This diploma thesis deals with separation of backgroud and moving objects in video. Video can be represented as series of frames and each frame represented as low - rank structure - matrix. This thesis describe sparse representation of signals and robust principal component analysis. It also presents and implements algorithms - models for reconstruction of real video.

Design space exploration (DSE) is a tool used to evaluate and compare designs as part of the design selection process. While evaluating every possible design in a design space is infeasible, understanding design behavior and response throughout the design space may be accomplished by evaluating a subset of designs and interpolating between them using surrogate models. Surrogate modeling is a technique that uses low-cost calculations to approximate the outcome of more computationally expensive calculations or analyses, such as finite element analysis (FEA). While surrogates make quick predictions, accuracy is not guaranteed and must be considered. This research addressed the need to improve the accuracy of surrogate predictions in order to improve DSE of structural responses. This was accomplished by performing comparative analyses of linear and nonlinear dimensionality-reduction-based radial basis function (RBF) surrogate models for emulating various FEA nodal results. A total of four dimensionality reduction methods were investigated, namely principal component analysis (PCA), kernel principal component analysis (KPCA), isometric feature mapping (ISOMAP), and locally linear embedding (LLE). These methods were used in conjunction with surrogate modeling to predict nodal stresses and coordinates of a compressor blade. The research showed that using an ISOMAP-based dual-RBF surrogate model for predicting nodal stresses decreased the estimated mean error of the surrogate by 35.7% compared to PCA. Using nonlinear dimensionality-reduction-based surrogates did not reduce surrogate error for predicting nodal coordinates. A new metric, the manifold distance ratio (MDR), was introduced to measure the nonlinearity of the data manifolds. When applied to the stress and coordinate data, the stress space was found to be more nonlinear than the coordinate space for this application. The upfront training cost of the nonlinear dimensionality-reduction-based surrogates was larger than that of their linear counterparts but small enough to remain feasible. After training, all the dual-RBF surrogates were capable of making real-time predictions. This same process was repeated for a separate application involving the nodal displacements of mode shapes obtained from a FEA modal analysis. The modal assurance criterion (MAC) calculation was used to compare the predicted mode shapes, as well as their corresponding true mode shapes obtained from FEA, to a set of reference modes. The research showed that two nonlinear techniques, namely LLE and KPCA, resulted in lower surrogate error in the more complex design spaces. Using a RBF kernel, KPCA achieved the largest average reduction in error of 13.57%. The results also showed that surrogate error was greatly affected by mode shape reversal. Four different approaches of identifying reversed mode shapes were explored, all of which resulted in varying amounts of surrogate error. Together, the methods explored in this research were shown to decrease surrogate error when performing DSE of a turbomachine compressor blade. As surrogate accuracy increases, so does the ability to correctly make engineering decisions and judgements throughout the design process. Ultimately, this will help engineers design better turbomachines.

This work deals with fouling in the recovery boiler at Montes del Plata, Uruguay. Multivariate data analysis has been used to analyze the large amount of data that was available in order to investigate how different parameters affect the fouling problems. Principal Component Analysis (PCA) and Partial Least Square Projection (PLS) have in this work been used. PCA has been used to compare average values between time periods with high and low fouling problems while PLS has been used to study the correlation structures between the variables and consequently give an indication of which parameters that might be changed to improve the availability of the boiler. The results show that this recovery boiler tends to have problems with fouling that might depend on the distribution of air, the black liquor pressure or the dry solid content of the black liquor. The results also show that multivariate data analysis is a powerful tool for analyzing these types of fouling problems. / Detta arbete handlar om inkruster i sodapannan pa Montes del Plata, Uruguay. Multivariat dataanalys har anvands for att analysera den stora datamangd som fanns tillganglig for att undersoka hur olika parametrar paverkar inkrusterproblemen. Principal·· Component Analysis (PCA) och Partial Least Square Projection (PLS) har i detta jobb anvants. PCA har anvants for att jamfora medelvarden mellan tidsperioder med hoga och laga inkrusterproblem medan PLS har anvants for att studera korrelationen mellan variablema och darmed ge en indikation pa vilka parametrar som kan tankas att andras for att forbattra tillgangligheten pa sodapannan. Resultaten visar att sodapannan tenderar att ha problem med inkruster som kan hero pa fdrdelningen av luft, pa svartlutens tryck eller pa torrhalten i svartluten. Resultaten visar ocksa att multivariat dataanalys ar ett anvandbart verktyg for att analysera dessa typer av inkrusterproblem.

