Today the multisensor array signal processing of noisy measurements has received much attention. The classical problem in array signal processing is determining the location of an energy-radiating source relative to the location of the array, in other words, direction-of-arrival (DOA) estimation. One is considering the signal estimation problem when together with the signal(s) of interest some noise and interfering signals are present. In this report a direction-of-arrival estimation system is described based on an antenna array for detecting arrival angles in azimuth plane of signals pitched by the antenna array. For this, the Multiple Signal Classication (MUSIC) algorithmis first of all considered. Studies show that in spite of its good reputation and popularity among researches, it has a certain limit of its performance. In this subspace-based method for DOA estimation of signal wavefronts, the term corresponding to additive noise is initially assumed spatially white. In our paper, we address the problem of DOA estimation of multiple target signals in a particular noise situation - in correlated spherically isotropic noise, which, in many practical cases, models a more real context than under the white noise assumption. The purpose of this work is to analyze the behaviour of the MUSIC algorithm and compare its performance with some other algorithms (such as the Capon and the Classical algorithms) and, uppermost, to explore the quality of the detected angles in terms of precision depending on different parameters, e.g. number of samples, noise variance, number of incoming signals. Some modifications of the algorithms are also done is order to increase their performance. Program MATLAB is used to conduct the studies. The simulation results on the considered antenna array system indicate that in complex conditions the algorithms in question (and first of all, the MUSIC algorithm) are unable to automatically detect and localize the DOA signals with high accuracy. Other algorithms andways for simplification the problem (for example, procedure of denoising) exist and may provide more precision but require more computation time.

Two methods for evaluating and improving plane wave beamforming have beendeveloped. The methods estimate the shape of the wavefront and use theinformation in the beamforming. One of the methods uses estimates of the timedelays between the sensors to approximate the shape of the wavefront, and theother estimates the wavefront by matching the received wavefront to sphericalwavefronts of different radii. The methods are compared to a third more commonmethod of beamforming, which assumes that the impinging wave is planar. Themethods’ passive ranging abilities are also evaluated, and compared to a referencemethod based on triangulation.Both methods were evaluated with both real and simulated data. The simulateddata was obtained using Raylab, which is a simulation program based on ray-tracing. The real data was obtained through a field-test performed in the Balticsea using a towed array sonar and a stationary source emitted tones.The performance of the matched beamformers depends on the distance to the tar-get. At a distance of 600 m near broadside the power received by the beamformerincreases by 0.5-1 dB compared to the plane wave beamformer. At a distance of300 m near broadside the improvement is approximately 2 dB. In general, obtain-ing an accurate distance estimation proved to be difficult, and highly dependenton the noise present in the environment. A moving target at a distance of 600 mat broadside can be estimated with a maximum error of 150 m, when recursiveupdating of the covariance matrix with a updating constant of 0.25 is used. Whenrecursive updating is not used the margin of error increases to 400 m.

The present paper develops a procedure based on multivariate copulas for simulating multivariate non-normal data that satisfies a pre-specified covariance matrix. The covariance matrix used, can comply with a specific moment structure form (e.g., a factor analysis or a general SEM model). So the method is particularly useful for Monte Carlo evaluation of SEM models in the context of non-normal data. The new procedure for non-normal data simulation is theoretically described and also implemented on the widely used R environment. The quality of the method is assessed by performing Monte Carlo simulations. Within this context a one-sample test on the observed VC-matrix is involved. This test is robust against normality violations. This test is defined through a particular SEM setting. Finally, an example for Monte Carlo evaluation of SEM modeling of non-normal data using this method is presented. (author's abstract) / Series: Research Report Series / Department of Statistics and Mathematics

