Phase-shifting Haar Wavelets For Image-based Rendering Applications

In this thesis, we establish the underlying research background necessary for tackling the problem of phase-shifting in the wavelet transform domain. Solving this problem is the key to reducing the redundancy and huge storage requirement in Image-Based Rendering (IBR) applications, which utilize wavelets. Image-based methods for rendering of dynamic glossy objects do not truly scale to all possible frequencies and high sampling rates without trading storage, glossiness, or computational time, while varying both lighting and viewpoint. This is due to the fact that current approaches are limited to precomputed radiance transfer (PRT), which is prohibitively expensive in terms of memory requirements when both lighting and viewpoint variation are required together with high sampling rates for high frequency lighting of glossy material. At the root of the above problem is the lack of a closed-form run-time solution to the nontrivial problem of rotating wavelets, which we solve in this thesis. We specifically target Haar wavelets, which provide the most efficient solution to solving the tripleproduct integral, which in turn is fundamental to solving the environment lighting problem. The problem is divided into three main steps, each of which provides several key theoretical contributions. First, we derive closed-form expressions for linear phase-shifting in the Haar domain for one-dimensional signals, which can be generalized to N-dimensional signals due to separability. Second, we derive closed-form expressions for linear phase-shifting for two-dimensional signals that are projected using the non-separable Haar transform. For both cases, we show that the coefficients of the shifted data can be computed solely by using the coefficients of the original data. We also derive closed-form expressions for non-integer shifts, which has not been reported before. As an application example of these results, we apply the new formulae to image shifting, rotation and interpolation, and demonstrate the superiority of the proposed solutions to existing methods. In the third step, we establish a solution for non-linear phase-shifting of two-dimensional non-separable Haar-transformed signals, which is directly applicable to the original problem of image-based rendering. Our solution is the first attempt to provide an analytic solution to the difficult problem of rotating wavelets in the transform domain

Quantitative imaging algorithms for in situ damage characterisation using guided waves

Guided wave based structural health monitoring has attracted tremendous attention in recent times from industry groups and research communities alike. This new approach holds great promises to supplement conventional quantitative non-destructive evaluation methods for high-value structural assests with in-situ techniques in the future. The aim of this research is to develop and validate quantitative imaging algorithms to determine the size and severity of structural damage from guided wave response measured using an array of active sensors. Three new imaging algorithms have been developed and validated viz. modified diffraction tomography, modified beamforming and modified time-reversal for digital reconstruction and characterisation of in-plane damage in plate-like structures using guided waves. The proposed algorithms treat damage as a flexural inhomogeneity within the framework of Mindlin plate theory. By applying the Born approximation theory, inverse solutions of the damage intensity can be derived using measured response as input. The imaging algorithms are applicable to early corrosion damage in metallic structures and impact damage in fibre-laminated plates, where the damage can be approximated as weak scatterers. Unlike existing imaging strategies using guided waves, the new algorithms lead to reconstruction integrals that have a very similar mathematical structure as that pertinent to far-field methods. Furthermore, the new algorithms consider the multi-static data matrix and Green’s function of the structure to provide damage characterisation in the near-field and compensation for multi-path wave interactions. The imaging algorithms are extensively tested using numerical data and finite element simulated data for four appropriate indicators of imaging performance viz. reconstruction quality, prediction of damage geometry as well as an estimate of damage size and severity. In the numerical studies, analytical solutions are used to generate the data matrix and Green’s function. Initially, the scatterers are simulated as a variation in wavespeed or refractive index during the process of formulating the algorithms. However, for testing of the algorithms using plate-waves, the scatterers are simulated as localised reductions in material thickness and inertia to model corrosion damage and delamination damage, respectively. The results show exceptional quality of reconstruction for a single scatterer, even when the scatterer and sensors are in close proximity. Additionally, the time-reversal based imaging algorithms exhibited the least susceptibility to noise in the data matrix. This result is significant in practice for locating the damage, along with providing an approximation to damage shape and size. Validation of the new imaging algorithms using synthetic data (multi-static scattering matrix and Green’s function) generated by the finite element analyses reveal that the imaging algorithms are capable of good estimation of damage shape, size and severity for a variety of cases including multi-site scatterers, arbitrary shaped damage and plate configurations featuring multi-path interactions. Amongst the new algorithms, the modified time-reversal formula provided the best imaging results for complex structures, even in the presence of strong multi-path wave interactions between the structural features and damage. Apart from these results, an approach that allows accurate reconstruction of the damage using minimal number of sensors is developed and implemented

An analysis of spending behaviour under liquidity constraints with an application to financial hedging

Imperial Users onl

Caustic echoes from a Schwarzschild black hole

We present the first numerical construction of the scalar Schwarzschild Green function in the time-domain, which reveals several universal features of wave propagation in black hole spacetimes. We demonstrate the trapping of energy near the photon sphere and confirm its exponential decay. The trapped wavefront propagates through caustics resulting in echoes that propagate to infinity. The arrival times and the decay rate of these caustic echoes are consistent with propagation along null geodesics and the large l-limit of quasinormal modes. We show that the four-fold singularity structure of the retarded Green function is due to the well-known action of a Hilbert transform on the trapped wavefront at caustics. A two-fold cycle is obtained for degenerate source-observer configurations along the caustic line, where the energy amplification increases with an inverse power of the scale of the source. Finally, we discuss the tail piece of the solution due to propagation within the light cone, up to and including null infinity, and argue that, even with ideal instruments, only a finite number of echoes can be observed. Putting these pieces together, we provide a heuristic expression that approximates the Green function with a few free parameters. Accurate calculations and approximations of the Green function are the most general way of solving for wave propagation in curved spacetimes and should be useful in a variety of studies such as the computation of the self-force on a particle.Comment: 18 pages, 23 figure

