MINA: {C}onvex Mixed-Integer Programming for Non-Rigid Shape Alignment

We present a convex mixed-integer programming formulation for non-rigid shape matching. To this end, we propose a novel shape deformation model based on an efficient low-dimensional discrete model, so that finding a globally optimal solution is tractable in (most) practical cases. Our approach combines several favourable properties: it is independent of the initialisation, it is much more efficient to solve to global optimality compared to analogous quadratic assignment problem formulations, and it is highly flexible in terms of the variants of matching problems it can handle. Experimentally we demonstrate that our approach outperforms existing methods for sparse shape matching, that it can be used for initialising dense shape matching methods, and we showcase its flexibility on several examples

SIGMA: Scale-Invariant Global Sparse Shape Matching

We propose a novel mixed-integer programming (MIP) formulation for generating precise sparse correspondences for highly non-rigid shapes. To this end, we introduce a projected Laplace-Beltrami operator (PLBO) which combines intrinsic and extrinsic geometric information to measure the deformation quality induced by predicted correspondences. We integrate the PLBO, together with an orientation-aware regulariser, into a novel MIP formulation that can be solved to global optimality for many practical problems. In contrast to previous methods, our approach is provably invariant to rigid transformations and global scaling, initialisation-free, has optimality guarantees, and scales to high resolution meshes with (empirically observed) linear time. We show state-of-the-art results for sparse non-rigid matching on several challenging 3D datasets, including data with inconsistent meshing, as well as applications in mesh-to-point-cloud matching.Comment: 14 page

Optimal Compression of Point Clouds

Image-based localization is a crucial step in many 3D computer vision applications, e.g., self-driving cars, robotics, and augmented reality among others. Unfortunately, many image-based-localization applications require the storage of large scenes, and many camera pose estimators struggle to scale when the scene representation is large. To alleviate the aforementioned problems, many applications compress a scene representation by reducing the number of 3D points of a point cloud. The state-of-the-art compresses a scene representation by using a K-cover-based algorithm. While the state-of-the-art selects a subset of 3D points that maximizes the probability of accurately estimating the camera pose of a new image, the state-of-the-art does not guarantee an optimal compression and has parameters that are hard to tune. We propose to compress a scene representation by means of a constrained quadratic program that resembles a one-class support vector machine (SVM). Thanks to this resemblance, we derived a variant of the sequential minimal optimization, a widely adopted algorithm to train SVMs. The proposed method uses the points corresponding to the support vectors as the subset to represent a scene. Our experiments on publicly large-scale image-based localization show that our proposed approach delivers four times fewer failed localizations than that of the state-of-the-art while scaling on average two orders of magnitude more favorably

3D Sensor Placement and Embedded Processing for People Detection in an Industrial Environment

Papers I, II and III are extracted from the dissertation and uploaded as separate documents to meet post-publication requirements for self-arciving of IEEE conference papers.At a time when autonomy is being introduced in more and more areas, computer vision plays a very important role. In an industrial environment, the ability to create a real-time virtual version of a volume of interest provides a broad range of possibilities, including safety-related systems such as vision based anti-collision and personnel tracking. In an offshore environment, where such systems are not common, the task is challenging due to rough weather and environmental conditions, but the result of introducing such safety systems could potentially be lifesaving, as personnel work close to heavy, huge, and often poorly instrumented moving machinery and equipment. This thesis presents research on important topics related to enabling computer vision systems in industrial and offshore environments, including a review of the most important technologies and methods. A prototype 3D sensor package is developed, consisting of different sensors and a powerful embedded computer. This, together with a novel, highly scalable point cloud compression and sensor fusion scheme allows to create a real-time 3D map of an industrial area. The question of where to place the sensor packages in an environment where occlusions are present is also investigated. The result is algorithms for automatic sensor placement optimisation, where the goal is to place sensors in such a way that maximises the volume of interest that is covered, with as few occluded zones as possible. The method also includes redundancy constraints where important sub-volumes can be defined to be viewed by more than one sensor. Lastly, a people detection scheme using a merged point cloud from six different sensor packages as input is developed. Using a combination of point cloud clustering, flattening and convolutional neural networks, the system successfully detects multiple people in an outdoor industrial environment, providing real-time 3D positions. The sensor packages and methods are tested and verified at the Industrial Robotics Lab at the University of Agder, and the people detection method is also tested in a relevant outdoor, industrial testing facility. The experiments and results are presented in the papers attached to this thesis.publishedVersio

A Tutorial on Clique Problems in Communications and Signal Processing

Since its first use by Euler on the problem of the seven bridges of K\"onigsberg, graph theory has shown excellent abilities in solving and unveiling the properties of multiple discrete optimization problems. The study of the structure of some integer programs reveals equivalence with graph theory problems making a large body of the literature readily available for solving and characterizing the complexity of these problems. This tutorial presents a framework for utilizing a particular graph theory problem, known as the clique problem, for solving communications and signal processing problems. In particular, the paper aims to illustrate the structural properties of integer programs that can be formulated as clique problems through multiple examples in communications and signal processing. To that end, the first part of the tutorial provides various optimal and heuristic solutions for the maximum clique, maximum weight clique, and $k$-clique problems. The tutorial, further, illustrates the use of the clique formulation through numerous contemporary examples in communications and signal processing, mainly in maximum access for non-orthogonal multiple access networks, throughput maximization using index and instantly decodable network coding, collision-free radio frequency identification networks, and resource allocation in cloud-radio access networks. Finally, the tutorial sheds light on the recent advances of such applications, and provides technical insights on ways of dealing with mixed discrete-continuous optimization problems