Dissertations / Theses on the topic 'Statistical shape modeling'

Nous présentons dans cette thèse un nouveau modèle statistique de forme et l'utilisons pour la segmentation d'images avec a priori. Ce modèle est représenté par un champ de Markov. Les noeuds du graphe correspondent aux points de contrôle situés sur le contour de la forme géométrique, et les arêtes du graphe représentent les dépendances entre les points de contrôle. La structure du champ de Markov est déterminée à partir d'un ensemble de formes, en utilisant des techniques d'apprentissage de variétés et de groupement non-supervisé. Les contraintes entre les points sont assurées par l'estimation des fonctions de densité de probabilité des longueurs de cordes normalisées. Dans une deuxième étape, nous construisons un algorithme de segmentation qui intègre le modèle statistique de forme, et qui le relie à l'image grâce à un terme région, à travers l'utilisation de diagrammes de Voronoi. Dans cette approche, un contour de forme déformable évolue vers l'objet à segmenter. Nous formulons aussi un algorithme de segmentation basé sur des détecteurs de points d'intérêt, où le terme de régularisation est lié à l'apriori de forme. Dans ce cas, on cherche à faire correspondre le modèle aux meilleurs points candidats extraits de l'image par le détecteur. L'optimisation pour les deux algorithmes est faite en utilisant des méthodes récentes et efficaces. Nous validons notre approche à travers plusieurs jeux de données en 2D et en 3D, pour des applications de vision par ordinateur ainsi que l'analyse d'images médicales.

La paralysie obstétricale du plexus brachial (POPB) est une paralysie du membre supérieur qui survient à la naissance et peut entraîner une déformation de l'articulation et un fonctionnement anormal de l'épaule. Bien que le traitement de la POPB tente de restaurer la fonction de l'épaule, la pathomécanique sous-jacente n'est pas encore clairement comprise. Les modèles computationnels sont efficaces pour fournir de telles informations, mais il n'existe aucun modèle d'articulation de l'épaule pédiatrique pour comprendre la POPB. Ainsi, ce travail de recherche a pour but de construire un framework combinant les avancées dans les domaines de la modélisation statistique de forme (MSF) et de la modélisation musculo-squelettique multi-corps (MCM). Due à l’insuffisance des données dans la cohorte pédiatrique, ce cadre a été mis en place pour l'articulation de l'épaule adulte. Pour cela, la précision de la MSF a été illustrée en prédisant 1) la forme de l'omoplate pré-morbide, et 2) les régions d'insertion musculaire sur l'omoplate et l'humérus. Cette méthode a ensuite été intégrée aux modèles MCM pour l'épaule adulte pour souligner l’importance des modèles spécifique-patient pour l’usage clinique. Pour le second objectif de cette thèse, j'ai développé un modèle MCM pédiatrique du complexe articulaire de l'épaule en utilisant le logiciel OpenSim. Grâce aux approches de cinématique et dynamique inverse, le modèle a permis de déterminer les différences de dynamique articulaires entre le côté sain et le côté pathologique. Les travaux futurs seront axés sur l’extension du travail réalisé pour la population pédiatrique afin de comprendre la pathomécanique de POPB
Obstetrician Brachial Plexus Palsy (OBPP) is a common birth injury in children leading to shoulder joint deformity and abnormal function. While the management of OBPP disorder focuses on restoring the shoulder joint function, the underlying pathomechanics is not clearly understood yet. Computational models are effective to provide such insights, however, there is no pediatric shoulder joint model to understand the OBPP disorder. Thus, the global aim of this research work was to build a computational framework combining the advances in statistical shape modeling (SSM) and multi-body musculoskeletal modeling (MSKM) domains. Due to a lack of sufficient data in the pediatric cohort, I first developed the framework for adult shoulder joint. For this, I illustrated the accuracy of SSM in predicting 1) missing part of the scapula, and 2) muscle insertion regions on scapula and humerus bones. This method was then integrated with adult shoulder MSKMs to show the differences between generic and subject specific constructs. For the second aim of this thesis, I developed a pediatric MSKM of the shoulder joint complex using OpenSim software. Pediatric MSKM represented scapulothoracic, sternoclavicular, acromioclavicular, and glenohumeral joints with 13 degrees of freedom, and actuated by 52 musculotendon actuators representing 14 shoulder muscles. Using inverse kinematics and inverse dynamics approaches, the model was used to determine the differences in joint kinematics, and joint dynamics between healthy and unhealthy side of a single OBPP subject. Future work is focused on completing the framework on pediatric population and understanding the pathomechanics of OBPP

Our motivation is to develop an automated technique for the segmentation of sub-cortical human brain structures from MR images. To this purpose, models of shape-and-appearance are constructed and fit to new image data. The statistical models are trained from 317 manually labelled T1-weighted MR images. Shape is modelled using a surface-based point distribution model (PDM) such that the shape space is constrained to the linear combination of the mean shape and eigenvectors of the vertex coordinates. In addition, to model intensity at the structural boundary, intensities are sampled along the surface normal from the underlying image. We propose a novel Bayesian appearance model whereby the relationship between shape and intensity are modelled via the conditional distribution of intensity given shape. Our fully probabilistic approach eliminates the need for arbitrary weightings between shape and intensity as well as for tuning parameters that specify the relative contribution between the use of shape constraints and intensity information. Leave-one-out cross-validation is used to validate the model and fitting for 17 structures. The PDM for shape requires surface parameterizations of the volumetric, manual labels such that vertices retain a one-to-one correspondence across the training subjects. Surface parameterizations with correspondence are generated through the use of deformable models under constraints that embed the correspondence criterion within the deformation process. A novel force that favours equal-area triangles throughout the mesh is introduced. The force adds stability to the mesh such that minimal smoothing or within-surface motion is required. The use of the PDM for segmentation across a series of subjects results in a set surfaces that retain point correspondence. The correspondence facilitates landmark-based shape analysis. Amongst other metrics, vertex-wise multivariate statistics and discriminant analysis are used to investigate local and global size and shape differences between groups. The model is fit, and shape analysis is applied to two clinical datasets.

