Les chutes chez les personnes âgées représentent un problème important de santé publique. Des études montrent qu’environ 30 % des personnes âgées de 65 ans et plus chutent chaque année au Canada, entraînant des conséquences néfastes sur les plans individuel, familiale et sociale. Face à une telle situation la vidéosurveillance est une solution efficace assurant la sécurité de ces personnes. À ce jour de nombreux systèmes d’assistance de services à la personne existent. Ces dispositifs permettent à la personne âgée de vivre chez elle tout en assurant sa sécurité par le port d'un capteur. Cependant le port du capteur en permanence par le sujet est peu confortable et contraignant. C'est pourquoi la recherche s’est récemment intéressée à l’utilisation de caméras au lieu de capteurs portables. Le but de ce projet est de démontrer que l'utilisation d'un dispositif de vidéosurveillance peut contribuer à la réduction de ce fléau. Dans ce document nous présentons une approche de détection automatique de chute, basée sur une méthode de suivi 3D du sujet en utilisant une caméra de profondeur (Kinect de Microsoft) positionnée à la verticale du sol. Ce suivi est réalisé en utilisant la silhouette extraite en temps réel avec une approche robuste d’extraction de fond 3D basée sur la variation de profondeur des pixels dans la scène. Cette méthode se fondera sur une initialisation par une capture de la scène sans aucun sujet. Une fois la silhouette extraite, les 10% de la silhouette correspondant à la zone la plus haute de la silhouette (la plus proche de l'objectif de la Kinect) sera analysée en temps réel selon la vitesse et la position de son centre de gravité. Ces critères permettront donc après analyse de détecter la chute, puis d'émettre un signal (courrier ou texto) vers l'individu ou à l’autorité en charge de la personne âgée. Cette méthode a été validée à l’aide de plusieurs vidéos de chutes simulées par un cascadeur. La position de la caméra et son information de profondeur réduisent de façon considérable les risques de fausses alarmes de chute. Positionnée verticalement au sol, la caméra permet donc d'analyser la scène et surtout de procéder au suivi de la silhouette sans occultation majeure, qui conduisent dans certains cas à des fausses alertes. En outre les différents critères de détection de chute, sont des caractéristiques fiables pour différencier la chute d'une personne, d'un accroupissement ou d'une position assise. Néanmoins l'angle de vue de la caméra demeure un problème car il n'est pas assez grand pour couvrir une surface conséquente. Une solution à ce dilemme serait de fixer une lentille sur l'objectif de la Kinect permettant l’élargissement de la zone surveillée. / Elderly falls are a major public health problem. Studies show that about 30% of people aged 65 and older fall each year in Canada, with negative consequences on individuals, their families and our society. Faced with such a situation a video surveillance system is an effective solution to ensure the safety of these people. To this day many systems support services to the elderly. These devices allow the elderly to live at home while ensuring their safety by wearing a sensor. However the sensor must be worn at all times by the subject which is uncomfortable and restrictive. This is why research has recently been interested in the use of cameras instead of wearable sensors. The goal of this project is to demonstrate that the use of a video surveillance system can help to reduce this problem. In this thesis we present an approach for automatic detection of falls based on a method for tracking 3D subject using a depth camera (Kinect from Microsoft) positioned vertically to the ground. This monitoring is done using the silhouette extracted in real time with a robust approach for extracting 3D depth based on the depth variation of the pixels in the scene. This method is based on an initial capture the scene without any body. Once extracted, 10% of the silhouette corresponding to the uppermost region (nearest to the Kinect) will be analyzed in real time depending on the speed and the position of its center of gravity . These criteria will be analysed to detect the fall, then a signal (email or SMS) will be transmitted to an individual or to the authority in charge of the elderly. This method was validated using several videos of a stunt simulating falls. The camera position and depth information reduce so considerably the risk of false alarms. Positioned vertically above the ground, the camera makes it possible to analyze the scene especially for tracking the silhouette without major occlusion, which in some cases lead to false alarms. In addition, the various criteria for fall detection, are reliable characteristics for distinguishing the fall of a person, from squatting or sitting. Nevertheless, the angle of the camera remains a problem because it is not large enough to cover a large surface. A solution to this dilemma would be to fix a lens on the objective of the Kinect for the enlargement of the field of view and monitored area.

