Dissertationen zum Thema „Geodesic distances“

O mapeamento de texturas é uma técnica bastante importante para adicionar detalhamento a modelos geométricos. O mapeamento de texturas baseadas em imagens costuma ser a abordagem preferida, mas faz uso de imagens pré-computadas que são mais adequadas à representação de padrões estáticos. Por outro lado, texturas procedurais oferecem uma alternativa que depende de funções para descrever os padrões das texturas. Elas garantem mais flexibilidade na definição dos padrões em cenas dinâmicas, tendo ainda uma representação mais compacta e dando um maior controle da aparência da textura através do ajuste de parâmetros. Quando mapeadas por coordenadas 3D, as texturas procedurais não consideram a forma da superfície domodelo, e com coordenadas 2D torna-se necessária a definição dessas coordenadas de forma coerente, que, em modelos complexos ,não é uma tarefa simples. Neste trabalho nós introduzimos o leitor às texturas procedurais e ao mapeamento de texturas, então apresentamos GeoTextures, uma nova abordagem que faz uso de distâncias geodésicas definidas com base em múltiplos pontos de origem sobre a superfície do modelo. As distâncias geodésicas são passadas como parâmetros que permitem que a textura procedural se adeqüe ao relevo do modelo texturizado. Nós validamos a proposta ao usar alguns exemplos de texturas procedurais aplicadas em tempo real na texturização de superfícies complexas, mudando tanto a textura do modelo como a forma, através do uso de tesselagem em hardware.
Texture mapping is an important technique to add detail to geometric models. Imagebased texture mapping is the preferred approach but employs pre-computed images, which are better suited for static patterns. On the other hand, procedural-based texture mapping offers an alternative that rely on functions to describe texturing patterns. This allows more flexibility to define patterns in dynamic scenes, while also having a more compact representation and more control for parametric adjustments on the texture visual appearance. When mapped with 3D coordinates, the procedural textures do not consider the model surface, and with 2D mapping the coordinates must be defined in a coherent way, which for complex models is not an easy task. In this work we give a introduction to procedural texturing and texture mapping, and introduce GeoTextures, an original approach that uses geodesic distance defined from multiple sources at different locations over the surface of the model. The geodesic distance is passed as a parameter that allows the shape of the model to be considered in the definition of the procedural texture. We validate the proposal using procedural textures that are applied in real-time to complex surfaces, and show examples that change both the shading of the models, as well as their shape using hardware-based tessellation.

La méthode de Microscopie par Localisation Ultrasonore (ULM) est une nouvelle méthode d'imagerie médicale super-résolue qui permet d'outrepasser le compromis précision/distance de pénétration dans les tissus pour l'imagerie du réseau vasculaire. Ce nouveau type d'images pose de nouveaux enjeux mathématiques, notamment pour la segmentation et l'analyse de ses images, étapes nécessaires pour arriver à des méthodes pour le diagnostic. Notre travail se positionne à l'intersection des méthodes géodésiques et des méthodes de Machine Learning. Dans cette thèse nous apportons trois contributions. Une première de ces contributions est centrée autour des contraintes liées aux images ULM et propose le tracking de l'entièreté de l'arbre vasculaire en passant par la détection des point-clés des vaisseaux sanguins apparaissant sur l'image. La deuxième contribution de cette thèse porte sur l'apprentissage de la définition de métriques Riemanniennes pour traiter des tâches de segmentation sur des données d'IRM cérébraux et d'images du fond de l'œil. La dernière partie de notre travail porte sur un problème inverse pour la reconstruction de trajectoires d'agents de contraste dans des images médicales dans le contexte de la super-résolution sans-grille
Ultrasound Localization Microscopy is a new method in super-resolved Medical Imaging that allow us to overcome compromise between precision and penetration distance in the tissues for the imaging of the vascular network. This new type of images raises new mathematical questions, especially for the segmentaton and analysis, necessary steps to achieve medical diagnostic of patients. Our work is positioned at the intersection of geodesic and Machine Learning methods. In this thesis, we make three contributions. The first of these is centered on the constraints linked to ULM images and proposes the tracking of the entire vascular tree through the detection of key points of blood vessels appearing on the image. The second contribution of this thesis deals with learning to define Riemannian metrics to handle segmentation tasks on brain MRI data and eye fundus images. The final part of our work focuses on an inverse problem for reconstructing contrast agent trajectories in medical images in the context of grid-free super-resolution

The medial axis is an important shape representation and the computation of the medial axis is a fundamental research problem in computer graphics. Practically, the medial axis is widely used in various aspects of computer graphics, such as shape analysis, image segmentation, skeleton extraction and mesh generation and so forth. However, the applications of the medial axis have been limited by its sensitivity to boundary perturbations. This characteristic may lead to a number of noise branches and increase the complexity of the medial axis. To solve the sensitivity problem, it is critical to simplify the medial axis. This thesis first investigates the algorithms for computing medial axes of different input shapes. Several algorithms for the filtration of medial axes are then reviewed, such as the local importance measurement algorithms, boundary smoothness algorithms, and the global algorithms. Two novel algorithms for the simplification of the medial axis are proposed to generate a stable and simplified medial axis as well as its reconstructed boundary. The developed Global Geodesic Slope(GGS) algorithm for the medial axis simplification is based on the global geodesic slope defined in this thesis, which combines the advantages of the global and the local algorithms. The GGS algorithm prunes the medial axis according to local features as well as the relative size of the shape. It is less sensitive to boundary noises than the local algorithms, and can maintain the features of the shape in highly concave regions while the global algorithms may not. The other simplification algorithm we propose is the Accumulated Hyperbolic Distance(AHD) algorithm. It directly uses the evaluation criterion of the error, accumulated hyperbolic distance defined in this thesis, as the pruning measurement in the filtration process. It guarantees the upper bound of the error between the reconstructed shape and the original one within the defined threshold. The AHD algorithm avoids sudden changes of the reconstructed shape as the defined threshold changes.
published_or_final_version
Computer Science
Master
Master of Philosophy