Differential railway track settlement in a transition zone – Field measurements and numerical simulations

In a transition zone between two different railway track forms, there is a discontinuity in track structure leading to a gradient in track stiffness. Examples include transitions between different superstructures, e.g., slab track to ballasted track, and/or between different substructures, e.g., embankment to a bridge or tunnel structure. Differences in loading and support conditions at the interfaces between track superstructure and substructure on either side of the transition may lead to differential track settlement and an irregularity in longitudinal rail level soon after construction because of densification of ballast and consolidation in the subsoil. This results in an amplification of the dynamic traffic loading along the transition. To ensure the safety of railway operation and reduce maintenance costs, it is necessary to monitor the condition of the transition zone and detect any operational change at an early stage.A methodology for the simulation of long-term differential track settlement, the development of voided sleepers leading to a redistribution of rail seat loads, and the evolving irregularity in vertical track geometry at a transition between two track forms, is presented. For a prescribed traffic load, the accumulated settlement is predicted using an iterative approach. It is based on a time-domain model of vertical dynamic vehicle–track interaction to calculate the contact forces between sleepers and ballast in the short term. These are used in an empirical model to determine the long-term settlement of the ballast and subgrade below each sleeper. Gravity loads and state-dependent track conditions are accounted for. The methodology is applied to a transition zone between a ballasted track and a slab track that is subjected to heavy haul traffic. The influence of higher axle loads and the implementation of under sleeper pads on sleeper settlement is assessed. Based on fibre Bragg grating sensors, a setup for in-situ long-term condition monitoring of track bed degradation in a transition zone has been developed and implemented to provide data for verification and calibration of the simulation model. The system is designed for measurements in an operational railway track in harsh conditions in the north of Sweden. The instrumentation along the transition comprises four clusters, each with an optical strain gauge array on the rail web in one sleeper bay, and an accelerometer and a displacement transducer on the sleeper end. Two additional accelerometers are installed far from the transition zone to measure a reference state. Combined, the data should not only provide details on long-term settlements, but also the change in dynamic response it underpins

Spatial and Temporal Considerations in Vehicle Path Tracking With an Emphasis on Spatial Robustness

This dissertation researches the task and path management of an autonomous vehicle with Ackerman-type steering. The task management problem was approached as a path training operation in which a human operator drives the desired path through an environment. A training trajectory is converted into a series of path segments that are driveable by the autonomous vehicle by first fitting a general path to the dataset. Next, transition segments are added to the general path to match the vehicle velocity and steering angle rate limit. The path management problem has been approached by first deriving a kine- matic model of the vehicle. The time domain model is expressed in the frequency domain and then converted into a spatial frequency domain. Next, a stability crite- rion is derived and used in the synthesis of a spatially-robust path controller

B Physics at the Tevatron: Run II and Beyond

This report provides a comprehensive overview of the prospects for B physics at the Tevatron. The work was carried out during a series of workshops starting in September 1999. There were four working groups: 1) CP Violation, 2) Rare and Semileptonic Decays, 3) Mixing and Lifetimes, 4) Production, Fragmentation and Spectroscopy. The report also includes introductory chapters on theoretical and experimental tools emphasizing aspects of B physics specific to hadron colliders, as well as overviews of the CDF, D0, and BTeV detectors, and a Summary.Comment: 583 pages. Further information on the workshops, including transparencies, can be found at the workshop's homepage: http://www-theory.lbl.gov/Brun2/. The report is also available in 2-up http://www-theory.lbl.gov/Brun2/report/report2.ps.gz or chapter-by-chapter http://www-theory.lbl.gov/Brun2/report

Computerised stereoscopic measurement of the human retina

The research described herein is an investigation into the problems of obtaining useful clinical measurements from stereo photographs of the human retina through automation of the stereometric procedure by digital stereo matching and image analysis techniques. Clinical research has indicated a correlation between physical changes to the optic disc topography (the region on the retina where the optic nerve enters the eye) and the advance of eye disease such as hypertension and glaucoma. Stereoscopic photography of the human retina (or fundus, as it is called) and the subsequent measurement of the topography of the optic disc is of great potential clinical value as an aid in observing the pathogenesis of such disease, and to this end, accurate measurements of the various parameters that characterise the changing shape of the optic disc topography must be provided. Following a survey of current clinical methods for stereoscopic measurement of the optic disc, fundus image data acquisition, stereo geometry, limitations of resolution and accuracy, and other relevant physical constraints related to fundus imaging are investigated. A survey of digital stereo matching algorithms is presented and their strengths and weaknesses are explored, specifically as they relate to the suitability of the algorithm for the fundus image data. The selection of an appropriate stereo matching algorithm is discussed, and its application to four test data sets is presented in detail. A mathematical model of two-dimensional image formation is developed together with its corresponding auto-correlation function. In the presense of additive noise, the model is used as a tool for exploring key problems with respect to the stereo matching of fundus images. Specifically, measures for predicting correlation matching error are developed and applied. Such measures are shown to be of use in applications where the results of image correlation cannot be independently verified, and meaningful quantitative error measures are required. The application of these theoretical tools to the fundus image data indicate a systematic way to measure, assess and control cross-correlation error. Conclusions drawn from this research point the way forward for stereo analysis of the optic disc and highlight a number of areas which will require further research. The development of a fully automated system for diagnostic evaluation of the optic disc topography is discussed in the light of the results obtained during this research