Principal Component Analysis (PCA) and Canonical Correlation Analysis (CCA) are widely-used mathematical models for decomposing multivariate data. They capture spatial relationships between variables, but ignore any temporal relationships that might exist between observations. Probabilistic PCA (PPCA) and Probabilistic CCA (ProbCCA) are versions of these two models that explain the statistical properties of the observed variables as linear mixtures of an alternative, hypothetical set of hidden, or latent, variables and explicitly model noise. Both the noise and the latent variables are assumed to be Gaussian distributed. This thesis introduces two new models, named PPCA-AR and ProbCCA-AR, that augment PPCA and ProbCCA respectively with autoregressive processes over the latent variables to additionally capture temporal relationships between the observations. To make PPCA-AR and ProbCCA-AR robust to outliers and able to model leptokurtic data, the Gaussian assumptions are replaced with infinite scale mixtures of Gaussians, using the Student-t distribution. Bayesian inference calculates posterior probability distributions for each of the parameter variables, from which we obtain a measure of confidence in the inference. It avoids the pitfalls associated with the maximum likelihood method: integrating over all possible values of the parameter variables guards against overfitting. For these new models the integrals required for exact Bayesian inference are intractable; instead a method of approximation, the variational Bayesian approach, is used. This enables the use of automatic relevance determination to estimate the model orders. PPCA-AR and ProbCCA-AR can be viewed as linear dynamical systems, so the forward-backward algorithm, also known as the Baum-Welch algorithm, is used as an efficient method for inferring the posterior distributions of the latent variables. The exact algorithm is tractable because Gaussian assumptions are made regarding the distribution of the latent variables. This thesis introduces a variational Bayesian forward-backward algorithm based on Student-t assumptions. The new models are demonstrated on synthetic datasets and on real remote sensing and EEG data.

Many applications lead to signals with nonnegative function values. Understanding the structure of the spaces of nonnegative signals is therefore of interest in many different areas. Hence, constructing effective representation spaces with suitable metrics and natural transformations is an important research topic. In this thesis, we present our investigations of the structure of spaces of nonnegative signals and illustrate the results with applications in the fields of multispectral color science and content-based image retrieval. The infinite-dimensional Hilbert space of nonnegative signals is conical and convex. These two properties are preserved under linear projections onto lower dimensional spaces. The conical nature of these coordinate vector spaces suggests the use of hyperbolic geometry. The special case of three-dimensional hyperbolic geometry leads to the application of the SU(1,1) or SO 2,1) groups. We introduce a new framework to investigate nonnegative signals. We use PCA-based coordinates and apply group theoretical tools to investigate sequences of signal coordinate vectors. We describe these sequences with oneparameter subgroups of SU(1,1) and show how to compute the one-parameter subgroup of SU(1,1) from a given set of nonnegative signals. In our experiments we investigate the following signal sequences: (i) blackbody radiation spectra; (ii) sequences of daylight/twilight spectra measured in Norrk¨oping, Sweden and in Granada, Spain; (iii) spectra generated by the SMARTS2 simulation program; and (iv) sequences of image histograms. The results show that important properties of these sequences can be modeled in this framework. We illustrate the usefulness with examples where we derive illumination invariants and introduce an efficient visualization implementation. Content-Based Image Retrieval (CBIR) is another topic of the thesis. In such retrieval systems, images are first characterized by descriptor vectors. Retrieval is then based on these content-based descriptors. Selection of contentbased descriptors and defining suitable metrics are the core of any CBIR system. We introduce new descriptors derived by using group theoretical tools. We exploit the symmetry structure of the space of image patches and use the group theoretical methods to derive low-level image filters in a very general framework. The derived filters are simple and can be used for multispectral images and images defined on different sampling grids. These group theoretical filters are then used to derive content-based descriptors, which will be used in a real implementation of a CBIR.