abstract: Tracking a time-varying number of targets is a challenging dynamic state estimation problem whose complexity is intensified under low signal-to-noise ratio (SNR) or high clutter conditions. This is important, for example, when tracking multiple, closely spaced targets moving in the same direction such as a convoy of low observable vehicles moving through a forest or multiple targets moving in a crisscross pattern. The SNR in these applications is usually low as the reflected signals from the targets are weak or the noise level is very high. An effective approach for detecting and tracking a single target under low SNR conditions is the track-before-detect filter (TBDF) that uses unthresholded measurements. However, the TBDF has only been used to track a small fixed number of targets at low SNR. This work proposes a new multiple target TBDF approach to track a dynamically varying number of targets under the recursive Bayesian framework. For a given maximum number of targets, the state estimates are obtained by estimating the joint multiple target posterior probability density function under all possible target existence combinations. The estimation of the corresponding target existence combination probabilities and the target existence probabilities are also derived. A feasible sequential Monte Carlo (SMC) based implementation algorithm is proposed. The approximation accuracy of the SMC method with a reduced number of particles is improved by an efficient proposal density function that partitions the multiple target space into a single target space. The proposed multiple target TBDF method is extended to track targets in sea clutter using highly time-varying radar measurements. A generalized likelihood function for closely spaced multiple targets in compound Gaussian sea clutter is derived together with the maximum likelihood estimate of the model parameters using an iterative fixed point algorithm. The TBDF performance is improved by proposing a computationally feasible method to estimate the space-time covariance matrix of rapidly-varying sea clutter. The method applies the Kronecker product approximation to the covariance matrix and uses particle filtering to solve the resulting dynamic state space model formulation. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2015

Nesta dissertação, foi utilizada a técnica SIFT (Scale Invariant Feature Transform) para o reconhecimento de imagens da área dos olhos (região periorbital). Foi implementada uma classificação das imagens em subgrupos internos ao banco de dados, utilizando-se das informações estatísticas provenientes dos padrões invariantes produzidos pela técnica SIFT. Procedeu-se a uma busca categorizada pelo banco de dados, ao invés da procura de um determinado padrão apresentado, através da comparação deste com cada padrão presente no banco de dados. A tais padrões foi aplicada uma abordagem estatística, através da geração da matriz de covariâncias dos padrões gerados, sendo esta utilizada para a categorização, tendo por base uma rede neural híbrida. A rede neural classifica e categoriza o banco de dados de imagens, criando uma topologia de busca. Foram obtidos resultados corretos de classificação de 76,3% pela rede neural híbrida, sendo que um algoritmo auxiliar determina uma hierarquia de busca, onde, ocorrendo uma errônea classificação, a busca segue em grupos de pesquisas mais prováveis.