Osteoporosis is the most common bone disease, with a significant morbidity and mortality caused by the increase of bone fragility and susceptibility to fracture. Dual Energy X-ray Absorptiometry (DXA) is the gold standard technique for osteoporosis and fracture risk evaluation at the spine. However, the standard analysis of DXA images only provides 2D measurements and does not differentiate between bone compartments; neither specifically assess bone density in the vertebral body, which is where most of the osteoporotic fractures occur. Quantitative Computed Tomography (QCT) is an alternative technique that overcomes limitations of DXA-based diagnosis. However, due to the high cost and radiation dose, QCT is not used for osteoporosis management. In this thesis, a method providing a 3D subject-specific shape and density estimation of the lumbar spine from a single anteroposterior DXA image is proposed. The method is based on a 3D statistical shape and density model built from a training set of QCT scans. The 3D subject-specific shape and density estimation is obtained by registering and fitting the statistical model onto the DXA image. Cortical and trabecular bone compartments are segmented using a model-based algorithm. 3D measurements are performed at different vertebral regions and bone compartments. The accuracy of the proposed methods is evaluated by comparing DXA-derived to QCT-derived 3D measurements. Two case-control studies are also performed: a retrospective study evaluating the ability of DXA-derived 3D measurements at lumbar spine to discriminate between osteoporosis-related vertebral fractures and control groups; and a study evaluating the association between DXA-derived 3D measurements at lumbar spine and osteoporosis-related hip fractures. In both studies, stronger associations are found between osteoporosis-related fractures and DXA-derived 3D measurements compared to standard 2D measurements. The technology developed within this thesis offers an insightful 3D analysis of the lumbar spine, which could potentially improve osteoporosis and fracture risk assessment in patients who had a standard DXA scan of the lumbar spine without any additional examination.
La osteoporosis es la enfermedad ósea más común, con una morbilidad y mortalidad significativas causadas por el aumento de la fragilidad ósea y la susceptibilidad a las fracturas. La absorciometría de rayos X de energía dual (DXA, por sus siglas en inglés) es la técnica de referencia para la evaluación de la osteoporosis y del riesgo de fracturas en la columna vertebral. Sin embargo, el análisis estándar de las imágenes DXA solo proporciona mediciones 2D y no diferencia entre los compartimentos óseos; tampoco evalúa la densidad ósea en el cuerpo vertebral, que es donde se producen la mayoría de las fracturas osteoporóticas. La tomografía computarizada cuantitativa (QCT, por sus siglas en inglés) es una técnica alternativa que supera las limitaciones del diagnóstico basado en DXA. Sin embargo, debido al alto costo y la dosis de radiación, la QCT no se usa para el diagnóstico de la osteoporosis. En esta tesis, se propone un método que proporciona una estimación personalizada de la forma 3D y la densidad de la columna vertebral en la zona lumbar a partir de una única imagen DXA anteroposterior. El método se basa en un modelo estadístico 3D de forma y densidad creado a partir de un conjunto de entrenamiento de exploraciones QCT. La estimación 3D personalizada de forma y densidad se obtiene al registrar y ajustar el modelo estadístico con la imagen DXA. Se segmentan los compartimentos óseos corticales y trabeculares utilizando un algoritmo basado en modelos. Se realizan mediciones 3D en diferentes regiones vertebrales y compartimentos óseos. La precisión de los métodos propuestos se evalúa comparando las mediciones 3D derivadas de DXA con las derivadas de QCT. También se realizan dos estudios de casos y controles: un estudio retrospectivo que evalúa la capacidad de las mediciones 3D derivadas de DXA en la columna lumbar para discriminar entre sujetos con fracturas vertebrales relacionadas con la osteoporosis y sujetos control; y un estudio que evalúa la asociación entre las mediciones 3D derivadas de DXA en la columna lumbar y las fracturas de cadera relacionadas con la osteoporosis. En ambos estudios, se encuentran asociaciones más fuertes entre las fracturas relacionadas con la osteoporosis y las mediciones 3D derivadas de DXA en comparación con las mediciones estándar 2D. La tecnología desarrollada dentro de esta tesis ofrece un análisis en 3D de la columna lumbar, que podría mejorar la evaluación de la osteoporosis y el riesgo de fractura en pacientes que se sometieron a una exploración DXA estándar de la columna lumbar sin ningún examen adicional.

This thesis is centered on the construction of a cardiac atlas to serve as a common reference frame in the Virtual Physiological Human (VPH). The construction covers the entire construction pipeline, starting from a set of 3D+t multislice computed tomography images, then performing a spatial normalization of these images, segmentation of the synthesized mean image, multi-structure meshing, and finally mapping of the mesh back to the population of images. In addition, two applications are presented in this thesis. First, the atlas is used to frame a spatio-temporal model of cardiac morphology which models the variability along both 'axes' simultaneously. Such a unified approach should be preferable over existing methods, which decouple the two sources of variation and then model them separately, in isolation. Second, the proposed atlas is applied to develop an acceleration technique for performing personalized simulation of cardiac electrophysiology (EP). The prior knowledge encapsulated in our atlas is used, in conjunction with a numerical solver of cardiac EP, to build a statistical model linking cardiac morphology with the steady states of myocardial cell models that pre condition detailed cardiac EP simulations. This application puts the proposed dynamic cardiac atlas in the context of VPH-related simulations, of which the computational costs are currently greatly in excess of what is acceptable for their adoption in current clinical practice.
Esta tesis está centrada en la construcción de un atlas cardiaco, para servir como marco común de referencia en el Virtual Physiological Human (VPH). La construcción consiste en la trayectoria completa, empezando con un conjunto de imágenes 3D+t de tomografía computacional multi-corte, y entonces hacer una normalización espacial de las imágenes, segmentación de la imagen promedio sintetizada, un mallado multi-estructura, y finalmente la transformación de la malla a la población de imágenes. Adicionalmente, la tesis presenta dos aplicaciones del atlas. Primero, el atlas se usa para enmarcar un modelo espacio-temporal de la morfología cardiaca que modela la variación a lo largo de ambos 'ejes' simultáneamente. Tal propuesta debe ser preferible sobre otros m\'etodos existentes, los cuales desacoplan las dos fuentes de variación para modelarlas separadamente, en isolación. Segundo, el atlas está aplicado al desarrollo de una técnica de aceleración para simulaciones personalizadas de electrofisiología (EF) cardiaca. El conocimiento previo encapsulado en nuestro atlas se usa, en conjunto con un solver de EF cardiaca, para construir un modelo estadístico conectando morfología cardiaca con los steady states de modelos celulares del miocardio que precondicionan a simulaciones detalladas de EF cardiaca. Esta aplicación posiciona el propuesto atlas dinámico cardiaco en el contexto de simulaciones relacionadas al VPH, cuyo costo computacional actual está en gran exceso de lo aceptable para su adopción en la práctica clínica de hoy en día.

