Probabilistic Solution of Inverse Problems

In this thesis we study the general problem of reconstructing a function, defined on a finite lattice from a set of incomplete, noisy and/or ambiguous observations. The goal of this work is to demonstrate the generality and practical value of a probabilistic (in particular, Bayesian) approach to this problem, particularly in the context of Computer Vision. In this approach, the prior knowledge about the solution is expressed in the form of a Gibbsian probability distribution on the space of all possible functions, so that the reconstruction task is formulated as an estimation problem. Our main contributions are the following: (1) We introduce the use of specific error criteria for the design of the optimal Bayesian estimators for several classes of problems, and propose a general (Monte Carlo) procedure for approximating them. This new approach leads to a substantial improvement over the existing schemes, both regarding the quality of the results (particularly for low signal to noise ratios) and the computational efficiency. (2) We apply the Bayesian appraoch to the solution of several problems, some of which are formulated and solved in these terms for the first time. Specifically, these applications are: teh reconstruction of piecewise constant surfaces from sparse and noisy observationsl; the reconstruction of depth from stereoscopic pairs of images and the formation of perceptual clusters. (3) For each one of these applications, we develop fast, deterministic algorithms that approximate the optimal estimators, and illustrate their performance on both synthetic and real data. (4) We propose a new method, based on the analysis of the residual process, for estimating the parameters of the probabilistic models directly from the noisy observations. This scheme leads to an algorithm, which has no free parameters, for the restoration of piecewise uniform images. (5) We analyze the implementation of the algorithms that we develop in non-conventional hardware, such as massively parallel digital machines, and analog and hybrid networks.

The Image Irradiance Equation: Its Solution and Application

How much information about the shape of an object can be inferred from its image? In particular, can the shape of an object be reconstructed by measuring the light it reflects from points on its surface? These questions were raised by Horn [HO70] who formulated a set of conditions such that the image formation can be described in terms of a first order partial differential equation, the image irradiance equation. In general, an image irradiance equation has infinitely many solutions. Thus constraints necessary to find a unique solution need to be identified. First we study the continuous image irradiance equation. It is demonstrated when and how the knowledge of the position of edges on a surface can be used to reconstruct the surface. Furthermore we show how much about the shape of a surface can be deduced from so called singular points. At these points the surface orientation is uniquely determined by the measured brightness. Then we investigate images in which certain types of silhouettes, which we call b-silhouettes, can be detected. In particular we answer the following question in the affirmative: Is there a set of constraints which assure that if an image irradiance equation has a solution, it is unique? To this end we postulate three constraints upon the image irradiance equation and prove that they are sufficient to uniquely reconstruct the surface from its image. Furthermore it is shown that any two of these constraints are insufficient to assure a unique solution to an image irradiance equation. Examples are given which illustrate the different issues. Finally, an overview of known numerical methods for computing solutions to an image irradiance equation are presented.

A novel process for converting coalmine-drained methane gas to syngas over nickel-magnesia solid solution catalysts

A novel process is developed in this paper for utilizing the coalmine-drained methane gas that is usually vented straight into the atmosphere in most coalmines worldwide. It is expected that low-cost syngas can be produced by the combined air partial oxidation and CO2 reforming of methane, because this process utilizes directly the methane, air, and carbon dioxide in the coalmine-drained gas without going through the separation step. For this purpose, a nickel-magnesia solid solution catalyst was prepared and its catalytic performance for the proposed process was investigated. It was found that calcination temperature has significant influence on the catalytic performance due to the different extent of solid solution formation in the catalysts. A uniform nickel-magnesia solid solution catalyst exhibits higher stability than the catalysts in which NiO has not completely formed solid solution with MgO. Its catalytic activity and selectivity remain stable during 120 h of reaction. The product H-2/CO ratio is mainly dependent on the feed gas composition. By changing CO2/air ratio of the feed gases, syngas with a H-2/CO ratio between 1 and 1.9 can be obtained. The influences of reaction temperature and nickel loading on the catalytic performance were also investigated. (c) 2004 Elsevier B.V All rights reserved.

Cobalt boride catalysts for hydrogen generation from alkaline NaBH4 solution

Cobalt boride precursors were synthesized via chemical reaction of aqueous sodium borohydride with cobalt chloride, and followed by heat-treating at various temperatures. The as-prepared Co-B catalysts were characterized and analyzed by X-ray diffraction (XRD), nitrogen adsorption-desorption and catalytic activity test; and were adopted to help accelerating hydrolysis reaction of NaBH4 alkaline solution. The Co-B catalyst treated at 500 degrees C exhibits the best catalytic activity, and achieves an average H, generation rate of 2970 ml/min/g, which may give a successive H, supply for a 481 W proton exchange membrane fuel cell (PEMFC) at 100% H-2 utilization. (c) 2005 Elsevier B.V. All rights reserved.

CO2Y the intelligent green solution: minimising carbon emissions by maximising shared travel opportunity.

It is in the interests of everybody that the environment is protected. In view of the recent leaps in environmental awareness it would seem timely and sensible, therefore, for people to pool vehicle resources to minimise the damaging impact of emissions. However, this is often contrary to how complex social systems behave – local decisions made by self-interested individuals often have emergent effects that are in the interests of nobody. For software engineers a major challenge is to help facilitate individual decision-making such that individual preferences can be met, which, when accumulated, minimise adverse effects at the level of the transport system. We introduce this general problem through a concrete example based on vehicle-sharing. Firstly, we outline the kind of complex transportation problem that is directly addressed by our technology (CO2y™ - pronounced “cosy”), and also show how this differs from other more basic software solutions. The CO2y™ architecture is then briefly introduced. We outline the practical advantages of the advanced, intelligent software technology that is designed to satisfy a number of individual preference criteria and thereby find appropriate matches within a population of vehicle-share users. An example scenario of use is put forward, i.e., minimisation of grey-fleets within a medium-sized company. Here we comment on some of the underlying assumptions of the scenario, and how in a detailed real-world situation such assumptions might differ between different companies, and individual users. Finally, we summarise the paper, and conclude by outlining how the problem of pooled transportation is likely to benefit from the further application of emergent, nature-inspired computing technologies. These technologies allow systems-level behaviour to be optimised with explicit representation of individual actors. With these techniques we hope to make real progress in facing the complexity challenges that transportation problems produce.

Asymptotic behaviour of the elastic solution near the tip of a crack situated at a nonideal interface

Mishuris, G; Kuhn, G., (2001) 'Asymptotic behaviour of the elastic solution near the tip of a crack situated at a nonideal interface', Zeitschrift f?r Angewandte Mathematik und Mechanik 81(12) pp.811-826 RAE2008