Orientador: Quintino Dalmolin
Co-orientador: Tarcisio Ferreira Silva
Dissertação (mestrado) - Universidade Federal do Paraná
Resumo: O procedimento clássico usado para determinar as distâncias interpilares de uma linha base multipilar para calibração de distanciômetros, consiste em avaliar essas distâncias diretamente, usando equipamentos de alta precisão. Nesse caso, a precisão final das distâncias interpilares fica limitada à precisão do próprio equipamento usado. Neste trabalho, foi desenvolvido um procedimento metodológico para definir as distâncias interpilares de uma linha base a partir de um campo de pontos planimétrico, em que os pontos da linha base foram incluídos. Para tanto, a configuração geométrica do campo de pontos foi adequadamente otimizada através de procedimentos de simulação. Garantiu-se assim que os resultados esperados para a precisão final dos pontos da rede fossem obtidos antes mesmo do trabalho de campo ser conduzido. O programa "NETZ2D" de análise e ajustamento de redes 2D foi usado como ferramenta computacional. Os experimentos realizados no processo de simulação e de medição do campo de pontos, foram conduzidos sobre a linha base da UFPE. Na medição do campo de pontos otimizado, garantiu-se o controle do processo de medição em termos de escolha adequada do período de medição e dos equipamentos. Verificou-se que a metodologia proposta, quando comparado ao procedimento clássico, apresentou vantagens em termos de facilidades de implementação bem como nos resultados obtidos. No experimento realizado, as distâncias interpilares da linha base da UFPE foram definidas com uma precisão cinco vezes maior que a precisão das medidas de distâncias avaliadas no campo de pontos. Por outro lado, resultado final equivalente foi obtido para os pontos da linha base simulando um campo de pontos com um único padrão metrológico de distância.
Abstract: The used classic proceeding to determine the interpillares distancies of one multipillar base line to calibration of eletronic distancies measuring (EDM), consist in to evaluate this distancies directing using equipmenty of high precision. In this case, the finish precision of the interpillares distancies stay limited the precision of proper equipment used. In this work, was developed a metodologic proceeding to define the interpillares distancies of one base line until of the network 2D, in that the points of base line was incluids. To that effect, the geometric configuration of network 2D was adequatement optimized through of proceeding of simulation. Was guaranted that the hoped results to the finish precision of the points of the net have was obtain before the work of field to be conduzed. The program "NETZ2D" of analysis and adjustment of the nets was used how computation instrument. The experiments realized in the simulation and measure process of the network, was conduzed about the base line of UFPE. On the measuring of network optmized, was guaranty the control of the measuring process adequad choose of the time of the measuring and of the equipments. Was verified that the offered metodology, when compared to the classic proceeding, showed advantagies of easilies implementation, as in the results obtained. On the experiment realized, the interpillares distancies of base line of the UFPE was define with one precision five time bigger than the precision o f the measure of the distancies evaluated on network. On the other hand, the equivalent finish result was obtained to the points of the base line, simulating one network with only one standart metrologic of the distance.

Dans cette thèse, on présente une notion de courbure géodésique pour les courbes lisses horizontales dans une variété sous-Riemannienne de contact, qui indique dans quelle mesure une courbe est différente d'une géodésique. Cette courbure géodésique se présente sous la forme de deux fonctions qui sont toutes deux identiquement nulles le long d'une courbe lisse horizontale si et seulement si cette dernière courbe est une géodésique. Le résultat principal de cette thèse réside dans l'interprétation métrique que l'on donne de ces fonctions de courbure. Cette interprétation consiste à extraire la courbure géodésique des premiers termes de correction dans le développement limité de la distance sous-Riemannienne entre deux points proches le long de la courbe
We present a notion of geodesic curvature for smooth horizontal curves in a contact sub-Riemannian manifold, measuring how far a horizontal curve is from being a geodesic. This geodesic curvature consists in two functions that both vanish along a smooth horizontal curve if and only if this curve is a geodesic. The main result of this thesis is the metric interpretation of these geodesic curvature functions. This interpretation consists in seeing the geodesic curvature functions as the first corrective coefficients in the Taylor expansion of the sub-Riemannian distance between two close points on the curve

Etant donne une distance d sur le bord d'un disque de dimension deux, nous cherchons dans cette these a prolonger d en une distance sur le disque tout entier, de telle sorte que l'espace metrique obtenu soit un espace de longueur, par exemple une metrique riemannienne ou finslerienne. Le prolongement est dit rigide s'il est unique a isometrie pres. Des resultats de rigidite ont ete obtenus par r. Michel, j. P. Otal et c. B. Croke en se restreignant aux metriques riemanniennes. Nous prouvons ici la rigidite des metriques euclidiennes a singularites coniques de courbures negatives. Nous donnons egalement des exemples de metriques riemanniennes non rigides. Nous montrons ensuite qu'un tel prolongement est entierement determine par la donnee de ses courbes geodesiques, ce qui permet de decrire l'ensemble des solutions du probleme. En imposant des conditions sur la distance sur le bord et le systeme de geodesiques, l'espace de longueur obtenu provient en fait d'une metrique finslerienne ou riemannienne. On obtient finalement un critere pour que deux prolongements ne soient pas isometriques