Statistical Shape Models (SSM) have wide applications in image segmentation, surface registration and morphometry. This thesis deals with an important issue in SSM, which is establishing correspondence between a set of shape surfaces on either 2D or 3D. Current methods involve either manual annotation of the data (current ‘gold standard’); or establishing correspondences by using segmentation or registration algorithms; or using an information technique, Minimum Description Length (MDL), as an objective function that measures the utility of a model (the state-of-the-art). This thesis presents in principle another framework for establishing correspondences completely automatically by treating it as a learning process. Shannon theory is used extensively to develop an objective function, which measures the performance of a model along each eigenvector direction, and a proper weighting is automatically calculated for each energy component. Correspondence finding can then be treated as optimizing the objective function. An efficient optimization method is also incorporated by deriving the gradient of the cost function. Experimental results on various data are presented on both 2D and 3D. In the end, a quantitative evaluation between the proposed algorithm and MDL shows that the proposed model has better Generalization Ability, Specificity and similar Compactness. It also shows a good potential ability to solve the so-called “Pile Up” problem that exists in MDL. In terms of application, I used the proposed algorithm to help build a facial contour classifier. First, correspondence points across facial contours are found automatically and classifiers are trained by using the correspondence points found by the MDL, proposed method and direct human observer. These classification schemes are then used to perform gender prediction on facial contours. The final conclusion for the experiments is that MEM found correspondence points built classification scheme conveys a relatively more accurate gender prediction result. Although, we have explored the potential of our proposed method to some extent, this is not the end of the research for this topic. The future work is also clearly stated which includes more validations on various 3D datasets; discrimination analysis between normal and abnormal subjects could be the direct application for the proposed algorithm, extension to model-building using appearance information, etc.

Les différentes étapes et processus de la fabrication additive (FA) induisent des erreurs de sources multiples et complexes qui soulèvent des problèmes majeurs au niveau de la qualité géométrique du produit fabriqué. Par conséquent, une modélisation effective des écarts géométriques est essentielle pour la FA. Le paradigme Skin Model Shapes (SMS) offre un cadre intégral pour la modélisation des écarts géométriques des produits manufacturés et constitue ainsi une solution efficace pour la modélisation des écarts géométriques en FA.Dans cette thèse, compte tenu de la spécificité de fabrication par couche en FA, un nouveau cadre de modélisation à base de SMS est proposé pour caractériser les écarts géométriques en FA en combinant une approche dans le plan et une approche hors plan. La modélisation des écarts dans le plan vise à capturer la variabilité de la forme 2D de chaque couche. Une méthode de transformation des formes est proposée et qui consiste à représenter les effets de variations sous la forme de transformations affines appliquées à la forme nominale. Un modèle paramétrique des écarts est alors établi dans un système de coordonnées polaires, quelle que soit la complexité de la forme. Ce modèle est par la suite enrichi par un apprentissage statistique permettant la collecte simultanée de données des écarts de formes multiples et l'amélioration des performances de la méthode.La modélisation des écarts hors plan est réalisée par la déformation de la couche dans la direction de fabrication. La modélisation des écarts hors plan est effectuée à l'aide d'une méthode orientée données. Sur la base des données des écarts obtenues à partir de simulations par éléments finis, deux méthodes d'analyse modale: la transformée en cosinus discrète (DCT) et l'analyse statistique des formes (SSA) sont exploitées. De plus, les effets des paramètres des pièces et des procédés sur les modes identifiés sont caractérisés par le biais d'un modèle à base de processus Gaussien.Les méthodes présentées sont finalement utilisées pour obtenir des SMSs haute-fidélité pour la fabrication additive en déformant les contours de la couche nominale avec les écarts prédits et en reconstruisant le modèle de surface non idéale complet à partir de ces contours déformés. Une toolbox est développée dans l'environnement MATLAB pour démontrer l'efficacité des méthodes proposées
The intricate error sources within different stages of the Additive Manufacturing (AM) process have brought about major issues regarding the dimensional and geometrical accuracy of the manufactured product. Therefore, effective modeling of the geometric deviations is critical for AM. The Skin Model Shapes (SMS) paradigm offers a comprehensive framework aiming at addressing the deviation modeling problem at different stages of product lifecycle, and is thus a promising solution for deviation modeling in AM. In this thesis, considering the layer-wise characteristic of AM, a new SMS framework is proposed which characterizes the deviations in AM with in-plane and out-of-plane perspectives. The modeling of in-plane deviation aims at capturing the variability of the 2D shape of each layer. A shape transformation perspective is proposed which maps the variational effects of deviation sources into affine transformations of the nominal shape. With this assumption, a parametric deviation model is established based on the Polar Coordinate System which manages to capture deviation patterns regardless of the shape complexity. This model is further enhanced with a statistical learning capability to simultaneously learn from deviation data of multiple shapes and improve the performance on all shapes.Out-of-plane deviation is defined as the deformation of layer in the build direction. A layer-level investigation of out-of-plane deviation is conducted with a data-driven method. Based on the deviation data collected from a number of Finite Element simulations, two modal analysis methods, Discrete Cosine Transform (DCT) and Statistical Shape Analysis (SSA), are adopted to identify the most significant deviation modes in the layer-wise data. The effect of part and process parameters on the identified modes is further characterized with a Gaussian Process (GP) model. The discussed methods are finally used to obtain high-fidelity SMSs of AM products by deforming the nominal layer contours with predicted deviations and rebuilding the complete non-ideal surface model from the deformed contours. A toolbox is developed in the MATLAB environment to demonstrate the effectiveness of the proposed methods

This thesis considers the registration of shapes, estimation of shape variability and the statistical modelling of human brain magnetic resonance images (MRI). Current shape registration techniques, such as Procrustes analysis, superimpose shapes in order to make inferences regarding the mean shape and shape variability. We apply Procrustes analysis to a subset of the landmarks and give distributional results for the Euclidean distance of a shape from a template. Procrustes analysis is then generalised to minimise a Mahalanobis norm, with respect to a symmetric, positive denite matrix, and the weighted Procrustes estimators for scaling, rotation and translation obtained. This weighted registration criterion is shown, through a simulation study, to reduce the bias and error in maximum likelihood estimates of the mean shape and covariance matrix compared to isotropic Procrustes. A Bayesian Markov chain Monte Carlo algorithm is also presented and shown to be less sensitive to prior information. We consider two MRI data sets in detail. We examine the first data set for large-scale shape dierences between two volunteer groups, healthy controls and schizophrenia patients. The images are registered to a template through modelling the voxel values and we maximise the likelihood over the transformation parameters. Using a suitable labelling and principal components analysis we show schizophrenia patients have less brain asymmetry than healthy controls. The second data set is a sequence of functional MRI scans of an individual's motor cortex taken while they repeatedly press a button. We construct a model with temporal correlations to estimate the trial-to-trial variability in the haemodynamic response using the Expectation-Maximisation algorithm. The response is shown to change with task and through time. For both data sets we compare our techniques with existing software packages and improvements to data pre-processing are suggested. We conclude by discussing potential areas for future research.

