En imagerie hyperspectrale, chaque pixel est associé à un spectre provenant de la réflectance observée en d points de mesure (i.e., longueurs d'onde). On se retrouve souvent dans une situation où la taille d'échantillon n est relativement faible devant le nombre d de variables. Ce phénomène appelé "fléau de la dimension" est bien connu en statistique multivariée. Plus d augmente devant n, plus les performances des méthodologies statistiques standard se dégradent. Les spectres de réflectance intègrent dans leur dimension spectrale un continuum qui leur confère une nature fonctionnelle. Un hyperspectre peut être modélisé par une fonction univariée de la longueur d'onde, sa représentation produisant une courbe. L'utilisation de méthodes fonctionnelles sur de telles données permet de prendre en compte des aspects fonctionnels tels que la continuité, l'ordre des bandes spectrales, et de s'affranchir des fortes corrélations liées à la finesse de la grille de discrétisation. L'objectif principal de cette thèse est d'évaluer la pertinence de l'approche fonctionnelle dans le domaine de la télédétection hyperspectrale lors de l'analyse statistique. Nous nous sommes focalisés sur le modèle non-paramétrique de régression fonctionnelle, couvrant la classification supervisée. Dans un premier temps, l'approche fonctionnelle a été comparée avec des méthodes multivariées usuellement employées en télédétection. L'approche fonctionnelle surpasse les méthodes multivariées dans des situations délicates où l'on dispose d'une petite taille d'échantillon d'apprentissage combinée à des classes relativement homogènes (c'est-à-dire difficiles à discriminer). Dans un second temps, une alternative à l'approche fonctionnelle pour s'affranchir du fléau de la dimension a été développée à l'aide d'un modèle parcimonieux. Ce dernier permet, à travers la sélection d'un petit nombre de points de mesure, de réduire la dimensionnalité du problème tout en augmentant l'interprétabilité des résultats. Dans un troisième temps, nous nous sommes intéressés à la situation pratique quasi-systématique où l'on dispose de données fonctionnelles contaminées. Nous avons démontré que pour une taille d'échantillon fixée, plus la discrétisation est fine, meilleure sera la prédiction. Autrement dit, plus d est grand devant n, plus la méthode statistique fonctionnelle développée est performante. / In hyperspectral imaging, each pixel is associated with a spectrum derived from observed reflectance in d measurement points (i.e., wavelengths). We are often facing a situation where the sample size n is relatively low compared to the number d of variables. This phenomenon called "curse of dimensionality" is well known in multivariate statistics. The mored increases with respect to n, the more standard statistical methodologies performances are degraded. Reflectance spectra incorporate in their spectral dimension a continuum that gives them a functional nature. A hyperspectrum can be modelised by an univariate function of wavelength and his representation produces a curve. The use of functional methods allows to take into account functional aspects such as continuity, spectral bands order, and to overcome strong correlations coming from the discretization grid fineness. The main aim of this thesis is to assess the relevance of the functional approach in the field of hyperspectral remote sensing for statistical analysis. We focused on the nonparametric fonctional regression model, including supervised classification. Firstly, the functional approach has been compared with multivariate methods usually involved in remote sensing. The functional approach outperforms multivariate methods in critical situations where one has a small training sample size combined with relatively homogeneous classes (that is to say, hard to discriminate). Secondly, an alternative to the functional approach to overcome the curse of dimensionality has been proposed using parsimonious models. This latter allows, through the selection of few measurement points, to reduce problem dimensionality while increasing results interpretability. Finally, we were interested in the almost systematic situation where one has contaminated functional data. We proved that for a fixed sample size, the finer the discretization, the better the prediction. In other words, the larger dis compared to n, the more effective the functional statistical methodis.