O presente texto descreve métodos e apresenta resultados do projeto de pesquisa de mestrado intitulado \"Dois Problemas em Análise de Formas de Estruturas de Ramificação\". Ambos os problemas abordados estão relacionados às sub-áreas da Análise de Formas denominadas Caracterização e Descrição de Formas. O primeiro problema consiste na investigação de um conjunto de características propostas para distingüir, primeiramente, entre estruturas de ramificação de vasos sangüíneos em imagens de retina segmentadas manualmente e automaticamente. A seguir, as mesmas características são aplicadas para discernir entre estruturas de ramificação de vasos sangüíneos em imagens de retina com e sem retinopatia diabética proliferativa (Proliferative Diabetic Retinopathy - PDR). A PDR é uma das patologias associadas à diabetes, que pode culminar na cegueira do indivíduo. Diagnósticos são possíveis por meio de imagens de fundo de olho e, quando efetuados precocemente, viabilizam intervenções oportunas evitando a perda da visão. Neste trabalho, 27 imagens digitais de fundo de olho foram segmentadas por dois processos distintos, isto é, segmentação manual por um especialista e a segmentação automática, mediante a transformada contínua Wavelet - CWT e classificadores estatísticos. Visando à caracterização destas formas, um conjunto de 08 características foi proposto. Este conjunto foi formado por três grupos, a saber: descritores tradicionais geométricos (Área, Perímetro e Circularidade), descritores associados à transformada wavelet ( 2o momento estatístico da distribuição de módulos da CWT, Entropia de Orientação da distribuição de fases da CWT e Curvatura) e um descritor fractal (Dimensão de Correlação - Global e Mediana). Uma Análise Discriminante Linear LDA revelou que as características geométricas tradicionais não detectam o início da retinopatia diabética proliferativa. A maior capacidade discriminante individual foi exibida pela Curvatura, com Área sob a curva ROC de 0.76. Um subconjunto com 6 características apresentou grande capacidade discriminante com Área sob a curva ROC de 0.90. O segundo problema diz respeito à extração de contorno de estruturas de ramificação bidimensionais de neurônios tridimensionais. Este trabalho contribui originalmente com uma solução para este problema, propondo dois algoritmos desenvolvidos para Rastreamento de Ramos e Extração do Contorno Paramétrico de estruturas de ramificação, capazes de transpor regiões críticas formadas por cruzamentos ocasionados pela projeção de estruturas 3D no plano das imagens 2D. Grande parte dos métodos baseados em contorno para análise de formas de estruturas de ramificação de células neuronais não produz representações corretas destas formas, devido à presença de sobreposições entre processos neuronais, levando os algoritmos tradicionais de extração de contorno a ignorar as regiões mais internas destas estruturas, gerando representações incompletas. O sistema proposto neste trabalho foi desenvolvido objetivando a solução do problema de extração de contorno, mesmo na presença de múltiplas sobreposições. Inicialmente, a imagem de entrada é pré-processada, gerando um esqueleto 8-conexo com ramos de um pixel de largura, um conjunto de sementes de sub-árvores dendríticas e um conjunto de regiões críticas (bifurcações e cruzamentos). Para cada sub-árvore, o algoritmo de rastreamento rotula todos os pixels válidos de um ramo, até chegar em uma região crítica, onde o algoritmo decide a direção em que deve continuar o rastreamento. Nosso algoritmo mostrou-se robusto, mesmo quando aplicado a imagens com segmentos paralelos muito próximos. Resultados obtidos com imagens reais (neurônios) são apresentados. / This document describes methods and presents results from the Master of Science\'s research project in computer science entitled \"Two Problems in Shape Analysis of Branching Structures\". Both tackled problems herein are related to Shape Analysis sub-fields, namely Characterization and Description of shapes. The former problem consists of an investigation on a proposed set of features aimed at discriminating, firstly, between blood vessels branching structures manually and automatically segmented. In the sequel, the same features are used to assess their discriminative capability in distinguishing between blood vessels branching structures with and withoud proliferative diabetic retinopathy (PDR). The PDR is a pathology related to diabetes, which may lead to the blindness. Diagnosis is possible through optic fundus image analysis, which may allow timely interventions preventing vision loss. In this work, 27 digital optic fundus images were segmented by two distinct segmentation processes, i.e. manual segmentation carried out by an especialist and automated segmentation, through the CWT (Continuous Wavelet Transform) and statistical classifiers. In order to characterize such a shapes, a set of 8 features has been proposed. The aforementioned set was comprised of three features groups, that is: traditional geometric descriptors (Area, Perimeter and Circularity), wavelet-based descriptors (2nd statistical moment from the CWT Modulus distribution, Orientation Entropy from the CWT Phase distribution and Curvature) and a fractal descriptor (Correlation Dimension - global and median). Linear Discriminant Analysis LDA revelead that the traditional geometric features are not able to detect early proliferative diabetic retinopathy. The largest singular discriminant capability was shown by the Curvature, with area under the ROC curve of 0.76. A subset of 6 features presented a good discriminating power with area under the curve of 0.90. The second problem concerns contour extraction from 2D branching structures of 3D neurons. This work contributes with an original solution for such a problem, proposing two algorithms devised for Branches Tracking and Branching Structures Contour Extraction. The proposed algorithms are able to traverse critical regions implied by the projection of 3D structures onto a 2D image plane. Most of contour-based methods intended to shape analysis of neuronal branching structures fall short of yielding proper shape representations, owing to the presence of overlapings among neuronal processes, causing the traditional algorithms for contour following to ignore the innermost regions, thus generating incomplete representations. The proposed framework system was developed aiming at the solution of the contour extraction problem, even in the presence of multiple overlapings. The input image is pre-processed, so as to obtain an 8-connected skeleton with one-pixel wide branches, a set of seeds of dendritic sub-trees and a set of critical regions (bifurcations, crossings and superpositions). For each sub-tree, the Branches Tracking Algorithm labels all valid pixels of a branch, until reaching a critical region, where the algorithm decides about the direction to go on with the tracking. Our algorithm has shown robustness, even in images plenty of very close parallel segments. Results with real images (neurons) are presented.