The shoulder joint is the most mobile and unstable joint in the human body. This makes it vulnerable to soft tissue pathologies and dislocation. Insight into the kinematics of the joint may enable improved diagnosis and treatment of different shoulder pathologies. Shoulder joint kinematics can be influenced by the articular geometry of the joint. The aim of this project was to develop an analysis framework for shoulder joint kinematics via the use of articulated statistical shape models (ASSMs). Articulated statistical shape models extend conventional statistical shape models by combining the shape variability of anatomical objects collected from different subjects (statistical shape models), with the physical variation of pose between the same objects (articulation). The developed pipeline involved manual annotation of anatomical landmarks selected on 3D surface meshes of scapulae and humeri and establishing dense surface correspondence across these data through a registration process. The registration was performed using a Gaussian process morphable model fitting approach. In order to register two objects separately, while keeping their shape and kinematics relationship intact, one of the objects (scapula) was fixed leaving the other (humerus) to be mobile. All the pairs of registered humeri and scapulae were brought back to their native imaged position using the inverse of the associated registration transformation. The glenohumeral rotational center and local anatomic coordinate system of the humeri and scapulae were determined using the definitions suggested by the International Society of Biomechanics. Three motions (flexion, abduction, and internal rotation) were generated using Euler angle sequences. The ASSM of the model was built using principal component analysis and validated. The validation results show that the model adequately estimated the shape and pose encoded in the training data. Developing ASSM of the shoulder joint helps to define the statistical shape and pose parameters of the gleno humeral articulating surfaces. An ASSM of the shoulder joint has potential applications in the analysis and investigation of population-wide joint posture variation and kinematics. Such analyses may include determining and quantifying abnormal articulation of the joint based on the range of motion; understanding of detailed glenohumeral joint function and internal joint measurement; and diagnosis of shoulder pathologies. Future work will involve developing a protocol for encoding the shoulder ASSM with real, rather than handcrafted, pose variation.

The femur is the longest bone in the human body and serves the important purposes of load-bearing and allowing bipedal locomotion. Accurate modelling of the variation in shape within the healthy adult population can be useful for a variety of applications: from the mere anatomical description of its features, in order to better understand its function, to more complex tasks such as pathology detection or surgical planning. Statistical Shape Modelling (SSM) is a well-established technique that enables to capture the variability within a set of training shapes and describes it with a reduced set of variables. The aim of this thesis is to evaluate the performance of a SSM based on a point cloud representation of shape, and introduce and test subsequent improvements to the modelling process that can increase its clinical relevance and scope of application. The standard approach to SSM employs a dimension-reducing technique, generally by means of Principal Component Analysis (PCA). However, this approach favours the compactness of the model, thus not focusing on other aspects that may be more relevant to clinical practice. Although rotation of the principal components is commonly performed as a post-processing step in statistical analysis involving PCA, it is not routinely applied in SSM. By applying this class of rotation, the components' effects are more localised, allowing a better interpretation, understanding and classification of pathological deformities. Among other possible representations, the Medial Axis Transform (MAT) could offer a further insight into shape modelling, since it allows the information about thickness to be decoupled from the rest of the shape. SSMs based on this representation can lead to a di erent perspective on the understanding of femoral anatomy and function,and can also enable the reconstruction of the complete anatomy starting from a reduced set of features, with diverse applications in the elds of surgical planning, forensic science and paleontology.

A Statistical Shape Model (SSM) is a statistical representation of a shape obtained from data to study variation in shapes. Work on shape modelling is constrained by many unsolved problems, for instance, difficulties in modelling local versus global variation. SSM have been successfully applied in medical image applications such as the analysis of brain anatomy. Since brain structure is so complex and varies across subjects, methods to identify morphological variability can be useful for diagnosis and treatment. The main objective of this research is to generate and develop a statistical shape model to analyse local variation in shapes. Within this particular context, this work addresses the question of what are the local elements that need to be identified for effective shape analysis. Here, the proposed method is based on a Point Distribution Model and uses a combination of other well known techniques: Fractal analysis; Markov Chain Monte Carlo methods; and the Curvature Scale Space representation for the problem of contour localisation. Similarly, Diffusion Maps are employed as a spectral shape clustering tool to identify sets of local partitions useful in the shape analysis. Additionally, a novel Hierarchical Shape Analysis method based on the Gaussian and Laplacian pyramids is explained and used to compare the featured Local Shape Model. Experimental results on a number of real contours such as animal, leaf and brain white matter outlines have been shown to demonstrate the effectiveness of the proposed model. These results show that local shape models are efficient in modelling the statistical variation of shape of biological structures. Particularly, the development of this model provides an approach to the analysis of brain images and brain morphometrics. Likewise, the model can be adapted to the problem of content based image retrieval, where global and local shape similarity needs to be measured.

La modélisation géométrique a été l'un des sujets les plus étudiés pour la représentation des structures anatomiques dans le domaine médical. Aujourd'hui, il n'y a toujours pas de méthode bien établie pour modéliser la forme d'un organe. Cependant, il y a plusieurs types d'approches disponibles et chaque approche a ses forces et ses faiblesses. La plupart des méthodes de pointe utilisent uniquement l'information surfacique mais un besoin croissant de modéliser l'information volumique des objets apparaît. En plus de la description géométrique, il faut pouvoir différencier les objets d'une population selon leur forme. Cela nécessite de disposer des statistiques sur la forme dans organe dans une population donné. Dans ce travail de thèse, on utilise une représentation capable de modéliser les caractéristiques surfaciques et internes d'un objet. La représentation choisie (s-rep) a en plus l'avantage de permettre de déterminer les statistiques de forme pour une population d'objets. En s'appuyant sur cette représentation, une procédure pour modéliser le cortex cérébral humain est proposée. Cette nouvelle modélisation offre de nouvelles possibilités pour analyser les lésions corticales et calculer des statistiques de forme sur le cortex. La deuxième partie de ce travail propose une méthodologie pour décrire de manière paramétrique l'intérieur d'un objet. La méthode est flexible et peut améliorer l'aspect visuel ou la description des propriétés physiques d'un objet. La modélisation géométrique enrichie avec des paramètres physiques volumiques est utilisée pour la simulation d'image par résonance magnétique pour produire des simulations plus réalistes. Cette approche de simulation d'images est validée en analysant le comportement et les performances des méthodes de segmentations classiquement utilisées pour traiter des images réelles du cerveau
Geometric modeling has been one of the most researched areas in the medical domain. Today, there is not a well established methodology to model the shape of an organ. There are many approaches available and each one of them have different strengths and weaknesses. Most state of the art methods to model shape use surface information only. There is an increasing need for techniques to support volumetric information. Besides shape characterization, a technique to differentiate objects by shape is needed. This requires computing statistics on shape. The current challenge of research in life sciences is to create models to represent the surface, the interior of an object, and give statistical differences based on shape. In this work, we use a technique for shape modeling that is able to model surface and internal features, and is suited to compute shape statistics. Using this technique (s-rep), a procedure to model the human cerebral cortex is proposed. This novel representation offers new possibilities to analyze cortical lesions and compute shape statistics on the cortex. The second part of this work proposes a methodology to parameterize the interior of an object. The method is flexible and can enhance the visual aspect or the description of physical properties of an object. The geometric modeling enhanced with physical parameters is used to produce simulated magnetic resonance images. This image simulation approach is validated by analyzing the behavior and performance of classic segmentation algorithms for real images