Dentro da biologia evolutiva, uma das questões centrais é a compreensão de como os processos evolutivos, em particular a seleção e o acaso (deriva genética) moldaram a diversidade obervada nos organismos. Dentro deste contexto, a utilização de abordagens como a integração morfológica e a genética quantitativa nos fornecem poderosas ferramentas. Enquanto a primeira descreve os padrões de relação entre caracteres e testa hipóteses sobre as relações de desenvolvimento e/ou funções subjacentes, a segunda possui ferramentas para investigar as forças que podem ter gerado os fenótipos atuais. Utilizando como modelo de estudo os gêneros de marsupiais da Ordem Didelphimorphia, analisei a evolução morfológica craniana unindo estas duas linhas de pesquisa. Central a genética quantitativa está a matriz de covariância genética (G) que descreve a porção da variância que é efetivamente herdada (no sentido de transmissão de valor entre gerações) e conseqüentemente serve como substrato à seleção. Apesar de ter sido desenvolvida inicialmente para estudos em escala microevolutiva, o arsenal matemático da genética quantitativa pode ser estendida a escalas macroevolutivas caso a matriz G permaneça relativamente estável. Entretanto, como a estimativa de uma matriz G requer um número grande de espécimes aparentados e com genealogia conhecida, utilizei ao longo deste trabalho sua correspondente fenotípica (P). Desta forma, no primeiro capítulo demonstrei a similaridade das matrizes de covariância e correlação P dos marsupiais Didelphimorphia. Em contrapartida, as magnitudes de integração morfológica, que medem o grau de associação entre os caracteres, se mostraram mais variáveis dentro do grupo. A história evolutiva (filogenia) e as distâncias morfológicas entre os gêneros não parecem ter tido influência sobre os padrões nem as magnitudes, já que não se correlacionaram significativamente a eles. No segundo capítulo, estendi estas análises para os gêneros ao longo do seu desenvolvimento e novamente os padrões se mostraram semelhantes, tanto quando comparei a ontogenia de um único gênero, quando analisei diferentes gêneros para diferentes classes etárias. Em contrapartida, as magnitudes de integração se mostraram mais variáveis, com uma tendência a diminuírem com o aumento da idade. Por conta destes resultados, comparei as matrizes de correlação empíricas com matrizes teóricas que expressam hipóteses de modularidade baseadas no desenvolvimento/função compartilhada pelas regiões do crânio. Testei para similaridade das duas regiões principais (face e neurocrânio), cinco sub-regiões (base e abóboda craniana, oral, nasal e zigomático), uma matriz 198 de integração somática (caracteres neurais vs. faciais) e uma de integração total, concatenando as cinco sub-regiões. Foram encontradas somente correlações significativas para as regiões da face e suas sub-regiões nasal e oral. Apesar das variações nas magnitudes de integração observadas nestes dois primeiros capítulos, as respostas evolutivas obtidas para estes gêneros foram todas muito similares. Este resultado, associado a constatação de que grande parte da variação entre os espécimes é devida ao tamanho, ou variações de forma associadas a ele (alometria), me levaram a analisar as conseqüências evolutivas associadas a estas variações alométricas. Assim, no terceiro capítulo analisei as direções de resposta à seleção simulada antes e após a remoção do tamanho. Variações alométricas exercem forte influência sobre estes crânios tornando-os muito integrados morfologicamente, ou seja, a percepção dos módulos que os compõem é muito difícil (baixa modularidade). Isto se reflete em uma maior variação ao longo da linha de menor resistência evolutiva (que resume o eixo de maior variação disponível entre os espécimes), já que os módulos não podem responder a seleção de forma independente (alta integração morfológica). Em marsupiais, esta linha é está alinhada na direção de variações de tamanho. Desta forma, não importa em que direção a seleção esteja atuando, as respostas evolutivas serão usualmente na direção desta linha de menor resistência e conseqüentemente de tamanho. Uma vez que o tamanho é removido, as magnitudes de integração diminuem e a modularidade do crânio aumenta. Por conseguinte, ele passa a ser capaz de responder à seleção em uma gama maior de direções porque aumenta também a relativa independência destes módulos em relação aos demais. Como estes resultados indicam que variações entre os Didelphimorphia são direcionadas a variações no tamanho, devido justamente às restrições impostas pela linha de menor resistência evolutiva, analisei as trajetórias ontegenéticas de dois gêneros irmãos, Didelphis e Philander, separando os efeitos da forma e tamanho nesta diversificação. Para tanto empreguei análises de morfometria tradicional, morfométrica e análises de coeficientes alométricos que apontaram para uma maior diferenciação no tamanho entre eles. Apesar da similaridade entre as trajetórias ontogenéticas destes dois gêneros, espécimes de Didelphis nascem maiores e crescem por mais tempo, como indicado pela sua trajetória mais longa. / One of the central goals in evolutionary biology is related to how evolutionary processes, mainly natural selection and genetic drift, shaped living organisms. The combined use of Morphologial Integration and Quantitative Genetics give us powerful tools to accomplish this goal. Morphological Integration is concerned of how characters are related, as well as their underlying genetics/developmental relationship, while Quantitative Genetics have methodologies designed to explore the phenotypic forces underlying diversity among organisms. Using Didelphimorphia marsupials as a study group, I combined these two approaches to study its morphologic cranial diversification. In Quantitative Genetics, the genetic additive covariance matrix (G) resume the genetic variation underlying resemblance among relatives, which is the portion of the variance responsive to selection. Initially developed to microevolutionary scale studies, it can be extended to a macroevolutionary scale if it remains relatively similar in that time scale. However, as G matrix estimations require a huge number of related specimens with known genealogy, I used its phenotypic (P) counterpart which was more easily obtained. In the first chapter I showed high similarities among Didelphimorphia marsupials covariance and correlation P matrices. On the other hand, integration magnitudes (which measure the average correlation among traits) vary among taxa. Neither phylogeny nor morphologic distances showed any association with the similarity in patterns and magnitudes of integration. In the second chapter, I did these same analyses, but throughout genera ontogeny. Again, there was a high similarity among taxa in patterns of integration, both when I analyzed the ontogeny for each genus separately or against each other (at different age class). Morphological integration magnitudes showed the same variation obtained for adults, with a tendency to decrease at older ages. Taking these results into account, I compared the phenotypic correlation matrices to theoretical matrices, based on hypotheses of shared developmental and functional units. I searched for modularity in the two main skull regions (face and neurocranium) and five sub regions (cranium base and vault, face, nasal, and oral). I also looked for modularity concerning somatic development (Neurocranium vs. Face) and total modularity, as the 200 summation of the five sub-regions. Only Face and its sub-regions nasal and oral, showed significant correlations to the phenotypic genera matrices. Despite integration magnitude differences, all evolutionary responses produced by taxa were highly similar. These results, combined with a huge size variation (or size related variation - allometry) across taxa, lead me to search for the evolutionary consequences due to size variation. In the third chapter, I compared evolutionary response directions produce by each genera matrices before and after size removal under a random selection simulation. Allometry strongly affect these skulls, turning them into highly integrated structures with lower modularity (skull modules are not easily distinguished). Because of this, modules cannot evolve relatively independent of other modules and evolutionary responses will strongly affect the whole cranium. This is related to the variation along the lines of least evolutionary resistance. This line is the multivariate direction of greatest genetic or phenotypic variation (the combination of a suite of traits that displays the maximum within-population variance). In Didelphimorphia marsupials, this line is aligned with size variation and regardless the selection direction, evolutionary change is usually aligned to this least resistance line. The removal of size variation diminish the magnitude of integration while increases modularity. Consequently, skulls become able to respond to selection in more directions as modules become relatively more independent of each other. In the last chapter I compared size and shape differences between ontogenetic trajectories of two sister genera Didelphis and Philander. Using traditional and geometric morphometric analysis plus allometric coefficient analysis, I could show that bigger differences between them are size related. Despite similarities, ontogenetic trajectory in Didelphis is longer, leading to bigger specimens.