EDELWEISS est une expérience de détection directe de matière noire froide non-baryonique sous forme de particules massives et faiblement interagissantes (connues sous l'acronyme de WIMPs), qui constituent actuellement les candidats les plus populaires pour rendre compte de la masse manquante de l'Univers. Dans ce but, EDELWEISS utilise des bolomètres de germanium opérés à température cryogénique (20 mK environ) dans le Laboratoire Souterrain de Modane (LSM) à la frontière franco-italienne. En particulier, depuis 2008, un nouveau type de détecteur est en fonctionnement, équipé d'électrodes concentriques pour optimiser le rejet des évènements de surface (détecteurs à grilles coplanaires). Cette thèse se décompose en plusieurs axes de recherche. Tout d'abord, nous avons réalisé des mesures concernant la collecte des charges dans les cristaux. Les lois de vitesse des porteurs (électrons et trous) ont été déterminées dans le germanium à 20 mK dans la direction <100>, et une étude complète de la répartition des charges a été menée, avec une évaluation de l'anisotropie du transport et de la diffusion transverse des porteurs. Ces résultats permettent d'avoir une meilleure compréhension du fonctionnement interne des détecteurs d'Edelweiss. Ensuite, des études portant sur l'amélioration des performances ont été effectuées. Nous avons en particulier permis d'optimiser la procédure de régénération des cristaux et améliorer le rejet passif des évènements de surface (β). Le volume utile de détection des détecteurs a été évalué en utilisant les raies de deux radio-isotopes activés cosmiquement, le 68Ge et le 65Zn. Enfin, une étude exhaustive portant sur l'étude des spectres à basse énergie a été menée, ce qui permet de mettre au point une méthode d'analyse systématique pour la recherche de WIMPs de basse masse dans EDELWEISS. / EDELWEISS is a direct non-baryonic cold dark matter detection experiment in the form of weakly interacting massive particles (also known as WIMPs), which currently constitute the most popular candidates to account for the missing mass in the Universe. To this purpose, EDELWEISS uses germanium bolometers at cryogenic temperature (20 mK approximately) in the Underground Laboratory of Modane (LSM) at the French-Italian border. Since 2008, a new type of detector is operated, equipped with concentric electrodes to optimize the rejection of surface events (coplanar-grid detectors). This thesis work is divided into several research orientations. First, we carried out measurements concerning charge collection in the crystals. The velocity laws of the carriers (electrons and holes) have been determined in germanium at 20 mK in the <100> orientation, and a complete study of charge sharing has been done, including an evaluation of the transport anisotropy and of the straggling of the carriers. These results lead to a better understanding of the inner properties of the EDELWEISS detectors. Then, studies relating to the improvement of the performances were carried out. In particular, we have optimized the space-charge cancellation procedure in the crystals and improved the passive rejection of surface events (β). The fiducial volume of the detectors has been evaluated using two X-ray lines from cosmically activated radionuclides: 68Ge and 65Zn. Lastly, an exhaustive study of the low energy spectra has been carried out, which makes it possible to develop a systematic analysis method for the search of low-mass WIMPs in EDELWEISS.

O presente texto descreve a tese de doutorado intitulada Análise de Formas usando Wavelets em Grafos. O tema está relacionado à área de Visão Computacional, particularmente aos tópicos de Caracterização, Descrição e Classificação de Formas. Dentre os métodos da extensa literatura em Análise de Formas 2D, percebe-se uma presença menor daqueles baseados em grafos com topologia arbitrária e irregular. As contribuições desta tese procuram preencher esta lacuna. É proposta uma metodologia baseada no seguinte pipeline : (i) Amostragem da forma, (ii) Estruturação das amostras em grafos, (iii) Função-base definida nos vértices, (iv) Análise multiescala de grafos por meio da Transformada Wavelet Espectral em grafos, (v) Extração de Características da Transformada Wavelet e (vi) Discriminação. Para cada uma das etapas (i), (ii), (iii), (v) e (vi), são inúmeras as abordagens possíveis. Um dos desafios é encontrar uma combinação de abordagens, dentre as muitas alternativas, que resulte em um pipeline eficaz para nossos propósitos. Em particular, para a etapa (iii), dado um grafo que representa uma forma, o desafio é identificar uma característica associada às amostras que possa ser definida sobre os vértices do grafo. Esta característica deve capturar a influência subjacente da estrutura combinatória de toda a rede sobre cada vértice, em diversas escalas. A Transformada Wavelet Espectral sobre os Grafos revelará esta influência subjacente em cada vértice. São apresentados resultados obtidos de experimentos usando formas 2D de benchmarks conhecidos na literatura, bem como de experimentos de aplicações em astronomia para análise de formas de galáxias do Sloan Digital Sky Survey não-rotuladas e rotuladas pelo projeto Galaxy Zoo 2 , demonstrando o sucesso da técnica proposta, comparada a abordagens clássicas como Transformada de Fourier e Transformada Wavelet Contínua 2D. / This document describes the PhD thesis entitled Shape Analysis by using Wavelets on Graphs. The addressed theme is related to Computer Vision, particularly to the Characterization, Description and Classication topics. Amongst the methods presented in an extensive literature on Shape Analysis 2D, it is perceived a smaller presence of graph-based methods with arbitrary and irregular topologies. The contributions of this thesis aim at fullling this gap. A methodology based on the following pipeline is proposed: (i) Shape sampling, (ii) Samples structuring in graphs, (iii) Function dened on vertices, (iv) Multiscale analysis of graphs through the Spectral Wavelet Transform, (v) Features extraction from the Wavelet Transforms and (vi) Classication. For the stages (i), (ii), (iii), (v) and (vi), there are numerous possible approaches. One great challenge is to nd a proper combination of approaches from the several available alternatives, which may be able to yield an eective pipeline for our purposes. In particular, for the stage (iii), given a graph representing a shape, the challenge is to identify a feature, which may be dened over the graph vertices. This feature should capture the underlying inuence from the combinatorial structure of the entire network over each vertex, in multiple scales. The Spectral Graph Wavelet Transform will reveal such an underpining inuence over each vertex. Yielded results from experiments on 2D benchmarks shapes widely known in literature, as well as results from astronomy applications to the analysis of unlabeled galaxies shapes from the Sloan Digital Sky Survey and labeled galaxies shapes by the Galaxy Zoo 2 Project are presented, demonstrating the achievements of the proposed technique, in comparison to classic approaches such as the 2D Fourier Transform and the 2D Continuous Wavelet Transform.