Ce travail présente un cadre générique pour la construction de maillages isogéométriques volumiques à partir d'une géométrie complexe avec une topologie arbitraire pour des applications relatives aux modèles d'ordres réduits. En effet, les maillages structurés tels que les maillages isogéométriques ou hexahédriques sont difficiles à obtenir de manière automatique. Les analyses statistiques de formes et les modèles d'ordres réduits nécessitent des données structurées et ordonnées pour être construits efficacement. Pour ce faire, nous utilisons les limites du modèle solide triangulé, la B-Rep CAD (Boundary Representation in Computer Aided Design). Tout d'abord, cette thèse inclut une intégration d'un algorithme de décomposition en pantalons et en cuboïdes prenant en compte les caractéristiques géométriques. La décomposition en cuboïdes divise une surface en un ensemble de patchs quadrilatéraux qui peuvent aider à définir un volume associé. Des champs de croix (cross fields), c'est-à-dire des champs de directions à 4 symétries, sont utilisés pour guider une paramétrisation globale alignée de la surface. Ce paramétrage est optimisé afin de minimiser la distorsion des éléments. Le processus d'optimisation est pensé pour concevoir des champs de croix avec des contraintes topologiques et géométriques. En utilisant la décomposition optimisée en cuboïdes, une structure volumétrique est extraite. Sur la base de la paramétrisation globale et de la structure volumétrique précédemment calculée, une paramétrisation isogéométrique trivariée est déduite. Les propriétés topologiques invariantes sont analysées tout au long du processus proposé. Pour finir, pour différentes occurrences géométriques de même topologie mais possédant des géométries différentes, notre méthode permet d'avoir la même représentation : des maillages isotopologiques isogéométriques trivariés détenant la même connectivité. L'efficacité et la robustesse de l'approche proposée sont illustrées par plusieurs exemples de modèles d'ordres réduits en utilisant l'IGA (IsoGeometric Analysis)
This work presents a generic framework to construct trivariate isogeometric meshes of complicated geometry and arbitrary topology required for reduced order model applications. Indeed, structured meshes such as isogeometric or pure hexahedral ones are difficult to obtain in an automatic manner. Statistical shape analysis and reduced order modeling require structured and ordered data to be efficient. For that purpose, we use the triangulated solid 3D model's boundary provided from B-Rep CAD (Boundary-Representation in Computer Aided Design) models. Firstable, the workflow includes an integration of a geometry-feature-aware pants-to-cuboids decomposition algorithm. The input triangulated mesh is decomposed into a set of cuboids in two steps: pants decomposition and cuboid decomposition. Cuboid decomposition splits a surface into a set of quadrilateral patches which can define a volumetric layout of the associated boundary surface. Cross fields, i.e., 4-symmetry direction fields are used to guide a surface aligned global parameterization. Optimizing this parameterization, patches of the quadrilateral layout inherited from the cuboid decomposition are re-positioned on the surface in a way to achieve low overall distortion. The optimization process is thought to design cross fields with topological and geometrical constraints. Using the optimized cuboid decomposition, a volumetric layout is extracted. Based on the global parameterization and the structured volumetric layout previously computed, a trivariate isogeometric parameterization is deducted. Learning generalized forms of theorems in the topology field, invariant topological properties are analyzed throughout the proposed process. To finish, for different geometrical instances with the same topology but different geometries, our method allows to have the same representation: trivariate isogeometric isotopological meshes holding the same connectivity. The efficiency and the robustness of the proposed approach are illustrated through several examples of reduced order models using IGA (IsoGeometric Analysis)

The accuracy of modern digital human models has led to the development of human simulation engines capable of performing a complex analysis of the biometrics and kinematics / dynamics of a digital model. While the capabilities of these simulations have seen much progress in recent years, they are hindered by a fundamental limitation regarding the diversity of the models compatible with the simulation engine, which in turn results in a reduction in the scope of the applications available to the simulation. This is typically due to the necessary implementation of a musculoskeletal structure within the model, as well as the inherent mass and inertial data that accompany it. As a result a significant amount of time and expertise is required to make a digital human model compatible with the simulation. In this research I present a solution to this limitation by outlining a process to develop a set of mutually compatible human models that spans the range of feasible body shapes and allows for a “free” exploration of body shape within the shape manifold. Additionally, a method is presented to represent the human body shapes with a reduction of dimensionality, via a spectral shape descriptor, that enables a statistical analysis that is both more computationally efficient and anthropometrically accurate than traditional methods. This statistical analysis is then used to develop a set of representative models that succinctly represent the full scope of human body shapes across the population, with applications reaching beyond the research-oriented simulations into commercial human-centered product design and digital modeling.

Thesis (M. S.)--Aerospace Engineering, Georgia Institute of Technology, 2008.
Committee Chair: Eric N. Johnson; Committee Co-Chair: Allen R. Tannenbaum; Committee Member: Anthony J. Calise; Committee Member: Eric Feron; Committee Member: Patricio A. Vela.

