solving similarity transformations for view-graph concatenation in hierarchical structure from motion and loop-closure in visual SLAM, both posed as a 2D-2D registration problem. The relative pose problem and all its generalizations constitute a family of similar symmetric eigenvalue problems, which allow us to compress data and find a geometrically meaningful solution by an efficient search in the space of rotations. While the derivation of a completely general closed-form solver appears intractable, we make use of a simple heuristic global energy minimization scheme based on local minimum suppression, returning outstanding performance in practically relevant scenarios. Efficiency and reliability of our algorithm are demonstrated on both simulated and real data, supporting our claim of superior performance with respect to both generalized 2D-3D and 3D-3D registration approaches. By directly employing image information, we avoid the common noise in point clouds occuring especially along the depth direction.This research is supported by the ARC Centre of Excellence for Robotic Vision, as well as the ARC grant DE150101365. The work is also supported by NSF Grant IIS-1219261, ONR Grant N00014-14-1- 0133 and NSF Graduate Research Fellowship Grant DGE- 1144085

Semi-Dense Visual Odometry for RGB-D Cameras Using Approximate Nearest Neighbour Fields

This paper presents a robust and efficient semidense visual odometry solution for RGB-D cameras. The core of our method is a 2D-3D ICP pipeline which estimates the pose of the sensor by registering the projection of a 3D semidense map of a reference frame with the 2D semi-dense region extracted in the current frame. The processing is speeded up by efficiently implemented approximate nearest neighbour fields under the Euclidean distance criterion, which permits the use of compact Gauss-Newton updates in the optimization. The registration is formulated as a maximum a posterior problem to deal with outliers and sensor noise, and the equivalent weighted least squares problem is consequently solved by iteratively reweighted least squares method. A variety of robust weight functions are tested and the optimum is determined based on the probabilistic characteristics of the sensor model. Extensive evaluation on publicly available RGB-D datasets shows that the proposed method predominantly outperforms existing state-of-the-art methods.The work is furthermore supported by ARC grants DE150101365. Yi Zhou acknowledges the financial support from the China Scholarship Council for his PhD Scholarship No.20140602009