Business Administration/Interdisciplinary
D.B.A.
Retail automotive literature that examines how the distance between a retail automotive facility and the prospective purchaser affects market performance is limited. Primary data for this study indicates that distance and purchase in the retail automotive sector move in opposite directions. This study examines similar goods that have high barriers of entry and proposes other methods of increasing market reach. This is a study of the conditions that affect the market performance for imported luxury vehicles. First, is the effect of distance on purchase decisions. Vehicular sales drop the further away a customer is from a car dealership. We call this phenomenon distance decay. Distance decay is defined as: the interaction between two locations declines as the distance between then increases. Secondly, when similar brands are viewed as substitutes, the consumer will choose the brand with the closest automotive service department to their residence or place of employment. Thirdly, door-to-door selling can decrease distance decay. Lastly, pick-up and delivery service can decrease distance decay. Data from 30,936 prospects and individuals who entered, phoned, or emailed a dealership inquiring about purchasing a new Audi were used in the study. These prospects will be categorized by who intended to buy and who actually purchased a car. In addition to the prospects, data from 6,153 individuals who purchased a new Audi from four Audi dealerships in the greater Philadelphia area and from the framed field experiment were used in the study. These categories will then be further labeled by ZIP code and city to determine the effects of distance. Then, possible solutions will be performed on test groups to determine what alternatives from other industries can be used to improve market performance involving long distances.
Temple University--Theses

In many real-world application problems, the availability of data labels for supervised learning is rather limited. Incompletely labeled datasets are common in many of the databases generated in some of the currently most active areas of research. It is often the case that a limited number of labeled cases is accompanied by a larger number of unlabeled ones. This is the setting for semi-supervised learning, in which unsupervised approaches assist the supervised problem and vice versa. A manifold learning model, namely Generative Topographic Mapping (GTM), is the basis of the methods developed in this thesis. The non-linearity of the mapping that GTM generates makes it prone to trustworthiness and continuity errors that would reduce the faithfulness of the data representation, especially for datasets of convoluted geometry. In this thesis, a variant of GTM that uses a graph approximation to the geodesic metric is first defined. This model is capable of representing data of convoluted geometries. The standard GTM is here modified to prioritize neighbourhood relationships along the generated manifold. This is accomplished by penalizing the possible divergences between the Euclidean distances from the data points to the model prototypes and the corresponding geodesic distances along the manifold. The resulting Geodesic GTM (Geo-GTM) model is shown to improve the continuity and trustworthiness of the representation generated by the model, as well as to behave robustly in the presence of noise. The thesis then leads towards the definition and development of semi-supervised versions of GTM for partially-labeled data exploration. As a first step in this direction, a two-stage clustering procedure that uses class information is presented. A class information-enriched variant of GTM, namely class-GTM, yields a first cluster description of the data. The number of clusters defined by GTM is usually large for visualization purposes and does not necessarily correspond to the overall class structure. Consequently, in a second stage, clusters are agglomerated using the K-means algorithm with different novel initialization strategies that benefit from the probabilistic definition of GTM. We evaluate if the use of class information influences cluster-wise class separability. A robust variant of GTM that detects outliers while effectively minimizing their negative impact in the clustering process is also assessed in this context. We then proceed to the definition of a novel semi-supervised model, SS-Geo-GTM, that extends Geo-GTM to deal with semi-supervised problems. In SS-Geo-GTM, the model prototypes are linked by the nearest neighbour to the data manifold constructed by Geo-GTM. The resulting proximity graph is used as the basis for a class label propagation algorithm. The performance of SS-Geo-GTM is experimentally assessed, comparing positively with that of an Euclidean distance-based counterpart and that of the alternative Laplacian Eigenmaps method. Finally, the developed models (the two-stage clustering procedure and the semi-supervised models) are applied to the analysis of a human brain tumour dataset (obtained by Nuclear Magnetic Resonance Spectroscopy), where the tasks are, in turn, data clustering and survival prognostic modeling.
Resum de la tesi (màxim 4000 caràcters. Si se supera aquest límit, el resum es tallarà automàticament al caràcter 4000) En muchos problemas de aplicación del mundo real, la disponibilidad de etiquetas de datos para aprendizaje supervisado es bastante limitada. La existencia de conjuntos de datos etiquetados de manera incompleta es común en muchas de las bases de datos generadas en algunas de las áreas de investigación actualmente más activas. Es frecuente que un número limitado de casos etiquetados venga acompañado de un número mucho mayor de datos no etiquetados. Éste es el contexto en el que opera el aprendizaje semi-supervisado, en el cual enfoques no-supervisados prestan ayuda a problemas supervisados y vice versa. Un modelo de aprendizaje de variaciones (manifold learning, en inglés), llamado Mapeo Topográfico Generativo (GTM, en acrónimo de su nombre en inglés), es la base de los métodos desarrollados en esta tesis. La no-linealidad del mapeo que GTM genera hace que éste sea propenso a errores de fiabilidad y continuidad, los cuales pueden reducir la fidelidad de la representación de los datos, especialmente para conjuntos de datos de geometría intrincada. En esta tesis, una extensión de GTM que utiliza una aproximación vía grafos a la métrica geodésica es definida en primer lugar. Este modelo es capaz de representar datos con geometrías intrincadas. En él, el GTM estándar es modificado para priorizar relaciones de vecindad a lo largo de la variación generada. Esto se logra penalizando las divergencias existentes entre las distancias Euclideanas de los datos a los prototipos del modelo y las correspondientes distancias geodésicas a lo largo de la variación. Se muestra que el modelo Geo-GTM resultante mejora la continuidad y fiabilidad de la representación generada y que se comporta de manera robusta en presencia de ruido. Más adelante, la tesis nos lleva a la definición y desarrollo de versiones semi-supervisadas de GTM para la exploración de conjuntos de datos parcialmente etiquetados. Como un primer paso en esta dirección, se presenta un procedimiento de agrupamiento en dos etapas que utiliza información de pertenencia a clase. Una extensión de GTM enriquecida con información de pertenencia a clase, llamada class-GTM, produce una primera descripción de grupos de los datos. El número de grupos definidos por GTM es normalmente grande para propósitos de visualización y no corresponde necesariamente con la estructura de clases global. Por ello, en una segunda etapa, los grupos son aglomerados usando el algoritmo K-means con diferentes estrategias de inicialización novedosas las cuales se benefician de la definición probabilística de GTM. Evaluamos si el uso de información de clase influye en la separabilidad de clase por grupos. Una extensión robusta de GTM que detecta datos atípicos a un tiempo que minimiza de forma efectiva su impacto negativo en el proceso de agrupamiento es evaluada también en este contexto. Se procede después a la definición de un nuevo modelo semi-supervisado, SS-Geo-GTM, que extiende Geo-GTM para ocuparse de problemas semi-supervisados. En SS-Geo-GTM, los prototipos del modelo son vinculados al vecino más cercano a la variación construída por Geo-GTM. El grafo de proximidad resultante es utilizado como base para un algoritmo de propagación de etiquetas de clase. El rendimiento de SS-Geo-GTM es valorado experimentalmente, comparando positivamente tanto con la contraparte de este modelo basada en la distancia Euclideana como con el método alternativo Laplacian Eigenmaps. Finalmente, los modelos desarrollados (el procedimiento de agrupamiento en dos etapas y los modelos semi-supervisados) son aplicados al análisis de un conjunto de datos de tumores cerebrales humanos (obtenidos mediante Espectroscopia de Resonancia Magnética Nuclear), donde las tareas a realizar son el agrupamiento de datos y el modelado de pronóstico de supervivencia.

