Globally-Optimal Inlier Set Maximisation for Camera Pose and Correspondence Estimation

Estimating the 6-DoF pose of a camera from a single image relative to a 3D point-set is an important task for many computer vision applications. Perspective-n-point solvers are routinely used for camera pose estimation, but are contingent on the provision of good quality 2D-3D correspondences. However, finding cross-modality correspondences between 2D image points and a 3D point-set is non-trivial, particularly when only geometric information is known. Existing approaches to the simultaneous pose and correspondence problem use local optimisation, and are therefore unlikely to find the optimal solution without a good pose initialisation, or introduce restrictive assumptions. Since a large proportion of outliers and many local optima are common for this problem, we instead propose a robust and globally-optimal inlier set maximisation approach that jointly estimates the optimal camera pose and correspondences. Our approach employs branch-and-bound to search the 6D space of camera poses, guaranteeing global optimality without requiring a pose prior. The geometry of SE(3) is used to find novel upper and lower bounds on the number of inliers and local optimisation is integrated to accelerate convergence. The algorithm outperforms existing approaches on challenging synthetic and real datasets, reliably finding the global optimum, with a GPU implementation greatly reducing runtime

Robust and Optimal Methods for Geometric Sensor Data Alignment

Geometric sensor data alignment - the problem of finding the rigid transformation that correctly aligns two sets of sensor data without prior knowledge of how the data correspond - is a fundamental task in computer vision and robotics. It is inconvenient then that outliers and non-convexity are inherent to the problem and present significant challenges for alignment algorithms. Outliers are highly prevalent in sets of sensor data, particularly when the sets overlap incompletely. Despite this, many alignment objective functions are not robust to outliers, leading to erroneous alignments. In addition, alignment problems are highly non-convex, a property arising from the objective function and the transformation. While finding a local optimum may not be difficult, finding the global optimum is a hard optimisation problem. These key challenges have not been fully and jointly resolved in the existing literature, and so there is a need for robust and optimal solutions to alignment problems. Hence the objective of this thesis is to develop tractable algorithms for geometric sensor data alignment that are robust to outliers and not susceptible to spurious local optima. This thesis makes several significant contributions to the geometric alignment literature, founded on new insights into robust alignment and the geometry of transformations. Firstly, a novel discriminative sensor data representation is proposed that has better viewpoint invariance than generative models and is time and memory efficient without sacrificing model fidelity. Secondly, a novel local optimisation algorithm is developed for nD-nD geometric alignment under a robust distance measure. It manifests a wider region of convergence and a greater robustness to outliers and sampling artefacts than other local optimisation algorithms. Thirdly, the first optimal solution for 3D-3D geometric alignment with an inherently robust objective function is proposed. It outperforms other geometric alignment algorithms on challenging datasets due to its guaranteed optimality and outlier robustness, and has an efficient parallel implementation. Fourthly, the first optimal solution for 2D-3D geometric alignment with an inherently robust objective function is proposed. It outperforms existing approaches on challenging datasets, reliably finding the global optimum, and has an efficient parallel implementation. Finally, another optimal solution is developed for 2D-3D geometric alignment, using a robust surface alignment measure. Ultimately, robust and optimal methods, such as those in this thesis, are necessary to reliably find accurate solutions to geometric sensor data alignment problems