Shetland boasts exceptionally well-preserved, but largely overlooked, field systems spanning a period of approximately 4000 years (Neolithic/Bronze Age – Viking/Norse). These have the potential to vastly increase our understanding of past agricultural practices and life styles. This study uses topographical survey, Shape Analysis, GIS, soil survey and micromorphology to answer questions relating to their location, form and function/management, pioneering the use of new tools and testing current models. An holistic landscape approach to the field systems is developed and tested against a multi-period site. Previously unknown types and periods of field systems are identified through survey and shape analysis, tools demonstrated to be valuable in refining the emerging model of field classification. GIS has illuminated pre-, during and post- construction factors influencing boundary form. New insights into location arise from the survey and GIS. Soils work has demonstrated that existing models of soil management over-simplify a complex situation, that thin acidic soils retain cultural information and that accretion was important to the sustainability of these peaty soils. While soils were sustainable over extended periods, the cultural inheritance of managed land appears to be limited. This thesis therefore presents the most holistic and comprehensive understanding of Shetland field systems which has so far been attempted.

Les chutes chez les personnes âgées représentent un problème important de santé publique. Des études montrent qu’environ 30 % des personnes âgées de 65 ans et plus chutent chaque année au Canada, entraînant des conséquences néfastes sur les plans individuel, familiale et sociale. Face à une telle situation la vidéosurveillance est une solution efficace assurant la sécurité de ces personnes. À ce jour de nombreux systèmes d’assistance de services à la personne existent. Ces dispositifs permettent à la personne âgée de vivre chez elle tout en assurant sa sécurité par le port d'un capteur. Cependant le port du capteur en permanence par le sujet est peu confortable et contraignant. C'est pourquoi la recherche s’est récemment intéressée à l’utilisation de caméras au lieu de capteurs portables. Le but de ce projet est de démontrer que l'utilisation d'un dispositif de vidéosurveillance peut contribuer à la réduction de ce fléau. Dans ce document nous présentons une approche de détection automatique de chute, basée sur une méthode de suivi 3D du sujet en utilisant une caméra de profondeur (Kinect de Microsoft) positionnée à la verticale du sol. Ce suivi est réalisé en utilisant la silhouette extraite en temps réel avec une approche robuste d’extraction de fond 3D basée sur la variation de profondeur des pixels dans la scène. Cette méthode se fondera sur une initialisation par une capture de la scène sans aucun sujet. Une fois la silhouette extraite, les 10% de la silhouette correspondant à la zone la plus haute de la silhouette (la plus proche de l'objectif de la Kinect) sera analysée en temps réel selon la vitesse et la position de son centre de gravité. Ces critères permettront donc après analyse de détecter la chute, puis d'émettre un signal (courrier ou texto) vers l'individu ou à l’autorité en charge de la personne âgée. Cette méthode a été validée à l’aide de plusieurs vidéos de chutes simulées par un cascadeur. La position de la caméra et son information de profondeur réduisent de façon considérable les risques de fausses alarmes de chute. Positionnée verticalement au sol, la caméra permet donc d'analyser la scène et surtout de procéder au suivi de la silhouette sans occultation majeure, qui conduisent dans certains cas à des fausses alertes. En outre les différents critères de détection de chute, sont des caractéristiques fiables pour différencier la chute d'une personne, d'un accroupissement ou d'une position assise. Néanmoins l'angle de vue de la caméra demeure un problème car il n'est pas assez grand pour couvrir une surface conséquente. Une solution à ce dilemme serait de fixer une lentille sur l'objectif de la Kinect permettant l’élargissement de la zone surveillée. / Elderly falls are a major public health problem. Studies show that about 30% of people aged 65 and older fall each year in Canada, with negative consequences on individuals, their families and our society. Faced with such a situation a video surveillance system is an effective solution to ensure the safety of these people. To this day many systems support services to the elderly. These devices allow the elderly to live at home while ensuring their safety by wearing a sensor. However the sensor must be worn at all times by the subject which is uncomfortable and restrictive. This is why research has recently been interested in the use of cameras instead of wearable sensors. The goal of this project is to demonstrate that the use of a video surveillance system can help to reduce this problem. In this thesis we present an approach for automatic detection of falls based on a method for tracking 3D subject using a depth camera (Kinect from Microsoft) positioned vertically to the ground. This monitoring is done using the silhouette extracted in real time with a robust approach for extracting 3D depth based on the depth variation of the pixels in the scene. This method is based on an initial capture the scene without any body. Once extracted, 10% of the silhouette corresponding to the uppermost region (nearest to the Kinect) will be analyzed in real time depending on the speed and the position of its center of gravity . These criteria will be analysed to detect the fall, then a signal (email or SMS) will be transmitted to an individual or to the authority in charge of the elderly. This method was validated using several videos of a stunt simulating falls. The camera position and depth information reduce so considerably the risk of false alarms. Positioned vertically above the ground, the camera makes it possible to analyze the scene especially for tracking the silhouette without major occlusion, which in some cases lead to false alarms. In addition, the various criteria for fall detection, are reliable characteristics for distinguishing the fall of a person, from squatting or sitting. Nevertheless, the angle of the camera remains a problem because it is not large enough to cover a large surface. A solution to this dilemma would be to fix a lens on the objective of the Kinect for the enlargement of the field of view and monitored area.