Orientador: Quintino Dalmolin
Co-orientador: Hideo Araki
Dissertação (mestrado) - Universidade Federal do Parana
Resumo: Uma das grandes preocupações no processo de automação em Fotogramentria esta relacionado com os algoritmos de reconhecimento de padrões. Apesar da metodologia ter avançado significativamente nos últimos anos, principalmente no que se refere ao tom de cinza, o reconhecimento de padrões de cores reais em imagens coloridas ainda se encontra em fase de desenvolvimento. Neste sentido objetiva-se realizar uma serie de ensaios com dados (cores) controlados e também com dados reais para comparar a performance dos métodos estatísticos de Máxima Verossimilhança, Distancia Mínima e de Fisher para reconhecimento das cores reais. A comparação entre os métodos estatísticos foi feita controlando o processo de classificação, ou seja, utilizando amostras determinísticas para treinamento das funções discriminantes e criando imagens para classificação no software (MATLAB). Com o intuito de que a comparação pudesse ser feita sem controle da imagem a ser classificada e das amostras, utilizou-se uma imagem retirada de uma foto digitalizada, para verificar a performance dos métodos frente a um caso real. A analise de desempenho dos métodos foi observada pela estatística kappa e a comparação pelo teste Z apropriado. Os resultados indicam que o Método de Distancia Mínima foi o melhor para classificação de cores reais sob todos os aspectos estudados.
Abstract: One o f the main issues in the photogrametry automation process is related to pattern recognition algorithms. Although there were significant advances in the last years, mainly in regard to the gray tones, color pattern recognition in colored images is still in a developmental stage. In this sense, a series o f tests with controlled data (colors) and also with real data is made to compare the performance o f the statistical methods: Maximum Likelihood, Minimum Distance, and Fisher's method in their ability to recognize real colors. The comparison among the statistical methods was performed by controlling the classification process, that is, using deterministic samples for the training o f discriminant functions and test images created by a software (MATLAB). For the case o f real images, the statistical methods were compared without controlling both the sample and the image by the utilization o f an image extracted from a digitized picture. The methods performance was analyzed using the kappa statistic and the Z test. The results indicated that the Minimum Distance Method was the best method to classify real colors under all assumptions.