Dans cette thèse, nous présentons de nouvelles méthodes de traitement d’images pourextraire ou rehausser les éléments fins d’une image. Pour ces opérateurs, issus de la morphologie mathématique,l’accent a été mis principalement sur la précision de détection et sur le temps de calcul,qui doivent être optimisés pour pouvoir répondre aux contraintes de temps imposées par différentesapplications industrielles. La première partie de ce mémoire présente ces méthodes, organisées enfonction de la tortuosité des objets à détecter. Nous commençons par proposer un algorithme rapidepour le calcul des ouvertures 1-D afin d’extraire des structures rectilignes des images. Puis, nous étudionsune nouvelle classe d’opérateurs rapides avec les ouvertures parcimonieuses par chemins, permettantd’analyser des structures ayant une tortuosité modérée. Enfin, nous proposons de nouveauxéléments structurants adaptatifs et des filtres connexes construits avec des attributs géodésiques etgéométriques pour extraire des structures filiformes ayant une tortuosité quelconque.Dans un second temps, nous avons développé une méthode d’analyse statistique en introduisantune nouvelle pénalisation adaptative. L’objectif consiste à créer un modèle prédictif précis, quiminimise en même temps une fonction de coût, indépendante des données. Lorsque cette fonctionde coût est liée au temps de calcul de chaque descripteur, il est alors possible de créer un modèleparcimonieux précis et qui minimise les temps de calcul. Cette méthode est une généralisation desrégressions linéaires et logistiques Ridge, Forward stagewise, Lar, ou Lasso.Les algorithmes développés dans cette thèse ont été utilisés pour trois applications industrielles,très différentes les unes des autres, mais toutes faisant intervenir une approche multidisciplinaire : letraitement d’images et l’analyse statistique. L’association de ces deux disciplines permet d’améliorerla généricité des stratégies proposées puisque les opérateurs de traitement d’images alliés à un apprentissagesupervisé ou non supervisé, permettent d’adapter le traitement à chaque application.Mots clés : Traitement d’images, morphologie mathématique, analyse statistique, caractérisation deformes, contrôles non destructifs, ouvertures parcimonieuses par chemins, region growing structuringelements, amincissements par attributs géodésiques et topologiques, adaptive coefficient shrinkage. / This PhD is dedicated to new image processing methods to extract or enhance thinobjects from an image. These methods stem from mathematical morphology, and they mainly focuson the accuracy of the detection and on the computation time. This second constraint is imposed bythe fact that we are dealing with high-throughput applications. The first part of this thesis presentsthese methods, organized according to the tortuosity of the objects to detect. We first propose afast algorithm for the computation of 1-D openings, used to extract thin and straight structures in theimages. Then, we study a new class of fast operators, parsimonious path openings, which can extractthin structures with moderate tortuosities. Finally, we propose new adaptive structuring elementsand new thinnings with geodesic and geometric attributes to filter out the noise and to enhance thinstructures of any tortuosity.Besides, we have developed a machine learning method by introducing a new adaptive penalization.We aim at creating a predictive model that minimizes a cost function (independent of the data)while preserving a good accuracy. When this cost function is linked to the computation time of eachfeature, the resulting models will optimize the timings, while preserving a good accuracy. This methodis a generalization of linear and logistic regressions with Ridge, Forward stagewise, Lar or Lassopenalization.The algorithms developed in this thesis have been used for three industrial applications. While theirobjectives are very different, the framework is the same (non-destructive testing) and they all involvea multidisciplinary approach (images processing and statistical analysis). The combination of thesetwo fields yields a higher flexibility in comparison with classical methods. Generic strategies are used,since image processing operators are associated to statistical learning (supervised or unsupervised)to make a specific treatment for each application.Keywords: Image processing, mathematical morphology, statistical analysis, pattern recognition,non destructive testing, parsimonious path openings, region growing structuring elements, geodesicand topologic attributes thinnings, adaptive coefficient shrinkage.

A escassez de dados hidrológicos no Brasil é um problema recorrente em muitas regiões, principalmente em se tratando de dados hidrométricos, produção de sedimentos e qualidade da água. A pesquisa por modelos de bacias hidrográficas tem aumentado nas últimas décadas, porém, a estimativa de dados hidrossedimentológicos a partir de modelos mais sofisticados demanda de grande número de variáveis, que devem ser ajustadas para cada sistema natural, o que dificulta a sua aplicação. O objetivo principal desta tese foi avaliar diferentes ferramentas de modelagem utilizadas para a estimativa da vazão, produção de sedimentos e qualidade da água e, em particular, comparar os resultados obtidos de um modelo hidrológico físico semi-distribuído, o Soil Water Assessment Tool (SWAT) com os resultados obtidos a partir de modelos hidrológicos concentrados, com base na metodologia do número da curva de escoamento do Soil Conservation Service (SCS-CN) e no modelo