Modern competitive market demands frequent change in product variety, increased production volume and shorten product/process change over time. These market requirements point towards development of key enabling technologies (KETs) to shorten product and process development cycle, improved production quality and reduced time-to-launch. One of the critical prerequisite to develop the aforementioned KETs is efficient and accurate modelling of product and process dimensional errors. It is especially critical for assembly processes with compliant parts as used in automotive body, appliance or wing and fuselage assemblies. Currently, the assembly process is designed under the assumption of ideal (nominal) products and then check by using variation simulation analysis (VSA). However, the VSA simulations are oversimplified as they are unable to accurately model or predict the effects of geometric and dimensional variations of compliant parts, as well as variations of key characteristics related to fixturing and joining process. This results in product failures and/or reduced quality due to un-modelled interactions in assembly process. Therefore, modelling and prediction of the geometric shape errors of complex sheet metal parts are of tremendous importance for many industrial applications. Further, as production yield and product quality are determined for production volume of real parts, thus not only shape errors but also shape variation model is required for robust assembly system development. Currently, parts shape variation can be measured during production by using recently introduced non-contact gauges which are fast, in-line and can capture entire part surface information. However, current applications of non-contact scanners are limited to single part inspection or reverse engineering applications and cannot be used for monitoring and statistical process control of shape variation. Further, the product shape variation can be reduced through appropriate assembly fixture design. Current approaches for assembly fixture design seldom consider shape variation of production parts during assembly process which result in poor quality and yield. To address the aforementioned challenges, this thesis proposes the following two enablers focused on modelling of shape errors and shape variation of compliant parts applicable during assembly process design phase as well as production phase: (i) modelling and characterisation of shape errors of individual compliant part with capabilities to quantify fabrication errors at part level; and (ii) modelling and characterisation of shape variation of a batch of compliant parts with capabilities to quantify the shape variation at production level. The first enabler focuses on shape errors modelling and characterisation which includes developing a functional data analysis model for identification and characterisation of real part shape errors that can link design (CAD model) with manufacturing (shape errors). A new functional data analysis model, named Geometric Modal Analysis (GMA), is proposed to extract dominant shape error xixmodes from the fabricated part measurement data. This model is used to decompose shape errors of 3D sheet metal part into orthogonal shape error modes which can be used for product and process interactions. Further, the enabler can be used for statistical process control to monitor shape quality; fabrication process mapping and diagnosis; geometric dimensioning and tolerancing simulation with free form shape errors; or compact storage of shape information. The second enabler aims to model and characterise shape variation of a batch of compliant parts by extending the GMA approach. The developed functional model called Statistical Geometric Modal Analysis (SGMA) represents the statistical shape variation through modal characteristics and quantifies shape variation of a batch of sheet metal parts a single or a few composite parts. The composite part(s) represent major error modes induced by the production process. The SGMA model, further, can be utilised for assembly fixture optimisation, tolerance analysis and synthesis. Further, these two enablers can be applied for monitoring and reduction of shape variation from assembly process by developing: (a) efficient statistical process control technique (based on enabler ‘i’) to monitor part shape variation utilising the surface information captured using non-contact scanners; and (b) efficient assembly fixture layout optimisation technique (based on enabler ‘ii’) to obtain improved quality products considering shape variation of production parts. Therefore, this thesis proposes the following two applications: The first application focuses on statistical process control of part shape variation using surface data captured by in-process or off-line scanners as Cloud-of-Points (CoPs). The methodology involves obtaining reduced set of statistically uncorrelated and independent variables from CoPs (utilising GMA method) which are then used to develop integrated single bivariate T2-Q monitoring chart. The joint probability density estimation using non-parametric Kernel Density Estimator (KDE) has enhanced sensitivity to detect part shape variation. The control chart helps speedy detection of part shape errors including global or local shape defects. The second application determines optimal fixture layout considering production batch of compliant sheet metal parts. Fixtures control the position and orientation of parts in an assembly process and thus significantly contribute to process capability that determines production yield and product quality. A new approach is proposed to improve the probability of joining feasibility index by determining an N-2-1 fixture layout optimised for a production batch. The SGMA method has been utilised for fixture layout optimisation considering a batch of compliant sheet metal parts. All the above developed methodologies have been validated and verified with industrial case studies of automotive sheet metal door assembly process. Further, they are compared with state-of-the-art methodologies to highlight the boarder impact of the research work to meet the increasing market requirements such as improved in-line quality and increased productivity.

The shape of particles is known to play an important role in soil behaviour, with significant effects of engineering responses. Investigating how the shape of particles can be measured and quantified is therefore considered increasingly important in modern soil mechanics. This is propelled by the advent of computer based image-analyses and discrete modelling algorithms, which have opened new ways to tackle this problem. This work demonstrates how these two techniques can be made to work together. Image analyses are performed on x-rays micro-tomographs (µ-CT) of triaxial sand specimens, focusing on the characterisation and quantification of particle shapes. Two with very different particle shape sands are studied in details: Caicos ooids (rounded) and Hostun sand (angular). A discrete Digital Volume Correlation (DVC) algorithm is then used to track the kinematics of individual grains (around 50000 for each sand specimen) during the triaxial test and measure, with good precision, their cumulated displacements and rotations. Joint analysis of the shape and kinematic databases acquired is performed to find how particle shape descriptors are related to observed kinematics at the microscale level. It appears that true sphericity is a good predictor of upper bound rotational restraint. Modelling is based on the Discrete Element Method (DEM). Models that introduce rolling resistance at the contact are widely employed in DEM simulations, these approaches offer substantial computational benefits at the prize of increased calibration complexity. In this work, the values of true sphericity obtained by image analysis of the grains, either directly by 3D acquisition or by correlation with simpler to obtain 2D shape measures, are used to establish mechanically equivalent rotational restrictions. An empirical relation between a contact parameter (rolling friction) and a 3D grain shape descriptor (true sphericity is first calibrated - using both specimen-scale and grain scale results from two triaxial tests in Hostun sand and Caicos ooids. It is then validated by simulating other triaxial tests (1) with the same sands, but in different conditions (2) with Ottawa sand, for which 3D grain images were also available for examination, and (3) with Ticino sand, for which only 2D grain images were available. Finally, results of large-scale DEM simulations on the Cone Penetration Test (CPT) - exploiting the new proposed contact model - are presented. Experimental data on the CPT performed in a Calibration Chamber (CC) comprised of Ticino sand are successfully fitted by the numerical penetration curves at different confining pressures and conditions. A parametric study about the influence of particle shape and particle shape variability put in evidence the strong-coupled effects of rolling and frictional resistances at the particles contacts. The work described in this thesis will ease the use of DEM for large-scale simulations of geotechnical engineering problems.
Se sabe que la forma de las partículas juega un papel importante en el comportamiento del suelo, con efectos significativos de las respuestas mecánicas relevantes en ingeniería geotécnica. Por lo tanto, investigar cómo se puede medir y cuantificar la forma de las partículas se considera cada vez más importante en la mecánica del suelo moderna. Esto se acrecienta debido a las técnicas de análisis computacionales de imágenes y algoritmos de modelado discreto (DEM), que han abierto nuevas formas de abordar este problema. Este trabajo demuestra cómo se pueden hacer que estas dos técnicas funcionen juntas. Los análisis de imagen se realizan sobre micro-tomografías de rayos X (µ-CT) de muestras de arena en celdas triaxiales, centrándose en la caracterización y cuantificación de la forma de las partículas. Se estudian en detalle dos arenas con la forma de sus partículas muy diferentes: Caicos ooids (redondeados) y Hostun sand (angular). Luego se utiliza un algoritmo discreto de correlación de volumen digital (DVC) para rastrear la cinemática de granos individuales (alrededor de 50000 por cada muestra de arena) durante la prueba triaxial y medir, con buena precisión, sus desplazamientos y rotaciones acumulados. El análisis conjunto de la forma y las bases de datos cinemáticas adquiridas se realiza para encontrar cómo los descriptores de forma de partículas se relacionan con la cinemática observada a nivel de micro-escala. Resulta que la esfericidad verdadera predice bien el límite superior de rotación de una partícula. La modelización numérica se basa en el Método de Elementos Discretos (DEM). Los modelos que introducen resistencia a la rotación en el contacto se emplean ampliamente en simulaciones DEM, estos enfoques ofrecen beneficios computacionales sustanciales a costa de una mayor complejidad de calibración. En este trabajo, los valores de esfericidad verdadera (i.e., true sphericity) obtenidos mediante análisis de imagen de los granos, ya sea directamente por adquisición 3D o por correlación con medidas de forma 2D más simples, se utilizan para establecer restricciones de rotación mecánicamente equivalentes. Una relación empírica entre un parámetro de contacto (rolling friction) y un descriptor de forma de grano 3D (la esfericidad verdadera) se calibra primero, utilizando los resultados de la escala de muestras y de la escala de granos de dos pruebas triaxiales en las arenas de Hostun y de Caicos. Luego se valida simulando otras pruebas triaxiales (1) con las mismas arenas, pero en diferentes condiciones (2) con arena de Ottawa, para la que también estaban disponibles imágenes 3D de granos para su examen, y (3) con arena de Ticino, para la cual solo estaban disponibles imágenes 2D de los granos. Finalmente, se presentan resultados de simulaciones DEM a gran escala de la prueba de penetración de cono (CPT), aprovechando el nuevo modelo de contacto propuesto. Los datos experimentales del CPT realizado en una cámara de calibración (CC) sobre arena de Ticino se ajustan con éxito por las curvas de penetración numérica a diferentes presiones y condiciones de confinamiento. Un estudio paramétrico sobre la influencia de la forma de las partículas y la variabilidad de las formas de las partículas puso de manifiesto los efectos fuertemente acoplados de las resistencias rotacional y friccional en los contactos entre partículas. El trabajo descrito en esta tesis facilitará el uso de DEM para simulaciones a gran escala en problemas de ingeniería geotécnica.