The main goal of our thesis is to make the implementation of a classification method called linear discriminant analysis more efficient. It is a model of multivariate statistics which, given samples and their membership to given groups, attempts to determine the group of a new sample. We focus especially on the high-dimensional case, meaning that the number of variables is higher than number of samples and the problem leads to a singular covariance matrix. If the number of variables is too high, it can be practically impossible to use the common methods because of the high computational cost. Therefore, we look at the topic from the perspective of numerical linear algebra and we rearrange the obtained tasks to their equivalent formulation with much lower dimension. We offer new ways of solution, provide examples of particular algorithms and discuss their efficiency. Powered by TCPDF (www.tcpdf.org)

Statisticians are interested in testing the structure of covariance matrices, especially under the high-dimensional scenario in which the dimensionality of data matrices exceeds the sample size. Many test statistics have been introduced to test whether the covariance matrix is equal to identity structure (<img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?H_%7B01%7D:%20%5CSigma%20=%20I_p" />), sphericity structure (<img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?H_%7B02%7D:%20%5CSigma%20=%20%5Csigma%5E2I_p" />) or diagonal structure (<img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?H_%7B03%7D:%20%5CSigma%20=%20diag(d_1,%20d_2,%5Cdots,d_p)" />). These test statistics work under the assumption that data follows the multivariate normal distribution. In our thesis work, we want to compare the performance of test statistics for each structure test under given assumptions and when the distributional assumption is violated, and compare the test sensitivity to outliers. We apply simulation studies with the help of significance level, power of test, and goodness of fit tests to evaluate the performance of structure test statistics. In conclusion, we identify the recommended test statistics that perform well under different scenarios. Moreover, we find out that the test statistics for the identity structure test are more sensitive to the changes of distribution assumptions and outliers compared with others. The test statistics for the diagonal structure test have a better tolerant to the change of the data matrices.