We analyse the Swedish central bank, the Riksbank’s, interest setting policy in a Taylor rule framework. In particular, we examine whether or not the Riksbank has reacted to fluctuations in asset prices during the period 1995:Q1 to 2016:Q2. This is done by estimating a forward-looking Taylor rule with interest rate smoothing, augmented with stock prices, house prices and the real exchange rate, using IV GMM. In general, we find that the Riksbank’s interest setting policy is well described by a forward-looking Taylor rule with interest rate smoothing and that the use of factors as instruments, derived from a PCA, serves to alleviate the weak-identification problem that tend to plague GMM. Moreover, apart from finding evidence that the Riksbank exhibit a substantial degree of policy rate inertia and has acted so as to stabilize inflation and the real economy, we also find evidence that the Riksbank has been reacting to fluctuations in stock prices, house prices, and the real exchange rate.

The purpose of this work is to present the development and validation of a novel method for reconstructing time-dependent, or 4D, cone-beam CT (4DCBCT) images. 4DCBCT can have a variety of applications in the radiotherapy of moving targets, such as lung tumors, including treatment planning, dose verification, and real time treatment adaptation. However, in its current incarnation it suffers from poor reconstruction quality and limited temporal resolution that may restrict its efficacy. Our algorithm remedies these issues by deforming a previously acquired high quality reference fan-beam CT (FBCT) to match the projection data in the 4DCBCT data-set, essentially creating a 3D animation of the moving patient anatomy. This approach combines the high image quality of the FBCT with the fine temporal resolution of the raw 4DCBCT projection data-set. Deformation of the reference CT is accomplished via a patient specific motion model. The motion model is constrained spatially using eigenvectors generated by a principal component analysis (PCA) of patient motion data, and is regularized in time using parametric functions of a patient breathing surrogate recorded simultaneously with 4DCBCT acquisition. The parametric motion model is constrained using forward iterative projection matching (FIPM), a scheme which iteratively alters model parameters until digitally reconstructed radiographs (DRRs) cast through the deforming CT optimally match the projections in the raw 4DCBCT data-set. We term our method FIPM-PCA 4DCBCT. In developing our algorithm we proceed through three stages of development. In the first, we establish the mathematical groundwork for the algorithm and perform proof of concept testing on simulated data. In the second, we tune the algorithm for real world use; specifically we improve our DRR algorithm to achieve maximal realism by incorporating physical principles of image formation combined with empirical measurements of system properties. In the third stage we test our algorithm on actual patient data and evaluate its performance against gold standard and ground truth data-sets. In this phase we use our method to track the motion of an implanted fiducial marker and observe agreement with our gold standard data that is typically within a millimeter.

