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

Kontextsensitive Modellhierarchien für Quantifizierung der höherdimensionalen Unsicherheit

We formulate four novel context-aware algorithms based on model hierarchies aimed to enable an efficient quantification of uncertainty in complex, computationally expensive problems, such as fluid-structure interaction and plasma microinstability simulations. Our results show that our algorithms are more efficient than standard approaches and that they are able to cope with the challenges of quantifying uncertainty in higher-dimensional, complex problems.Wir formulieren vier kontextsensitive Algorithmen auf der Grundlage von Modellhierarchien um eine effiziente Quantifizierung der Unsicherheit bei komplexen, rechenintensiven Problemen zu ermöglichen, wie Fluid-Struktur-Wechselwirkungs- und Plasma-Mikroinstabilitätssimulationen. Unsere Ergebnisse zeigen, dass unsere Algorithmen effizienter als Standardansätze sind und die Herausforderungen der Quantifizierung der Unsicherheit in höherdimensionalen, komplexen Problemen bewältigen können

Evolutionary Algorithms and Computational Methods for Derivatives Pricing

This work aims to provide novel computational solutions to the problem of derivative pricing. To achieve this, a novel hybrid evolutionary algorithm (EA) based on particle swarm optimisation (PSO) and differential evolution (DE) is introduced and applied, along with various other state-of-the-art variants of PSO and DE, to the problem of calibrating the Heston stochastic volatility model. It is found that state-of-the-art DEs provide excellent calibration performance, and that previous use of rudimentary DEs in the literature undervalued the use of these methods. The use of neural networks with EAs for approximating the solution to derivatives pricing models is next investigated. A set of neural networks are trained from Monte Carlo (MC) simulation data to approximate the closed form solution for European, Asian and American style options. The results are comparable to MC pricing, but with offline evaluation of the price using the neural networks being orders of magnitudes faster and computationally more efficient. Finally, the use of custom hardware for numerical pricing of derivatives is introduced. The solver presented here provides an energy efficient data-flow implementation for pricing derivatives, which has the potential to be incorporated into larger high-speed/low energy trading systems

LIPIcs, Volume 258, SoCG 2023, Complete Volume

LIPIcs, Volume 258, SoCG 2023, Complete Volum

Image similarity in medical images

Recent experiments have indicated a strong influence of the substrate grain orientation on the self-ordering in anodic porous alumina. Anodic porous alumina with straight pore channels grown in a stable, self-ordered manner is formed on (001) oriented Al grain, while disordered porous pattern is formed on (101) oriented Al grain with tilted pore channels growing in an unstable manner. In this work, numerical simulation of the pore growth process is carried out to understand this phenomenon. The rate-determining step of the oxide growth is assumed to be the Cabrera-Mott barrier at the oxide/electrolyte (o/e) interface, while the substrate is assumed to determine the ratio β between the ionization and oxidation reactions at the metal/oxide (m/o) interface. By numerically solving the electric field inside a growing porous alumina during anodization, the migration rates of the ions and hence the evolution of the o/e and m/o interfaces are computed. The simulated results show that pore growth is more stable when β is higher. A higher β corresponds to more Al ionized and migrating away from the m/o interface rather than being oxidized, and hence a higher retained O:Al ratio in the oxide. Experimentally measured oxygen content in the self-ordered porous alumina on (001) Al is indeed found to be about 3% higher than that in the disordered alumina on (101) Al, in agreement with the theoretical prediction. The results, therefore, suggest that ionization on (001) Al substrate is relatively easier than on (101) Al, and this leads to the more stable growth of the pore channels on (001) Al

Likelihood Asymptotics in Nonregular Settings: A Review with Emphasis on the Likelihood Ratio

This paper reviews the most common situations where one or more regularity conditions which underlie classical likelihood-based parametric inference fail. We identify three main classes of problems: boundary problems, indeterminate parameter problems -- which include non-identifiable parameters and singular information matrices -- and change-point problems. The review focuses on the large-sample properties of the likelihood ratio statistic. We emphasize analytical solutions and acknowledge software implementations where available. We furthermore give summary insight about the possible tools to derivate the key results. Other approaches to hypothesis testing and connections to estimation are listed in the annotated bibliography of the Supplementary Material