Whereas manually drawn contours could contain artifacts related to hand tremor, automatically detected contours could contain noise and inaccuracies due to limitations or errors in the procedures for the detection and segmentation of the related regions. To improve the further step of description, modeling procedures are desired to eliminate the artifacts in a given contour, while preserving the important and significant details present in the contour. In this work, are presented a couple of polygonal modeling methods, first a method applied direct on the original contour and other derived from the turning angle function. Both methods use the following parametrization Smin e µmax to infer about removing or maintain a given segment. By the using of the mentioned parameters the proposed methods could be configured according to the application problem. Both methods have been shown eficient to reduce the influence of noise and artifacts while preserving relevant characteristic for further analysis. Systems to support the diagnosis by images (CAD) and retrieval of images by content (CBIR) use shape descriptor methods to make possible to infer about factors existing in a given contour or as base to classify groups with dierent patterns. Shape factors methods should represent a value that is aected by the shape of an object, thus it is possible to characterize the presence of a factor in the contour or identify similarity among contours. Shape factors should be invariant to rotation, translation or scale. In the present work there are proposed the following shape features: index of the presence of convex region (XRTAF ), index of the presence of concave regions (V RTAF ), index of convexity (CXTAF ), two measures of fractal dimension (DFTAF e DF1 TAF ) and the index of spiculation (ISTAF ). All derived from the smoothed turning angle function. The smoothed turning angle function represent the contour in terms of their concave and convex regions. The polygonal modeling and the shape descriptors methods were applied on the breast masses classification issue to evaluate their performance. The polygonal modeling procedure proposed in this work provided higher compression and better polygonal fitness. The best classification accuracies, on discriminating between benign masses and malignant tumors, obtain for XRTAF , V RTAF , CXTAF , DFTAF , DF1 TAF and ISTAF , in terms of area under the receiver operating characteristics curve, were 0:92, 0:92, 0:93, 0:93, 0:92 e 0:94, respectively. / Contornos obtidos manualmente podem conter ruídos e artefatos oriundos de tremores da mão bem como contornos obtidos automaticamente podem os conter dado a problemas na etapa de segmentação. Para melhorar os resultados da etapa de representação e descrição, são necessários métodos capazes de reduzir a influência dos ruídos e artefatos enquanto mantém características relevantes da forma. Métodos de aproximação poligonal têm como objetivo a remoção de ruídos e artefatos presentes nos contornos e a melhor representação da forma com o menor número possível de segmentos de retas. Nesta disserta ção são propostos dois métodos de aproximação poligonal, um aplicado diretamente no contorno e outro que é obtido a partir da função tangencial do contorno original. Ambos os métodos fazem uso dos parâmetros Smin e µmax para inferirem sobre a permanência ou remoção de um dado segmento. Com a utilização destes parâmetros os métodos podem ser configurados para serem utilizados em vários tipos de aplicações. Ambos os métodos mostram-se eficientes na remoção de ruídos e artefatos, enquanto que características relevantes para etapas de pós-processamento são mantidas. Sistemas de apoio ao diagnóstico por imagens e de recuperação de imagens por conte údo fazem uso de métodos descritores de forma para que seja possível inferir sobre características presentes em um dado contorno ou ainda como base para medir a dissimilaridade entre contornos. Métodos descritores de características são capazes de representar um contorno por um número, assim é possível estabelecer a presença de uma característica no contorno ou ainda identificar uma possível similaridade entre os contornos. Métodos para extração de características devem ser invariantes a rotação, translação e escala. Nesta dissertação são propostos os seguintes métodos descritores de características: índice de presença de regiões convexas (XRTAF ), índice da presença de regiões côncavas (V RTAF ), índice de convexidade (CXTAF ), duas medidas de dimensão fractal (DFTAF e DF1 TAF ) e o índice de espículos (ISTAF ). Todos aplicados sobre a função tangencial suavizada. A função tangencial suavizada representa o contorno em termos de suas regiões côncavas e regiões convexas. Os métodos de aproximação poligonal e descritores de características foram aplicados para o problema de classificação de lesões de mama. Os resultados obtidos, mostraram que os métodos de aproximação poligonal propostos neste trabalho resultam em polígonos mais compactos e com melhor representação do contorno original. Os melhores resultados de classificação, na discriminação entre lesões benignas e tumores malignos, obtidos por XRTAF , V RTAF , CXTAF , DFTAF , DF1 TAF e ISTAF , em termos da área sob a curva ROC, foram 0:92, 0:92, 0:93, 0:93, 0:92 e 0:94, respectivamente. / Mestre em Ciência da Computação