L’analyse de visages 3D y compris la reconnaissance des visages et des expressions faciales 3D est devenue un domaine actif de recherche ces dernières années. Plusieurs méthodes ont été développées en utilisant des images 2D pour traiter ces problèmes. Cependant, ces méthodes présentent un certain nombre de limitations dépendantes à l’orientation du visage, à l’éclairage, à l’expression faciale, et aux occultations. Récemment, le développement des capteurs d’acquisition 3D a fait que les données 3D deviennent de plus en plus disponibles. Ces données 3D sont relativement invariables à l’illumination et à la pose, mais elles restent sensibles à la variation de l’expression. L’objectif principal de cette thèse est de proposer de nouvelles techniques de reconnaissance/vérification de visages et de reconnaissance d’expressions faciales 3D. Tout d’abord, une méthode de reconnaissance de visages en utilisant des matrices de covariance comme des descripteurs de régions de visages est proposée. Notre méthode comprend les étapes suivantes : le prétraitement et l’alignement de visages, un échantillonnage uniforme est ensuite appliqué sur la surface faciale pour localiser un ensemble de points de caractéristiques. Autours de chaque point, nous extrayons une matrice de covariance comme un descripteur de région du visage. Deux méthodes d’appariement sont ainsi proposées, et différentes distances (géodésiques / non-géodésique) sont appliquées pour comparer les visages. La méthode proposée est évaluée sur troisbases de visages GAVAB, FRGCv2 et BU-3DFE. Une description hiérarchique en utilisant trois niveaux de covariances est ensuite proposée et validée. La deuxième partie de cette thèse porte sur la reconnaissance des expressions faciales 3D. Pour ce faire, nous avons proposé d’utiliser les matrices de covariances avec les méthodes noyau. Dans cette contribution, nous avons appliqué le noyau de Gauss pour transformer les matrices de covariances en espace d’Hilbert. Cela permet d’utiliser les algorithmes qui sont déjà implémentés pour l’espace Euclidean (i.e. SVM) dans cet espace non-linéaire. Des expérimentations sont alors entreprises sur deux bases d’expressions faciales 3D (BU-3DFE et Bosphorus) pour reconnaître les six expressions faciales prototypiques. / 3D face analysis including 3D face recognition and 3D Facial expression recognition has become a very active area of research in recent years. Various methods using 2D image analysis have been presented to tackle these problems. 2D image-based methods are inherently limited by variability in imaging factors such as illumination and pose. The recent development of 3D acquisition sensors has made 3D data more and more available. Such data is relatively invariant to illumination and pose, but it is still sensitive to expression variation. The principal objective of this thesis is to propose efficient methods for 3D face recognition/verification and 3D facial expression recognition. First, a new covariance based method for 3D face recognition is presented. Our method includes the following steps : first 3D facial surface is preprocessed and aligned. A uniform sampling is then applied to localize a set of feature points, around each point, we extract a matrix as local region descriptor. Two matching strategies are then proposed, and various distances (geodesic and non-geodesic) are applied to compare faces. The proposed method is assessed on three datasetsincluding GAVAB, FRGCv2 and BU-3DFE. A hierarchical description using three levels of covariances is then proposed and validated. In the second part of this thesis, we present an efficient approach for 3D facial expression recognition using kernel methods with covariance matrices. In this contribution, we propose to use Gaussian kernel which maps covariance matrices into a high dimensional Hilbert space. This enables to use conventional algorithms developed for Euclidean valued data such as SVM on such non-linear valued data. The proposed method have been assessed on two known datasets including BU-3DFE and Bosphorus datasets to recognize the six prototypical expressions.

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