Le monde est face à une crise environnementale majeure, ceci alors que la consommation d'énergie ne cesse d'augmenter. Quelles solutions pouvons-nous trouver pour fournir l'énergie demandée, tout en réduisant les émissions de gaz à effet de serre ? L'une d'entre elles consiste à améliorer l'efficacité énergétique des procédés industriels, notamment par le biais de la catalyse hétérogène. Les catalyseurs hétérogènes, ici des solides poreux, sont utilisés en raffinage et pétrochimie, en particulier pour la génération de biocarburant.La question se pose de caractériser l'efficacité de ces catalyseurs. Une description morphologique fournit des informations clés, au sens où des corrélations ont été établies entre propriétés structurales et performances de ces matériaux. Néanmoins, la catalyse hétérogène est un processus complexe et les descripteurs traditionnellement utilisés sont insuffisants, dans l'optique d'une aide aux choix de ces matériaux.Ce travail de thèse vise à développer de nouveaux descripteurs numériques de microstructures, facilement interprétables, efficients et complémentaires à l'état de l'art, afin d'aider in fine à choisir les catalyseurs appropriés à une application donnée. Ces descripteurs permettent une caractérisation géométrique et topologique du réseau poreux, quelle que soit sa complexité et indépendamment des phénomènes physico-chimiques pouvant être en jeu.Nous mettons en œuvre à la fois la percolation, capacité à traverser une microstructure ; la tortuosité géométrique, sinuosité et interconnectivité d'un réseau ; et l'hétérogénéité. Ces descripteurs relèvent pour l'essentiel de méthodes morphologiques. Les caractéristiques géométriques et topologiques liées aux fonctionnelles de Minkowski en 3D sont adaptées au domaine d'intérêt par estimation de l'accessibilité à une microstructure pour une sphère de taille donnée (A-protocole), décrite par érosion morphologique calculée de façon efficace grâce aux cartes de distances. Nous caractérisons ensuite la topologie des pores via un nouvel opérateur, la M-tortuosité, applicable à tout volume segmenté, sans définition arbitraire de points ou de plans sources. Nous proposons un estimateur efficace de la M-tortuosité par calcul de cartes de distances ; dont une généralisation par facteurs puissances est définie. Cet opérateur est ensuite étendu de différentes façons.Tout d'abord, au cas d'une sonde de taille finie (M-tortuosité-par-érosions-itératives), caractérisant les goulots d'étranglement, habituellement décrits par la constrictivité. Puis, pour caractériser la dépendance en échelle spatiale de la tortuosité (H-tortuosité), ce qui quantifie, entre autres, l'hétérogénéité de la structure. Enfin, ces deux aspects sont regroupés dans la H-tortuosité-par-érosions-itératives.Dans un second temps, ces opérateurs ensemblistes, valables pour des images binaires, reçoivent une extension fonctionnelle permettant de décrire des images à niveaux de gris (F-tortuosité et HF-tortuosité). Les objectifs sont multiples : tenir compte d'informations locales lors de l'estimation de la tortuosité globale de microstructures, et discriminer des images tomographiques, sans segmentation précise de la structure.Le pouvoir discriminant de ces opérateurs ensemblistes et fonctionnels, et leur comportement, sont évalués au fil des définitions, sur des cas d'école et sur des modèles booléens multi-échelles de Cox. Leurs similitudes et complémentarités sont analysées sur ces mêmes images synthétiques.En catalyse et biocatalyse, trois types de microstructures sont considérés : les zéolithes, les MOFs (Metal-Organic Framework) et les alumines. Ces applications montrent l'étendue du champ applicatif, par l'adaptabilité et la complémentarité des descripteurs proposés, entrainant la considération de leur utilisation en dehors du cadre de la catalyse, notamment pour certains domaines des neurosciences et l'analyse des milieux turbides
In a technologically advanced world, energy consumption is rapidly increasing deepening the ongoing environmental crisis. Therefore, solutions must be found to provide the required energy, while reducing greenhouse gas emissions.Catalysis is an excellent way to improve the energy efficiency of industrial processes. Heterogeneous catalysts, here porous microstructures, are at the heart of this process, particularly for refining and petrochemical industry, specifically for biofuel generation.Their morphological description provides key information. Thus far, correlations have been established between the structural properties and performance of these materials. Nevertheless, heterogeneous catalysis is a very complex process and the traditional numerical descriptors provide insufficient information and fail to assist in material selection. The work addressed in this thesis aims to develop new digital descriptors of microstructures that are easily interpretable, efficient and complementary to the current state-of-the-art solutions. The objective is to complete the set of descriptors, to help in the optimal selection of the appropriate catalysts for a given application. More specifically, we focus our work on a geometric and topological characterization of the porous network, without taking into account physicochemical phenomena, and not being limited by the complexity of the microstructure studied.Our different approaches focus on the concepts of percolation, ability to cross a microstructure; geometric tortuosity, sinuosity and interconnectivity of a network; and heterogeneity. The geometric and topological characteristics linked to the Minkowski functionals in 3D are fitted to catalysis field by estimating accessibility of a microstructure for a given sphere size (A-protocol), described by morphological erosion efficiently calculated by distance maps. To characterize the pore topology, we define an operator, the M-tortuosity, that can be applied to any segmented volume, without arbitrarily defining source points or planes. We propose an efficient M-tortuosity estimator by calculating distance maps; which is then generalized by power factors. This operator is then extended to distinct ways.First, to the case of a probe of finite size (M-tortuosity-by-iterative-erosions), characterizing bottleneck effects which are usually quantified using constrictivity. Then, to characterize the spatial scale dependence of tortuosity (H-tortuosity), characterizing, among others, the heterogeneity of the structure. Finally, both aspects are gathered into the H-tortuosity-by-iterative-erosions.Secondly, these ensemble operators, suitable for binary images, are extended to the functional case, to discriminate grayscale images (F-tortuosity and HF-tortuosity). These functional extensions have various purposes: combining local information with tortuosity assessment of the overall structure, and characterizing tomographic images without accurate segmentation.The discrimination power of these operators, ensemble and functional, is assessed on toy cases and on multi-scale Boolean Cox schemes. Moreover, their similarities and complementarities are analysed using these very same stochastic models.In catalysis and biocatalysis, three types of catalysts are considered: zeolites, MOFs (Metal-Organic Framework) and aluminas. These applications highlight their wide scope, and lead to consider their usefulness out of catalyst domain; in neuroscience and for turbid media characterization