Statistical modelling has become a ubiquitous tool for analysing of morphological variation of bone structures in medical images. For radiological images, the shape, relative pose between the bone structures and the intensity distribution are key features often modelled separately. A wide range of research has reported methods that incorporate these features as priors for machine learning purposes. Statistical shape, appearance (intensity profile in images) and pose models are popular priors to explain variability across a sample population of rigid structures. However, a principled and robust way to combine shape, pose and intensity features has been elusive for four main reasons: 1) heterogeneity of the data (data with linear and non-linear natural variation across features); 2) sub-optimal representation of three-dimensional Euclidean motion; 3) artificial discretization of the models; and 4) lack of an efficient transfer learning process to project observations into the latent space. This work proposes a novel statistical modelling framework for multiple bone structures. The framework provides a latent space embedding shape, pose and intensity in a continuous domain allowing for new approaches to skeletal joint analysis from medical images. First, a robust registration method for multi-volumetric shapes is described. Both sampling and parametric based registration algorithms are proposed, which allow the establishment of dense correspondence across volumetric shapes (such as tetrahedral meshes) while preserving the spatial relationship between them. Next, the framework for developing statistical shape-kinematics models from in-correspondence multi-volumetric shapes embedding image intensity distribution, is presented. The framework incorporates principal geodesic analysis and a non-linear metric for modelling the spatial orientation of the structures. More importantly, as all the features are in a joint statistical space and in a continuous domain; this permits on-demand marginalisation to a region or feature of interest without training separate models. Thereafter, an automated prediction of the structures in images is facilitated by a model-fitting method leveraging the models as priors in a Markov chain Monte Carlo approach. The framework is validated using controlled experimental data and the results demonstrate superior performance in comparison with state-of-the-art methods. Finally, the application of the framework for analysing computed tomography images is presented. The analyses include estimation of shape, kinematic and intensity profiles of bone structures in the shoulder and hip joints. For both these datasets, the framework is demonstrated for segmentation, registration and reconstruction, including the recovery of patient-specific intensity profile. The presented framework realises a new paradigm in modelling multi-object shape structures, allowing for probabilistic modelling of not only shape, but also relative pose and intensity as well as the correlations that exist between them. Future work will aim to optimise the framework for clinical use in medical image analysis.

Laser technologies have made distinguished contributions to modern industry. These have typically been realised through the important role played by lasers in the advancement of manufacturing technology in many areas such as welding, which has become an important joining technique and thus promoted the use of lasers in a wide variety of applications in the oil, gas, aerospace, aircraft, automotive, electronics and medical industries. A detailed review of previous work in the use of lasers for advanced manufacturing, and in particular, laser beam welding is given. The work reported in this thesis aims to develop a new method of laser welding. This is connected with investigations relating to the production of net shape welds for bead-on-plate welding and butt welding of mild steel plates. Based on the nature of its operation, use of a fibre laser was considered most suitable compared to other solid state lasers. Net-shape welds were demonstrated on mild steel plates using an IPG 1 kW single mode fibre laser with a maximum power output of 1000 W.The thesis shows results from experimental and modelling (based on finite element and computational fluid dynamic modelling) to validate the idea and the understanding of underlying scientific principles. The thesis is presented in the form of a collection of published work generated by the author during the course of this project. In addition, some results that are not yet published are also included. Design of experiments and statistical modelling has been used in the experimental work to understand the process parameter interactions. Microstructural and mechanical testing have been carried out to evaluate the performance of the welds. Net shaped (the weld bead is flat to the parent material surface) welds have been achieved and compared with standard welds. The understanding of net-shape weld formation and the effect of the laser welding parameters was enhanced by the theoretical modelling. The thesis concludes with a summary of scientific findings and an overview of future work.

We design, implement and evaluate statistical methods for managing uncertainty when consuming and provisioning resources in a federated computational market. To enable efficient allocation of resources in this environment, providers need to know consumers' risk preferences, and the expected future demand. The guarantee levels to offer thus depend on techniques to forecast future usage and to accurately capture and model uncertainties. Our main contribution in this thesis is threefold; first, we evaluate a set of techniques to forecast demand in computational markets; second, we design a scalable method which captures a succinct summary of usage statistics and allows consumers to express risk preferences; and finally we propose a method for providers to set resource prices and determine guarantee levels to offer. The methods employed are based on fundamental concepts in probability theory, and are thus easy to implement, as well as to analyze and evaluate. The key component of our solution is a predictor that dynamically constructs approximations of the price probability density and quantile functions for arbitrary resources in a computational market. Because highly fluctuating and skewed demand is common in these markets, it is difficult to accurately and automatically construct representations of arbitrary demand distributions. We discovered that a technique based on the Chebyshev inequality and empirical prediction bounds, which estimates worst case bounds on deviations from the mean given a variance, provided the most reliable forecasts for a set of representative high performance and shared cluster workload traces. We further show how these forecasts can help the consumers determine how much to spend given a risk preference and how providers can offer admission control services with different guarantee levels given a recent history of resource prices.
QC 20100909

The thesis is focussed on the reconstruction of a damaged skull represented by a polygonal model. The reconstruction is based on a statistical shape model of the skull. The thesis covers the registration of skulls by using a thin-plate spline method, aligning polygonal models by generalized procrustes analysis, the identification of missing parts of a skull by means of statistical shape models outliers analysis. Finally, missing parts of the skull are reconstructed and the accuracy of the reconstruction is estimated.