Le but de ce travail est d'étudier l'influence de la microstructure de roches poreuses hétérogènes sur le comportement à l'échelle macroscopique. Ainsi, nous avons caractérisé la microstructure et les propriétés micromécaniques (grâce à des tests de nano-indentation) de deux roches oolithiques poreuses (calcaire de Lavoux et minerai de fer) pour calculer leurs propriétés mécaniques et thermiques effectives. Les roches oolithiques sont constituées d'un assemblage de grains poreux (oolithes), de pores et de cristaux intergranulaires. La microscopie électronique à balayage et la tomographie 3D aux rayons X ont été utilisées pour identifier les différents composants de ces roches. Une attention particulière a été accordée à la tomographie aux rayons X car cette méthode analytique permet de caractériser le réseau poreux (taille, distribution spatiale et fraction volumique), ainsi que la forme des oolithes et des cristaux inter-oolithiques. La nouveauté de ce travail réside dans la prise en compte de la forme 3D réelle des pores. Par conséquent, nous avons approximé les oolites poreuses par des sphères et les pores de forme irrégulière par des ellipsoïdes. Cette approximation a été réalisée grâce à l'analyse en composantes principales (ACP), qui fournit les propriétés géométriques telles que la longueur des demi-axes et l'orientation des ellipsoïdes résultants. La sphéricité des oolites approximées a été calculée et les valeurs proches de 1 nous ont permis de considérer les oolithes comme des sphères. Pour vérifier l'approximation dans le cas des pores, nous avons évalué la contribution de ces pores tridimensionnels de forme irrégulière aux propriétés élastiques et thermiques effectives. Ainsi, les tenseurs de contribution de souplesse pour les pores irréguliers 3D et leurs approximations ellipsoïdales ont été calculés en utilisant la méthode des éléments finis (FEM). Ces tenseurs ont été comparés et une erreur relative a été estimée pour évaluer la précision de l'approximation. Cette erreur produit une distance maximale de 4,5% entre les deux solutions pour les pores et les ellipsoïdes, ce qui vérifie la procédure d'approximation proposée basée sur ACP. La méthode numérique FEM a été vérifiée en comparant la solution numérique des tenseurs de contribution des ellipsoïdes à la solution analytique basée sur la théorie d'Eshelby. La différence entre ces deux solutions ne dépasse pas 3%. La même méthode numérique a été utilisée pour calculer les tenseurs de contribution de résistivité thermique. Les tenseurs de souplesse et de résistivité calculés ont été utilisés pour évaluer les propriétés élastiques effectives (module élastique et coefficient de cisaillement) et la conductivité thermique effective en considérant le schéma d'homogénéisation de Maxwell en deux étapes. Les résultats ont montré une influence importante de la porosité sur les propriétés effectives. Enfin, les résultats obtenus pour les pores irréguliers ont été comparés à ceux des ellipsoïdes et ils ont montré un bon accord avec un écart maximal de 4% ce qui vérifie l'approximation des pores de forme irrégulière par des ellipsoïdes triaxiaux / The aim of this work is to study the influence of the microstructure of heterogeneous porous rocks on the behavior at the macroscopic scale. Thus, we characterized the microstructure and micromechanical properties (thanks to nano-indentation tests) of two porous oolitic rocks (Lavoux limestone and iron ore) to calculate their effective mechanical and thermal properties. Oolitic rocks are constituted by an assemblage of porous grains (oolites), pores and inter-granular crystals. Scanning electron microscopy and X-ray 3D Computed Tomography were used to identify the different components of these rocks. Particular attention was given to X-Ray computed tomography since this analytical method allows the characterization of the porous network (size, spatial distribution, and volume fraction), and the shapes of oolites and inter-oolitic crystals. The novelty of this work lies in taking into account the 3D real shape of pores. Hence, we approximated porous oolites by spheres and irregularly shaped pores by ellipsoids. This approximation was performed thanks to the principal component analysis (PCA), which provides the geometrical properties such as length of semi-axes and orientation of resulting ellipsoids. The sphericity of the approximated oolites was calculated and the values close to 1 allowed us to consider oolites as spheres. To verify the approximation in the case of pores, we evaluated the contribution of these irregularly shaped three-dimensional pores to the overall elastic properties. Thus, compliance contribution tensors for 3D