Les performances d’un système de reconnaissance de formes dépendent en bonne partie de la qualité de l’image segmentée. Malgré les progrès effectués, une segmentation complète (c’est-à-dire avec des contours entiers) ne peut pas être toujours atteinte. Dans un premier temps, nous nous plaçons dans le cas où seulement certaines parties de la forme entière sont disponibles. D’abord, afin d’assurer l’invariance des parties de formes aux transformations géométriques, nous développons une méthode d’optimisation de l’analyse procustéenne qui consiste à retrouver les points extrémités optimaux qui minimisent la distance de Procutse. Ensuite, nous proposons une approche de reconnaissance de parties de formes et une approche de reconnaissance de formes partielles. Ces deux approches, basées-contour, sont fondées sur un recalage robuste entre les parties de formes. La méthode de recalage proposée consiste à optimiser une mesure de similarité basée sur les géodésiques dans l’espace de formes. Ainsi, nous exploitons le résidu du recalage pour définir une nouvelle métrique pour la reconnaissance de parties de formes. Puis, nous décrivons une stratégie de combinaison avec cette même métrique pour la reconnaissance de formes partielles. Par la suite, nous proposons d’utiliser la distance géodésique proposée pour la reconnaissance des parties de formes dans la définition d’une métrique globale pour la reconnaissance de formes entières. Les tests de reconnaissance (classification et recherche) sont effectués sur des parties requêtes et des formes entières de la base d’images MPEG-7, puis sur des images réelles segmentées. Les résultats expérimentaux montrent la supériorité de nos méthodes par rapport aux autres méthodes de l’état de l’art
The quality of the segmentation process directly affects the performance of the shape recognition. Despite the progress that has been made, it is often unreachable to segment the entire object (i.e. closed contour). In fact, only some parts/fragments of objects can be detected. We first develop a new alignment method based on Procrustes analysis in order to ensure invariance of shape parts to geometric transformations (translation, rotation and scale factor). The proposed method consists in finding optimal extremities which minimize the Procrustes distance. Then, we propose a shape part recognition approach and a partial shape recognition approach. These two contour-based approaches are based on matching between shape parts to compare. This matching process consists in establishing a robust registration between shape parts based on geodesics in the shape space. Thus, we exploit the registration residual to define a novel distance for shape part recognition. Later, for partial shape recognition, we describe a geodesics-based combining strategy with the same distance. As well, we propose to use the geodesics distance proposed for shape part recognition to define a global distance for entire shape recognition. Experiments are carried out on parts of shapes and entire shapes of theMPEG-7 database, then on parts issued from segmented real images. The obtained results demonstrate the effectiveness of our proposed recognition schemes. The proposed approaches are shown to significantly outperform previous works for classification and retrieval applications

La fabrication d'additive par arcs électriques (WAAM) est en train de devenir la principale technologie de Fabrication Additive (FA) utilisée pour produire des pièces à parois minces de taille moyenne à grande (Ordre de grandeur : 1 m) à un coût moindre. Pour fabriquer une pièce avec cette technologie, la stratégie de planification du trajet utilisée est la 2.5D. Cette stratégie consiste à découper un modèle 3D en différentes couches planes et parallèles les unes aux autres. L'utilisation de cette stratégie limite la complexité des topologies réalisables en WAAM, notamment celles présentant de grandes variations de courbure, et implique plusieurs départs/arrêt de l'arc lors de son passage d'une couche à l'autre. Ceci induit des phénomènes transitoires dans lesquels le contrôle de l'approvisionnement en énergie et en matière est complexe. Dans cette thèse, une nouvelle stratégie de fabrication visant à réduire au minimum les phases de démarrage et d'arrêt de l'arc est présentée. L'objectif de cette stratégie, appelée "Génération de Trajectoire Continue Tridimensionnelle" (GTCT), est de générer une trajectoire continue en forme de spirale pour des pièces minces en boucle fermée. Une vitesse de fil constante couplée à une vitesse de déplacement adaptative permet une modulation de la géométrie de dépôt qui assure un approvisionnement continu en énergie et en matière tout au long du processus de fabrication. L'utilisation de la stratégie 5 axes couplées à la GTCT permet la fabrication de pièces fermées avec une procédure pour déterminer la zone de fermeture optimale, et des pièces sur des substrats non-plans utiles pour ajouter des fonctionnalités à une structure existante. La fabrication de ces pièces avec la GTCT et plusieurs évaluations numériques ont montré la fiabilité de cette stratégie et sa capacité à produire de nouvelles formes complexes avec une bonne restitution géométrique, difficile ou impossible à atteindre aujourd'hui en 2.5D avec la technologie WAAM
Wire Arc Additive Manufacturing (WAAM) is becoming the primary Additive Manufacturing (AM) technology used to produce medium to large (order of magnitude: 1 m) thin-walled parts at lower cost. To manufacture a part with this technology, the path planning strategy used is 2.5D. This strategy consists in cutting a 3D model into different plane layers parallel to each other. The use of this strategy limits the complexity of the topologies achievable in WAAM, especially those with large variations in curvature. It also implies several start/stop of the arc during its passage from one layer to another, which induces transient phenomena in which the control of energy and material supply is complex. In this thesis, a new manufacturing strategy to reduce the arc start/stop phases to a single cycle is presented. The objective of this strategy, called "Continuous Three-dimensional Path Planning" (CTPP), is to generate a continuous spiral-shaped trajectory for thin parts in a closed loop. An adaptive wire speed coupled with a constant travel speed allows a modulation of the deposition geometry that ensures a continuous supply of energy and material throughout the manufacturing process. The use of the 5-axis strategy coupled with CTPP allows the manufacturing of closed parts with a procedure to determine the optimal closure zone and parts on non-planar substrates useful for adding functionality to an existing structure. Two geometries based on continuous manufacturing with WAAM technology are presented to validate this approach. The manufacturing of these parts with CTPP and several numerical evaluations have shown the reliability of this strategy and its ability to produce new complex shapes with good geometrical restitution, difficult or impossible to achieve today in 2.5D with WAAM technology