L'objectif de cette étude était de réaliser des revêtements de TiO2 présentant une large variété de morphologies et d'établir des corrélations entre la structure de ces couches et leurs propriétés fonctionnelles, notamment la photocatalyse. Deux voies de synthèse employant le même précurseur, le tétra-isopropropoxide (TTIP) de titane, ont été utilisées, le procédé sol-gel et le dépôt chimique en phase vapeur (MOCVD). L'emploi de ces deux techniques permet de produire TiO2 sous une large gamme de morphologies mais avec des variétés polymorphiques similaires. Les revêtements synthétisés ont été caractérises afin de déterminer leur composition polymorphique, la taille des cristallites, la surface spécifique, la rugosité et l'épaisseur. Puis leur activité photocalytique pour la dégradation du bleu de méthylène a été déterminée. Par voie sol-gel, des dispersions de nano-cristallites de TiO2 dans l'eau, stables sur une longue durée (plus d'un an) en termes de composition polymorphique, taille d'agglomérats et de cristallites ont été synthétisées. Les revêtements ont été réalisés par tape-casting et dip-coating. Pour la synthèse en MOCVD, un plan d'expérience (PeX) a été utilisé, à notre connaissance pour la première fois. Il a permis de déterminer, d'une manière efficace et économique (avec un nombre minimum de tests expérimentaux), les paramètres les plus importants du procédé contrôlant les diverses propriétés quantifiables du revêtement. Il a aussi permis de mettre en évidence les interactions entre les paramètres de synthèse et leur effet sur la structure du revêtement. Les conclusions tirées du PeX sont en accord avec les résultats obtenus lors des études précédentes. L'analyse en composantes principales (ACP) a été réalisée pour avoir une vue globale de la façon dont les diverses propriétés des revêtements sont reliées entre elles / The overall objectives of this study was to find an environmental-friendly and simple procedure to synthesize titanium-dioxide, as well as, to determine the relation between the structural and functional properties of titanium dioxide coatings. Both of these objective have been attained in this study. By the sol-gel technique, titanium dioxide sols were synthesized by the hydrolysis of titanium(IV)isopropoxide. Nanocrystalline dispersions of TiO2 in water were prepared that were suitable for coatings and having long-term stability (more than 1 year) in terms of polymorphic composition, crystallite and agglomerate size. A design of experiments (DoE) was utilised, to our knowledge, for the first time in MOCVD for the synthesis of TiO2 coatings. It was employed to determine, in a timely and economical manner, the most significant process parameters for any quantifiable property of the coating and to highlight the interaction between these operating parameters, as well as, the correlation between the structure of the coating and the process. The conclusions drawn from the DoE were compared to results obtained by previous studies and were found to concur. Therefore, the DoE was successful in screening the most important process parameters, with a minimum number of experimental trials. For most of the properties that were under investigation, the DoE showed that, the deposition temperature and reactor pressure were, often-times, the most significant. Therefore, to change the microstructure and composition of MOCVD coatings, changing these process parameters will ensure the highest impact. It has to be stressed that the conclusions drawn from the DoE are restricted to the experimental range that was under investigation. Principal Component Analysis (PCA) was conducted to have an overall view of how the different properties of the coatings related with one another. The interpretations made from this analysis were that the photocatalytic (PC) activity of the coatings produced did not relate strongly to the polymorphic composition, which is contrary to literature review and is explained to be a result of the different morphologies that lead to different porosities and specific surface area. The PC activity did not depend on the mass over a critical mass. With this analysis it appeared to be clear that the porosity and specific surface area played a larger role than polymorphic composition. This hypothesis has to be verified because we did not succeed in determining the specific surface area of our coatings during this study. However, some preliminary tests have been conducted showing that cyclic voltametry could be used to evaluate the surface area of our films

The term "personality" nowadays occurs more often not only in psychological studies of humans but also in animal studies. Studying of personality help us to define the behavioural characteristics which can vary within the age, sexes, species or enviroments. Behavioral experiments are used to detect these behavioral patterns and they can divide the animals into the different groups. The subject of our research became three populations of house mouse (Mus musculus sensu lato) which we tested in a series of experiments involving free exploration, forced exploration, hole- board test, test of vertical activity and Elevated plus-maze. These experiments should reveal wheter the mice differ in their behaviour through the context of sex, comensalism or subspecies. We found (with in excepcion of one test) that intrapopulation variability differences are very small but interpopulation differences purely increase in the cas of comensalism and effects of subspecies. Keywords: Mus musculus, comensalism, open fieldtest, Elevated plus-maze, Principal Component Analysis (PCA)

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