irregular pores and their ellipsoidal approximations were calculated using the finite element method (FEM). These tensors were compared and a relative error was estimated to evaluate the accuracy of the approximation. This error produces a maximum discrepancy of 4.5% between the two solutions for pores and ellipsoids which verifies the proposed approximation procedure based on PCA. The FEM numerical method was verified by comparing the numerical solution for compliance contribution tensors of ellipsoids to the analytical solution based on Eshelby’s theory. The difference between these two solutions does not exceed 3%. The same numerical method was used to calculate thermal resistivity contribution tensors. Calculated compliance and resistivity contribution tensors were used to evaluate effective elastic properties (bulk modulus and shear coefficient) and effective thermal conductivity by considering the two-step Maxwell homogenization scheme. The results showed an important influence of the porosity on effective properties. Finally, the results obtained for irregular pores were compared to those for ellipsoidal ones and they showed a good agreement with a maximum deviation of 4% which verifies once again the approximation of irregularly shaped pores by tri-axial ellipsoids

O presente texto descreve a tese de doutorado intitulada Análise de Formas usando Wavelets em Grafos. O tema está relacionado à área de Visão Computacional, particularmente aos tópicos de Caracterização, Descrição e Classificação de Formas. Dentre os métodos da extensa literatura em Análise de Formas 2D, percebe-se uma presença menor daqueles baseados em grafos com topologia arbitrária e irregular. As contribuições desta tese procuram preencher esta lacuna. É proposta uma metodologia baseada no seguinte pipeline : (i) Amostragem da forma, (ii) Estruturação das amostras em grafos, (iii) Função-base definida nos vértices, (iv) Análise multiescala de grafos por meio da Transformada Wavelet Espectral em grafos, (v) Extração de Características da Transformada Wavelet e (vi) Discriminação. Para cada uma das etapas (i), (ii), (iii), (v) e (vi), são inúmeras as abordagens possíveis. Um dos desafios é encontrar uma combinação de abordagens, dentre as muitas alternativas, que resulte em um pipeline eficaz para nossos propósitos. Em particular, para a etapa (iii), dado um grafo que representa uma forma, o desafio é identificar uma característica associada às amostras que possa ser definida sobre os vértices do grafo. Esta característica deve capturar a influência subjacente da estrutura combinatória de toda a rede sobre cada vértice, em diversas escalas. A Transformada Wavelet Espectral sobre os Grafos revelará esta influência subjacente em cada vértice. São apresentados resultados obtidos de experimentos usando formas 2D de benchmarks conhecidos na literatura, bem como de experimentos de aplicações em astronomia para análise de formas de galáxias do Sloan Digital Sky Survey não-rotuladas e rotuladas pelo projeto Galaxy Zoo 2 , demonstrando o sucesso da técnica proposta, comparada a abordagens clássicas como Transformada de Fourier e Transformada Wavelet Contínua 2D. / This document describes the PhD thesis entitled Shape Analysis by using Wavelets on Graphs. The addressed theme is related to Computer Vision, particularly to the Characterization, Description and Classication topics. Amongst the methods presented in an extensive literature on Shape Analysis 2D, it is perceived a smaller presence of graph-based methods with arbitrary and irregular topologies. The contributions of this thesis aim at fullling this gap. A methodology based on the following pipeline is proposed: (i) Shape sampling, (ii) Samples structuring in graphs, (iii) Function dened on vertices, (iv) Multiscale analysis of graphs through the Spectral Wavelet Transform, (v) Features extraction from the Wavelet Transforms and (vi) Classication. For the stages (i), (ii), (iii), (v) and (vi), there are numerous possible approaches. One great challenge is to nd a proper combination of approaches from the several available alternatives, which may be able to yield an eective pipeline for our purposes. In particular, for the stage (iii), given a graph representing a shape, the challenge is to identify a feature, which may be dened over the graph vertices. This feature should capture the underlying inuence from the combinatorial structure of the entire network over each vertex, in multiple scales. The Spectral Graph Wavelet Transform will reveal such an underpining inuence over each vertex. Yielded results from experiments on 2D benchmarks shapes widely known in literature, as well as results from astronomy applications to the analysis of unlabeled galaxies shapes from the Sloan Digital Sky Survey and labeled galaxies shapes by the Galaxy Zoo 2 Project are presented, demonstrating the achievements of the proposed technique, in comparison to classic approaches such as the 2D Fourier Transform and the 2D Continuous Wavelet Transform.