Cette thèse est divisée en deux parties. La première est consacrée à la méthode du barycentre, introduite en 1995 par G. Besson, G. Courtois et S. Gallot pour résoudre la conjecture de l'Entropie Minimale. Dans le Chapitre 1 nous décrivons ses développements les plus récents, notamment l'extension de cette méthode au cadre des variétés dont la courbure sectionnelle est de signe quelconque (voir les énoncés 1.2.1 et 1.4.1). Dans le Chapitre 2 et 3 nous présentons des résultats dans lesquels la méthode du barycentre joue un rôle important. Le problème “deux variétés dont les flots géodésiques sont conjugués sont-elles isométriques ?” (problème de la rigidité par conjugaison des flots) est le thème du Chapitre 2. Après avoir montré que deux telles variétés ont la même géométrie à grande échelle, on montre comment on peut utiliser ce résultat et la méthode du barycentre pour donner une nouvelle preuve de la rigidité (par conjugaison des flots) des variétés plates. Dans le Chapitre 3 nous utilisons la méthode du barycentre (en courbure de signe quelconque) et des inégalités de Sobolev itérées pour démontrer un théorème de comparaison entre les spectres de deux variétés riemanniennes (Y , g) et (X , g') de volumes proches, sachant qu'il existe une approximation de Gromov-Hausdorff de degré non nul entre ces deux variétés. Il s'agit d'un résultat d'approximation avec majoration de l'erreur d'approximation (et pas seulement d'un résultat de convergence). Remarquons qu'il n'est fait aucune autre hypothèse géométrique (et en particulier aucune hypothèse de courbure) sur la variété (Y , g), ce qui autorise un grand nombre de contre-exemples prouvant que le résultat est optimal. Dans la deuxième partie de la thèse (chapitre 4), on démontre un Lemme de Margulis sans hypothèse sur la courbure, qui s'applique aux variétés dont les groupes fondamentaux sont des produits libres (et qui ne possèdent pas d'élément de torsion d'ordre 2). Nous donnons également une borne inférieure de la systole des variétés dont le diamètre et l'entropie volumique sont majorés et dont le groupe fondamental est isomorphe à un produit libre sans torsion. Comme conséquences de ce dernier résultat nous obtenons des résultats de précompacité et de finitude topologique ou différentiable pour les variétés riemanniennes et une minoration de leur volume, tout ceci sans faire d'hypothèse de courbure
This Ph.D. Thesis is divided into two parts. In the first part we present the barycenter method, a technique which has been introduced by G. Besson, G. Courtois and S. Gallot in 1995, in order to solve the Minimal Entropy conjecture. In Chapter 1 we are interested in the more recent developments of this method, more precisely in the recent extension of the method to the case of manifolds having sectional curvature of variable sign. In Chapters 2 and 3 we shall present some new results whose proofs make use of the barycenter method. The Conjugacy Rigidity problem is the theme of Chapter 2. First we show a general result which provide a comparison between the large scale geometry of the Riemannian universal coverings of two compact manifolds whose geodesic flows are conjugates. Then we shall show how we can apply the latter result and the barycenter method in curvature of variable sign in order to give a new proof of the conjugacy rigidity of flat manifolds. In Chapter 3 we shall give a proof of a spectra comparison theorem for a compact Riemannian manifold which admits a Gromov-Hausdorff-approximation of non zero absolute degree on a fixed compact manifold (X,g') and which has volume almost smaller than the one of the reference manifold. The proof relies on the barycenter method in curvature of variable sign and on iterated Sobolev inequalities. We underline that it is an approximation result (and not just a convergence result) and that no curvature assumptions are made or inferred on (Y,g). The second part of the Thesis consists of a single chapter. In this chapter we prove a Margulis Lemma without curvature assumptions for Riemannian manifolds having decomposable 2-torsionless fundamental group. We shall give also a proof of a universal lower bound for the homotopy systole of compact Riemannian manifolds having bounded volume entropy and diameter, and decomposable torsionless fundamental group. As a consequence of the latter result we shall deduce a Precompactness and Finiteness theorem and a Volume estimate without curvature assumptions