Generalized Watershed Loading Function (GWLF). Buscou-se avaliar e apresentar em quais condições o uso de cada modelo deve ser recomendado, ou seja, quando o esforço necessário para executar o modelo semi-distribuído leva a melhores resultados efetivos. Em relação à simulação da vazão, os resultados dos dois modelos foram altamente influenciados pelos dados de precipitação, indicando que existem, possivelmente, falhas ou erros de medição que poderiam ter influenciado negativamente os resultados. Portanto, foi proposto aplicar o modelo semi-distribuído com dados de precipitação interpolados (DPI) de alta resolução para verificar a eficiência de seus resultados em comparação com os resultados obtidos com a utilização dos dados de precipitação observados (DPO). Para simulação da produção de sedimentos, e das concentrações de nitrogênio e fósforo, o SWAT realiza uma simulação hidrológica mais detalhada, portanto, fornece resultados ligeiramente melhores para parâmetros de qualidade da água. O uso do modelo semi-distribuído também foi ampliado para simular uma bacia hidrográfica sob a influência do reservatório, a fim de verificar a potencialidade do modelo para esse propósito. Os modelos também foram aplicados para identificar quais os impactos potenciais das mudanças no uso do solo previstas e em andamento. Os cenários estudados foram: I – cenário atual, II – cenário tendencial, com o aumento da mancha urbana e substituição do solo exposto e de parte da mata nativa por uso agrícola; III – cenário desejável, complementa o crescimento urbano tendencial com aumento de áreas de reflorestamento. As metodologias foram aplicadas em duas bacias hidrográficas localizadas no Sudeste do Brasil. A primeira é a bacia do rio Jacaré-Guaçu, incluída na Unidade de Gerenciamento de Recursos Hídricos 13 (UGRHI-13), a montante da confluência do rio das Cruzes, com uma área de 1934 km2. O segundo caso de estudo, é a bacia do rio Atibaia, inserida na UGRHI-5, tem uma área de 2817,88 km2 e abrange municípios dos estados de São Paulo e Minas Gerais. Como principal conclusão, o desempenho do modelo semi-distribuído para estimar a produção de sedimentos, e as concentrações de nitrogênio e fósforo foi ligeiramente melhor do que as simulações do modelo concentrado SCS-CN e GWLF, mas essa vantagem pode não compensar o esforço adicional de calibrá-lo e validá-lo. / The lack of hydrological data in Brazil is a recurrent problem in many regions, especially in hydrometric data, sediment yield and water quality. The research by simplified models has increased in the last decades, however, the estimation of hydrossedimentological data from these more sophisticated models demands many variables, which must be adjusted for each natural system, which makes it difficult to apply. At times it is necessary to respond quickly without much precision in the results, in these situations, simpler models with few parameters can be the solution. The objective of this research is to evaluate different modelling tools used estimate streamflow, sediments yield and nutrients loads values, and namely to compare the results obtained from a physically-based distributed hydrological model (SWAT) with the results from a lumped hydrological, the Soil Conservation Service (SCS-CN) and the Generalized Watershed Loading Function (GWLF) model. Both models use the curve number (CN) concept, determined from land use, soil hydrologic group and antecedent soil moisture conditions and were run with a daily time step. We are particularly interested in understanding under which conditions the use of each model is to be recommended, namely when does the addition effort required to run the distributed model leads to effective better results. The input variables and parameters of the lumped model are assumed constant throughout the watershed, while the SWAT model performs the hydrological analysis at a small unit level, designated as hydrological response units (HRUs), and integrates the results at a sub-basin level. In relation to the flow simulation, the results of the two models were highly influenced by the rainfall data, indicating that, possibly, faults or measurement errors could have negatively influenced the results. Therefore, it was proposed to apply the distributed model with high-resolution grids of daily precipitation to verify the efficiency of its results when compared to rainfall data. For simulation of sediment, nitrogen and phosphorus, SWAT performs a more detailed simulation and thus provides slightly better results. The use of the SWAT was also extended to simulate the influence of reservoir, in order to verify the potentiality of the model, in relation to the simulation. The models also were used to identify which are potential impacts of the ongoing land use changes. The scenarios were: I - Current scenario, II - trend scenario, with the increase of urban land and replacement of the exposed soil and part of the native forest by agricultural use; III - desirable scenario complements the trend urban growth with the replacement of exposed soil and part of the agricultural use by reforestation. The methodologies were applied on two watersheds located in the Southeast of Brazil. The first one is the Jacaré-Guaçu river basin, included in the Water Resources Management Unit 13 (UGRHI-13), upstream of Cruzes river confluence, with an area of 1934 km2. The second watershed is the Atibaia River Basin, a part of Water Resources Management Unit 5 (UGRHI-5). It has an area of 2817.88 km2 and covers municipalities of the states of São Paulo and Minas Gerais.