O presente texto descreve métodos e apresenta resultados do projeto de pesquisa de mestrado intitulado \"Dois Problemas em Análise de Formas de Estruturas de Ramificação\". Ambos os problemas abordados estão relacionados às sub-áreas da Análise de Formas denominadas Caracterização e Descrição de Formas. O primeiro problema consiste na investigação de um conjunto de características propostas para distingüir, primeiramente, entre estruturas de ramificação de vasos sangüíneos em imagens de retina segmentadas manualmente e automaticamente. A seguir, as mesmas características são aplicadas para discernir entre estruturas de ramificação de vasos sangüíneos em imagens de retina com e sem retinopatia diabética proliferativa (Proliferative Diabetic Retinopathy - PDR). A PDR é uma das patologias associadas à diabetes, que pode culminar na cegueira do indivíduo. Diagnósticos são possíveis por meio de imagens de fundo de olho e, quando efetuados precocemente, viabilizam intervenções oportunas evitando a perda da visão. Neste trabalho, 27 imagens digitais de fundo de olho foram segmentadas por dois processos distintos, isto é, segmentação manual por um especialista e a segmentação automática, mediante a transformada contínua Wavelet - CWT e classificadores estatísticos. Visando à caracterização destas formas, um conjunto de 08 características foi proposto. Este conjunto foi formado por três grupos, a saber: descritores tradicionais geométricos (Área, Perímetro e Circularidade), descritores associados à transformada wavelet ( 2o momento estatístico da distribuição de módulos da CWT, Entropia de Orientação da distribuição de fases da CWT e Curvatura) e um descritor fractal (Dimensão de Correlação - Global e Mediana). Uma Análise Discriminante Linear LDA revelou que as características geométricas tradicionais não detectam o início da retinopatia diabética proliferativa. A maior capacidade discriminante individual foi exibida pela Curvatura, com Área sob a curva ROC de 0.76. Um subconjunto com 6 características apresentou grande capacidade discriminante com Área sob a curva ROC de 0.90. O segundo problema diz respeito à extração de contorno de estruturas de ramificação bidimensionais de neurônios tridimensionais. Este trabalho contribui originalmente com uma solução para este problema, propondo dois algoritmos desenvolvidos para Rastreamento de Ramos e Extração do Contorno Paramétrico de estruturas de ramificação, capazes de transpor regiões críticas formadas por cruzamentos ocasionados pela projeção de estruturas 3D no plano das imagens 2D. Grande parte dos métodos baseados em contorno para análise de formas de estruturas de ramificação de células neuronais não produz representações corretas destas formas, devido à presença de sobreposições entre processos neuronais, levando os algoritmos tradicionais de extração de contorno a ignorar as regiões mais internas destas estruturas, gerando representações incompletas. O sistema proposto neste trabalho foi desenvolvido objetivando a solução do problema de extração de contorno, mesmo na presença de múltiplas sobreposições. Inicialmente, a imagem de entrada é pré-processada, gerando um esqueleto 8-conexo com ramos de um pixel de largura, um conjunto de sementes de sub-árvores dendríticas e um conjunto de regiões críticas (bifurcações e cruzamentos). Para cada sub-árvore, o algoritmo de rastreamento rotula todos os pixels válidos de um ramo, até chegar em uma região crítica, onde o algoritmo decide a direção em que deve continuar o rastreamento. Nosso algoritmo mostrou-se robusto, mesmo quando aplicado a imagens com segmentos paralelos muito próximos. Resultados obtidos com imagens reais (neurônios) são apresentados. / This document describes methods and presents results from the Master of Science\'s research project in computer science entitled \"Two Problems in Shape Analysis of Branching Structures\". Both tackled problems herein are related to Shape Analysis sub-fields, namely Characterization and Description of shapes. The former problem consists of an investigation on a proposed set of features aimed at discriminating, firstly, between blood vessels branching structures manually and automatically segmented. In the sequel, the same features are used to assess their discriminative capability in distinguishing between blood vessels branching structures with and withoud proliferative diabetic retinopathy (PDR). The PDR is a pathology related to diabetes, which may lead to the blindness. Diagnosis is possible through optic fundus image analysis, which may allow timely interventions preventing vision loss. In this work, 27 digital optic fundus images were segmented by two distinct segmentation processes, i.e. manual segmentation carried out by an especialist and automated segmentation, through the CWT (Continuous Wavelet Transform) and statistical classifiers. In order to characterize such a shapes, a set of 8 features has been proposed. The aforementioned set was comprised of three features groups, that is: traditional geometric descriptors (Area, Perimeter and Circularity), wavelet-based descriptors (2nd statistical moment from the CWT Modulus distribution, Orientation Entropy from the CWT Phase distribution and Curvature) and a fractal descriptor (Correlation Dimension - global and median). Linear Discriminant Analysis LDA revelead that the traditional geometric features are not able to detect early proliferative diabetic retinopathy. The largest singular discriminant capability was shown by the Curvature, with area under the ROC curve of 0.76. A subset of 6 features presented a good discriminating power with area under the curve of 0.90. The second problem concerns contour extraction from 2D branching structures of 3D neurons. This work contributes with an original solution for such a problem, proposing two algorithms devised for Branches Tracking and Branching Structures Contour Extraction. The proposed algorithms are able to traverse critical regions implied by the projection of 3D structures onto a 2D image plane. Most of contour-based methods intended to shape analysis of neuronal branching structures fall short of yielding proper shape representations, owing to the presence of overlapings among neuronal processes, causing the traditional algorithms for contour following to ignore the innermost regions, thus generating incomplete representations. The proposed framework system was developed aiming at the solution of the contour extraction problem, even in the presence of multiple overlapings. The input image is pre-processed, so as to obtain an 8-connected skeleton with one-pixel wide branches, a set of seeds of dendritic sub-trees and a set of critical regions (bifurcations, crossings and superpositions). For each sub-tree, the Branches Tracking Algorithm labels all valid pixels of a branch, until reaching a critical region, where the algorithm decides about the direction to go on with the tracking. Our algorithm has shown robustness, even in images plenty of very close parallel segments. Results with real images (neurons) are presented.