碩士
國立成功大學
資訊工程學系碩博士班
90
Due to the fast development of three dimensional model in many fileds, like game, animation, network, mechanical engineering and entertainments, we believe that searching three dimensional models in database will become more important. A traditional searching method, keyword searching, is not a stable method. Because the classify standard of each people is different, it can’t satisfy our requirement in three dimensional retrieval. In two dimensional image retrieval, the problem is easier because only one information, color, in a image. But in three dimensional model retrieval problem, there isn’t a standard function which can evaluate similarity between two models. We use a matching method to evaluate similarity between two skeletal graphs of models, namely 2-pass axis-to-axis matching method. The method is like a jigsaw puzzle. We first use geodesic distance to establish a skeletal graph - Reeb graph. It can roughly represent the skeleton of model and invariant to translation, rotation, scaling. Then we match two Reeb graphs and evaluate similarity. When matching two Reeb graphs, a concept of matching significant node first is used. It is different to depth-first and width-first, and we will matching most significant node first. We don’t need to subdivide triangles of model by using modified fast marching method, and we can approximate the geodesic distance. Building Reeb graph by geodesic distance and evaluating similarity between two Reeb graph by using our 2-pass axis-to-axis matching method.

No
Both prominent feature points and geodesic distance are key factors for mesh segmentation. With these two factors, this paper proposes a graph cut based mesh segmentation method. The mesh is first preprocessed by Laplacian smoothing. According to the Gaussian curvature, candidate feature points are then selected by a predefined threshold. With DBSCAN (Density-Based Spatial Clustering of Application with Noise), the selected candidate points are separated into some clusters, and the points with the maximum curvature in every cluster are regarded as the final feature points. We label these feature points, and regard the faces in the mesh as nodes for graph cut. Our energy function is constructed by utilizing the ratio between the geodesic distance and the Euclidean distance of vertex pairs of the mesh. The final segmentation result is obtained by minimizing the energy function using graph cut. The proposed algorithm is pose-invariant and can robustly segment the mesh into different parts in line with the selected feature points.

碩士
國立臺灣海洋大學
資訊工程學系
99
Protein functions are highly correlated to structural conformation of biomolecular components, and especially some specific functions of proteins would be evoked by deforming the surface conformation to interact with other proteins. It is therefore important to identify the similarity and congruence between the original protein surface and its deformed conformation for protein structure-function analysis. Most existing structure comparison methods treat protein structures as rigid bodies. Though conventional approaches possessed translation and rotation invariant characteristics, the problems of deformed structures could not be correctly identified during surface comparison. To solve these dilemmas, this thesis proposes two local shape descriptors based on geodesic distance features which possess deformation invariant characteristics. The first descriptor is the Linear Geodesic Vector (LGV) obtained by taking average geodesic distances among the target residue and its sequentially neighboring residues, and the second descriptor is the Conformational Geodesic Adjacency Matrix (CGAM) formulated by calculating the geodesic distances among the target residue and its surface neighboring residues within a specified spatial radius. Each vector or matrix represents corresponding local shape characteristics of a protein surface and it can be adopted as a shape profile for efficient protein surface comparison. Values of scoring function and matrix correlation are computed for evaluating surface similarity between two proteins. In this thesis, we collected 401 protein structures from a 3D domain swapping dataset which was clustered into 32 groups, and each group of deformed proteins was trained for optimizing system default parameters. The results have shown that the deformed proteins could be correctly identified with an average rank of 1.13 and both of the sensitivity and precision rates achieved 92.7%. The hinge atlas dataset from MolMovDB was also applied to compare the performance of existing shape descriptors. As the results of comparison, the E-measure of proposed methods was 37.2% and outperformed all other descriptors. In addition, the proposed shape features and comparison methods can stably handle the phenomena of self-connection on surface or topological changes caused by serious shape deformation.

The present dissertation develops an invariant framework for 3D gesture comparison studies. 3D gesture comparison without Lagrangian models is challenging not only because of the lack of prediction provided by physics, but also because of a dual geometry representation, spatial dimensionality and non-linearity associated to 3D-kinematics. In 3D spaces, it is difficult to compare curves without an alignment operator since it is likely that discrete curves are not synchronized and do not share a common point in space. One has to assume that each and every single trajectory in the space is unique. The common answer is to assert the similitude between two or more trajectories as estimating an average distance error from the aligned curves, provided that the alignment operator is found. In order to avoid the alignment problem, the method uses differential geometry for position and orientation curves. Differential geometry not only reduces the spatial dimensionality but also achieves view invariance. However, the nonlinear signatures may be unbounded or singular. Yet, it is shown that pattern recognition between intrinsic signatures using correlations is robust for position and orientation alike. A new mapping for orientation sequences is introduced in order to treat quaternion and Euclidean intrinsic signatures alike. The new mapping projects a 4D-hyper-sphere for orientations onto a 3D-Euclidean volume. The projection uses the quaternion invariant distance to map rotation sequences into 3D-Euclidean curves. However, quaternion spaces are sectional discrete spaces. The significance is that continuous rotation functions can be only approximated for small angles. Rotation sequences with large angle variations can only be interpolated in discrete sections. The current dissertation introduces two multi-scale approaches that improve numerical stability and bound the signal energy content of the intrinsic signatures. The first is a multilevel least squares curve fitting method similar to Haar wavelet. The second is a geodesic distance anisotropic kernel filter. The methodology testing is carried out on 3D-gestures for obstetrics training. The study quantitatively assess the process of skill acquisition and transfer of manipulating obstetric forceps gestures. The results show that the multi-scale correlations with intrinsic signatures track and evaluate gesture differences between experts and trainees.