Image understanding and feature extraction for applications in industry and mapping

Bibliography: p. 212-220.The aim of digital photogrammetry is the automated extraction and classification of the three dimensional information of a scene from a number of images. Existing photogrammetric systems are semi-automatic requiring manual editing and control, and have very limited domains of application so that image understanding capabilities are left to the user. Among the most important steps in a fully integrated system are the extraction of features suitable for matching, the establishment of the correspondence between matching points and object classification. The following study attempts to explore the applicability of pattern recognition concepts in conjunction with existing area-based methods, feature-based techniques and other approaches used in computer vision in order to increase the level of automation and as a general alternative and addition to existing methods. As an illustration of the pattern recognition approach examples of industrial applications are given. The underlying method is then extended to the identification of objects in aerial images of urban scenes and to the location of targets in close-range photogrammetric applications. Various moment-based techniques are considered as pattern classifiers including geometric invariant moments, Legendre moments, Zernike moments and pseudo-Zernike moments. Two-dimensional Fourier transforms are also considered as pattern classifiers. The suitability of these techniques is assessed. These are then applied as object locators and as feature extractors or interest operators. Additionally the use of fractal dimension to segment natural scenes for regional classification in order to limit the search space for particular objects is considered. The pattern recognition techniques require considerable preprocessing of images. The various image processing techniques required are explained where needed. Extracted feature points are matched using relaxation based techniques in conjunction with area-based methods to 'obtain subpixel accuracy. A subpixel pattern recognition based method is also proposed and an investigation into improved area-based subpixel matching methods is undertaken. An algorithm for determining relative orientation parameters incorporating the epipolar line constraint is investigated and compared with a standard relative orientation algorithm. In conclusion a basic system that can be automated based on some novel techniques in conjunction with existing methods is described and implemented in a mapping application. This system could be largely automated with suitably powerful computers

Least-Squares Wavelet Analysis and Its Applications in Geodesy and Geophysics

The Least-Squares Spectral Analysis (LSSA) is a robust method of analyzing unequally spaced and non-stationary data/time series. Although this method takes into account the correlation among the sinusoidal basis functions of irregularly spaced series, its spectrum still shows spectral leakage: power/energy leaks from one spectral peak into another. An iterative method called AntiLeakage Least-Squares Spectral Analysis (ALLSSA) is developed to attenuate the spectral leakages in the spectrum and consequently is used to regularize data series. In this study, the ALLSSA is applied to regularize and attenuate random noise in seismic data down to a certain desired level. The ALLSSA is subsequently extended to multichannel, heterogeneous and coarsely sampled seismic and related gradient measurements intended for geophysical exploration applications that require regularized (equally spaced) data free from aliasing effects. A new and robust method of analyzing unequally spaced and non-stationary time/data series is rigorously developed. This method, namely, the Least-Squares Wavelet Analysis (LSWA), is a natural extension of the LSSA that decomposes a time series into the time-frequency domain and obtains its spectrogram. It is shown through many synthetic and experimental time/data series that the LSWA supersedes all state-of-the-art spectral analyses methods currently available, without making any assumptions about or preprocessing (editing) the time series, or even applying any empirical methods that aim to adapt a time series to the analysis method. The LSWA can analyze any non-stationary and unequally spaced time series with components of low or high amplitude and frequency variability over time, including datum shifts (offsets), trends, and constituents of known forms, and by taking into account the covariance matrix associated with the time series. The stochastic confidence level surface for the spectrogram is rigorously derived that identifies statistically significant peaks in the spectrogram at a certain confidence level; this supersedes the empirical cone of influence used in the most popular continuous wavelet transform. All current state-of-the-art cross-wavelet transforms and wavelet coherence analyses methods impose many stringent constraints on the properties of the time series under investigation, requiring, more often than not, preprocessing of the raw measurements that may distort their content. These methods cannot generally be used to analyze unequally spaced and non-stationary time series or even two equally spaced time series of different sampling rates, with trends and/or datum shifts, and with associated covariance matrices. To overcome the stringent requirements of these methods, a new method is developed, namely, the Least-Squares Cross-Wavelet Analysis (LSCWA), along with its statistical distribution that requires no assumptions on the series under investigation. Numerous synthetic and geoscience examples establish the LSCWA as the method of methods for rigorous coherence analysis of any experimental series