Nesta tese apresentamos alguns resultados teóricos e práticos da modelagem de seqüências simbólicas com cadeias estocásticas parcimoniosas. As cadeias estocásticas parcimoniosas, que incluem as cadeias estocásticas de memória variável, constituem uma generalização das cadeias de Markov de alcance fixo. As seqüências simbólicas às quais foram aplicadas as ferramentas desenvolvidas são as cadeias de aminoácidos. Primeiramente, introduzimos um novo algoritmo, chamado de SPST, para selecionar o modelo de cadeia estocástica parcimoniosa mais ajustado a uma amostra de seqüências. Em seguida, utilizamos esse algoritmo para estudar dois importantes problemas da genômica; a saber, a classificação de proteínas em famílias e o estudo da evolução das seqüências biológicas. Finalmente, estudamos a velocidade de convergência de algoritmos relacionados com a estimação de uma subclasse das cadeias estocásticas parcimoniosas, as cadeias estocásticas de memória variável. Assim, generalizamos um resultado prévio de velocidade exponencial de convergência para o algoritmo PST, no caso de cadeias de memória ilimitada. Além disso, obtemos um resultado de velocidade de convergência para uma versão generalizada do Critério da Informação Bayesiana (BIC), também conhecido como Critério de Schwarz. / In this thesis we present some theoretical and practical results, concerning symbolic sequence modeling with parsimonious stochastic chains. Parsimonious stochastic chains, which include variable memory stochastic chains, constitute a generalization of fixed order Markov chains. The symbolic sequences modeled with parsimonious stochastic chains were the sequences of amino acids. First, we introduce a new algorithm, called SPST, to select the model of parsimonious stochastic chain that fits better to a sample of sequences. Then, we use the SPST algorithm to study two important problems of genomics. These problems are the classification of proteins into families and the study of the evolution of biological sequences. Finally, we find upper bounds for the rate of convergence of some algorithms related with the estimation of a subclass of parsimonious stochastic chains; namely, the variable memory stochastic chains. In consequence, we generalize a previous result about the exponential rate of convergence of the PST algorithm, in the case of unbounded variable memory stochastic chains. On the other hand, we prove a result about the rate of convergence of a generalized version of the Bayesian Information Criterion (BIC), also known as Schwarz\' Criterion.

Cette thèse étudie les approches de classification automatique basées sur les modèles de mélange gaussiens et les critères de choix de modèles pour la classification automatique de données discrétisées. Quatorze algorithmes binned-EM et quatorze algorithmes bin-EM-CEM sont développés pour quatorze modèles de mélange gaussiens parcimonieux. Ces nouveaux algorithmes combinent les avantages des données discrétisées en termes de réduction du temps d’exécution et les avantages des modèles de mélange gaussiens parcimonieux en termes de simplification de l'estimation des paramètres. Les complexités des algorithmes binned-EM et bin-EM-CEM sont calculées et comparées aux complexités des algorithmes EM et CEM respectivement. Afin de choisir le bon modèle qui s'adapte bien aux données et qui satisfait les exigences de précision en classification avec un temps de calcul raisonnable, les critères AIC, BIC, ICL, NEC et AWE sont étendus à la classification automatique de données discrétisées lorsque l'on utilise les algorithmes binned-EM et bin-EM-CEM proposés. Les avantages des différentes méthodes proposées sont illustrés par des études expérimentales. / This thesis studies the Gaussian mixture model-based clustering approaches and the criteria of model selection for binned data clustering. Fourteen binned-EM algorithms and fourteen bin-EM-CEM algorithms are developed for fourteen parsimonious Gaussian mixture models. These new algorithms combine the advantages in computation time reduction of binning data and the advantages in parameters estimation simplification of parsimonious Gaussian mixture models. The complexities of the binned-EM and the bin-EM-CEM algorithms are calculated and compared to the complexities of the EM and the CEM algorithms respectively. In order to select the right model which fits well the data and satisfies the clustering precision requirements with a reasonable computation time, AIC, BIC, ICL, NEC, and AWE criteria, are extended to binned data clustering when the proposed binned-EM and bin-EM-CEM algorithms are used. The advantages of the different proposed methods are illustrated through experimental studies.

In response to global climate change, many important earth-systems-oriented science programs have been established in the past. One such program, the Fluxnet program, studies the response of world forests and other natural ecosystems by measuring biospheric fluxes of carbon dioxide (CO2), water vapour, and energy with eddy-covariance (EC) techniques to assess the role of world ecosystems in offsetting increases in CO2 emissions and related impacts on global climate. The EC methodology has its limitations particularly when weather is inclement and during system stoppages. These limitations create non-trivial problems by creating data gaps in the monitored data stream, diminishing the integrity of the dataset and increasing uncertainty with data interpretation. This Thesis deals with the development of a parsimonious, semi-empirical approach for gap filling of net ecosystem productivity (NEP) data. The approach integrates the effects of environmental controls on diurnal NEP. The approach, because of its limited number of parameters, can be rapidly optimized when appropriate meteorological, site, and NEP target values are provided. The procedure is verified by applying it to several gap-filling case studies, including timeseries collected over balsam fir (Abies Balsamea (L.) Mill.) forests in New Brunswick (NB), Canada and several other forests along a north-south temperaturemoisture gradient from northern Europe to the Middle East. The evaluation showed that the model performed relatively well for most sites; i.e., r2 ranged from 0.68-0.83 and modelling efficiencies, from 0.89-0.97, demonstrating the possibility of applying the model to forests outside NB. Inferior model performance was associated with sites with less than complete input datasets.