Characterization of vertical cracks using lock-in vibrothermography

214 p.Esta tesis se centra en la aplicación de la vibrotermografía lock-in para la detección y caracterización dedefectos verticales sumergidos. En esta técnica, la pieza se excita mediante ultrasonidos, que generancalor en los defectos por fricción o deformación plástica. Este calor se difunde por el material y susefectos se pueden detectar midiendo la temperatura superficial mediante una cámara infrarroja. Con el finde caracterizar defectos es necesario resolver el problema inverso, que consiste en recuperar la geometríade las fuentes de calor a partir de la distribución de temperatura superficial medida. Éste es un problemamal puesto, ya que su solución es fuertemente dependiente de pequeños errores en los datos y la inversiónes inestable. Se ha implementado un algoritmo de inversión robusto, basado en minimización pormínimos cuadrados estabilizados mediante términos de penalización basados en los funcionales deTikhonov, Total Variation y L1, capaz de reconstruir distribuciones de fuentes de calor partiendo de datosde vibrotermografía. El algoritmo se ha analizado con datos sintéticos y se ha optimizado con el fin deextender su aplicación a la caracterización del mayor rango de geometrías de fuentes de calor posible.Los resultados obtenidos se han verificado con datos experimentales obtenidos en ensayos devibrotermografía lock-in, utilizando muestras con fuentes de calor verticales calibradas. Finalmente, se hahecho uso del algoritmo de inversión para caracterizar grietas reales en una muestra soldada de Inconel718 y los resultados están en buena correlación cualitativa con los resultados del ensayo de líquidospenetrantes realizado posteriormente

Killing and conformal Killing tensors

This thesis describes the prolongation connection of Killing tensors in terms of Young symmetrizers. The goal is to give an interpretation to sections of the prolongation bundle for Killing tensors on a manifold as generalized curvature tensors on the cone over that manifold. As a result, this method allows to treat the components of the prolongation bundle as a single object with well-understood symmetries. The developed formalism is then explored in three applications. The first result gives an isomorphism between the symmetric algebra of Killing tensors on a manifold of constant curvature and an algebra generated by parallel two-forms on the cone. That provides a geometric proof of the decomposition of Killing tensors on constant curvature manifolds and the Delong-Takeuchi-Thompson formula, previously obtained by Takeuchi and Thompson. Secondly, this technique, together with some branching rules for holonomy subgroups, yields a new characterization of Sasakian and 3-Sasakian manifolds in terms of Killing tensors satisfying additional curvature conditions. The third application is a new short proof of the result by Dairbekov and Sharafutdinov that the codimension of the zero set of a non-trivial, trace free, conformal Killing tensor is at least two. Throughout this work, special emphasis is placed on the representation theory of the appearing tensor bundles. Therefore, the Killing- and conformal Killing operators are introduced as Stein-Weiss operators. Since Young symmetrizers are a well-established tool in describing tensor representations this approach fits perfectly with the goals of the thesis. A natural consequence of this choice are new, geometric proofs of some established results. Besides those mentioned above these cover: (1) A Weitzenböck formula, which implies that all trace free, conformal Killing tensors on manifolds with non-positive sectional curvature are parallel. (2) The decomposition of occurring representations with respect to the reduced holonomy of a Riemannian product yields that the space of trace free, conformal Killing two-tensors on the product is generated by pullbacks of Killing one- and two-tensors on the factors. Furthermore, this thesis recasts the known examples of Killing tensors on compact Riemannian manifolds in the modern and coordinate free language of differential geometry. It is shown how the example found by Page and Pope generalizes to a construction on all Riemannian submersions with totally geodesic fibres. This technique provides non-parallel symmetric Killing two-tensors on compact Kähler manifolds. That contrasts the fact that on such n-dimensional manifolds do not exist non-parallel Killing forms of degree other than one or n-1. Furthermore, this construction gives a method to compute some eigenvalues of the Lichnerowicz-Laplace operator acting on symmetric two-tensors

The computation of multiple roots of a polynomial using structure preserving matrix methods.

Solving polynomial equations is a fundamental problem in several engineering and science fields. This problem has been handled by several researchers and excellent algorithms have been proposed for solving this problem. The computation of the roots of ill-conditioned polynomials is, however, still drawing the attention of several researchers. In particular, a small round off error due to floating point arithmetic is sufficient to break up a multiple root of a polynomial into a cluster of simple closely spaced roots. The problem becomes more complicated if the neighbouring roots are closely spaced. This thesis develops a root finder to compute multiple roots of an inexact polynomial whose coefficients are corrupted by noise. The theoretical development of the developed root solver involves the use of structured matrix methods, optimising parameters using linear programming, and solving least squares equality and nonlinear least squares problems. The developed root solver differs from the classical methods, because it first computes the multiplicities of the roots, after which the roots are computed. The experimental results show that the developed root solver gives very good results without the need for prior knowledge about the noise level imposed on the coefficients of the polynomial

International Conference on Mathematical Analysis and Applications in Science and Engineering – Book of Extended Abstracts

The present volume on Mathematical Analysis and Applications in Science and Engineering - Book of Extended Abstracts of the ICMASC’2022 collects the extended abstracts of the talks presented at the International Conference on Mathematical Analysis and Applications in Science and Engineering – ICMA2SC'22 that took place at the beautiful city of Porto, Portugal, in June 27th-June 29th 2022 (3 days). Its aim was to bring together researchers in every discipline of applied mathematics, science, engineering, industry, and technology, to discuss the development of new mathematical models, theories, and applications that contribute to the advancement of scientific knowledge and practice. Authors proposed research in topics including partial and ordinary differential equations, integer and fractional order equations, linear algebra, numerical analysis, operations research, discrete mathematics, optimization, control, probability, computational mathematics, amongst others. The conference was designed to maximize the involvement of all participants and will present the state-of- the-art research and the latest achievements.info:eu-repo/semantics/publishedVersio

Characterization of vertical cracks using lock-in vibrothermography

214 p.Esta tesis se centra en la aplicación de la vibrotermografía lock-in para la detección y caracterización dedefectos verticales sumergidos. En esta técnica, la pieza se excita mediante ultrasonidos, que generancalor en los defectos por fricción o deformación plástica. Este calor se difunde por el material y susefectos se pueden detectar midiendo la temperatura superficial mediante una cámara infrarroja. Con el finde caracterizar defectos es necesario resolver el problema inverso, que consiste en recuperar la geometríade las fuentes de calor a partir de la distribución de temperatura superficial medida. Éste es un problemamal puesto, ya que su solución es fuertemente dependiente de pequeños errores en los datos y la inversiónes inestable. Se ha implementado un algoritmo de inversión robusto, basado en minimización pormínimos cuadrados estabilizados mediante términos de penalización basados en los funcionales deTikhonov, Total Variation y L1, capaz de reconstruir distribuciones de fuentes de calor partiendo de datosde vibrotermografía. El algoritmo se ha analizado con datos sintéticos y se ha optimizado con el fin deextender su aplicación a la caracterización del mayor rango de geometrías de fuentes de calor posible.Los resultados obtenidos se han verificado con datos experimentales obtenidos en ensayos devibrotermografía lock-in, utilizando muestras con fuentes de calor verticales calibradas. Finalmente, se hahecho uso del algoritmo de inversión para caracterizar grietas reales en una muestra soldada de Inconel718 y los resultados están en buena correlación cualitativa con los resultados del ensayo de líquidospenetrantes realizado posteriormente

Parallel Manipulators

In recent years, parallel kinematics mechanisms have attracted a lot of attention from the academic and industrial communities due to potential applications not only as robot manipulators but also as machine tools. Generally, the criteria used to compare the performance of traditional serial robots and parallel robots are the workspace, the ratio between the payload and the robot mass, accuracy, and dynamic behaviour. In addition to the reduced coupling effect between joints, parallel robots bring the benefits of much higher payload-robot mass ratios, superior accuracy and greater stiffness; qualities which lead to better dynamic performance. The main drawback with parallel robots is the relatively small workspace. A great deal of research on parallel robots has been carried out worldwide, and a large number of parallel mechanism systems have been built for various applications, such as remote handling, machine tools, medical robots, simulators, micro-robots, and humanoid robots. This book opens a window to exceptional research and development work on parallel mechanisms contributed by authors from around the world. Through this window the reader can get a good view of current parallel robot research and applications