Els forats negres acústics en mecànica (coneguts per les sigles ABHs, de l’anglès Acoustic Black Holes) solen estar formats per osques en bigues i plaques, el gruix de les quals decau segons una llei potencial. L’efecte de l’ABH és el d’alentir les velocitats de fase i de grup de les ones de flexió incidents de tal manera que, en teoria, faria falta un temps infinit perquè les ones arribessin al centre de l’ABH, si el gruix d’aquest últim fos exactament zero. Tanmateix, a la pràctica això no és possible tot i que es pot aconseguir una forta dissipació col·locant una capa de material esmorteïdor al centre de l’ABH, on es concentra la major part de l’energia de les ones. En els darrers anys, els ABHs no només s’han explotat com a mètode passiu per reduir vibracions estructurals i l’emissió corresponent de soroll, sinó que també s’ha explorat el seu potencial per altres aplicacions com la manipulació d’ones o la captació d’energia. Aquesta tesi té tres objectius principals. Així, doncs, després d'una introducció general als ABHs, el treball s’ha dividit en tres grans seccions. La primera aborda aplicacions dels ABHs en bigues rectes i plaques planes. Per començar, es proposa i s’analitza un voladís piezoelèctric amb un acabament d’ABH per capturar energia. A continuació es presenten ABHs en forma d’anell per tal d’aïllar punts d’excitació externs en plaques planes i així evitar la transmissió de vibracions. Finalment, es contemplen configuracions periòdiques de matrius d’ABHs per tal de col·limar feixos d'ones de flexió i concentrar la seva energia en zones predeterminades d’una placa. La segona part de la tesi proposa nous dissenys d’ABHs per a estructures amb curvatura. Aquestes són molt habituals en els sectors naval, aeronàutic i industrial, de manera que val la pena investigar si els ABH poden resultar alguns casos. La secció comença analitzant la inclusió d’ABHs en bigues circulars i es veu com això dona peu a l’aparició de fenòmens típics en sistemes periòdics. Acte seguit es proposa un ABH anular per reduir les vibracions en conductes cilíndrics. En concret, es tracten els casos d’un conducte simplement suportat amb un ABH anular, i el d’un conducte amb ABH, suports periòdics i rigidificadors. Per finalitzar la secció, s’investiguen els efectes dels ABH anulars en la radiació acústica del conducte tenint en compte el nivell de potència acústica, l’eficiència de radiació i la intensitat supersònica. La tercera part de la tesi és més curta que les anteriors i simula l’aïllament d'una placa amb múltiples ABHs, en el rang de mitja i alta freqüència. A tal efecte s’empra el mètode de l’anàlisi estadística de distribució modal d'energia (SmEdA: statistical modal energy distribution analysis). En aquesta secció, l’estructura amb ABHs ja no s’analitza com un element individual sinó que s’acobla a dues cavitats d’aire, formant part d’un sistema mecànic més complex. Al llarg de la tesi s’utilitza repetidament el mètode d’expansió gaussiana (GEM: Gaussian expansion method). Pel GEM entenem prendre funcions gaussianes com a base per resoldre equacions diferencials en derivades parcials en el marc del mètode de Rayleigh-Ritz. El GEM s’assembla molt als enfocaments d’ondetes, però ofereix alguns avantatges en el cas de condicions de contorn periòdiques. Al principi de la tesi s’exposa un breu repàs del GEM i, quan és necessari, s’aborda la seva reformulació per a un problema particular en el capítol corresponent.
Los agujeros negros acústicos en mecánica (conocidos por las siglas ABHs, del inglés Acoustic Black Holes) suelen estar formados por muescas en vigas y placas, el grueso de las cuales decae según una ley potencial. El efecto del ABH es el de ralentizar las velocidades de fase y de grupo de las ondas de flexión incidentes de tal modo que, en teoría, haría falta un tiempo infinito para que las ondas alcanzaran el centro del ABH, si el grueso de este último fuera exactamente cero. Sin embargo, en la práctica esto no es posible, aunque se puede conseguir una fuerte disipación colocando una capa de material amortiguador en el centro del ABH, donde se concentra la mayor parte de la energía de las ondas. En los últimos años, los ABHs no sólo se han explotado como método pasivo para reducir vibraciones estructurales y la consecuente emisión de ruido, sino que también se ha explorado su potencial para otras aplicaciones como la manipulación de ondas o la captación de energía. Esta tesis tiene tres objetivos principales. Así pues, tras una introducción general a los ABHs, el trabajo se ha dividido en tres grandes secciones. La primera aborda aplicaciones de los ABHs en vigas rectas y placas planas. Para empezar, se propone y analiza un voladizo piezoeléctrico con un acabado de ABH para capturar energía. A continuación, se presentan ABHs en forma de anillo para aislar puntos de excitación externos en placas planas y así evitar la transmisión de vibraciones. Finalmente, se contemplan configuraciones periódicas de matrices de ABHs para colimar haces de ondas de flexión y concentrar su energía en zonas predeterminadas de una placa. La segunda parte de la tesis propone nuevos diseños de ABHs para estructuras con curvatura. Estas son muy habituales en los sectores naval, aeronáutico e industrial, por lo que merece la pena investigar si los ABH pueden dar buenos resultados en algunos casos. La sección comienza analizando la inclusión de ABHs en vigas circulares y se ve como estos dan pie a la aparición de fenómenos típicos de sistemas periódicos. Seguidamente se propone un ABH anular para reducir las vibraciones en conductos cilíndricos. En concreto, se tratan los casos de un conducto simplemente soportado con un ABH anular, y el de un conducto con ABH, soportes periódicos y rigidificadores. Para finalizar la sección, se investigan los efectos de los ABH anulares en la radiación acústica del conducto teniendo en cuenta el nivel de potencia acústica, la eficiencia de radiación y la intensidad supersónica. La tercera parte de la tesis es más corta que las anteriores y simula el aislamiento de una placa con múltiples ABHs, en el rango de media y alta frecuencia. A tal efecto se emplea el método del análisis estadístico de distribución modal de energía (SmEdA: statistical modal energy distribution analysis). En esta sección, la estructura con ABHs ya no se analiza como un elemento individual, sino que se acopla a dos cavidades de aire formando parte de un sistema mecánico más complejo. A lo largo de la tesis se utiliza repetidamente el método de expansión gaussiana (GEM: Gaussian expansión method). Por GEM entendemos tomar funciones gaussianas como base para resolver ecuaciones diferenciales en derivadas parciales en el marco del método de Rayleigh-Ritz. El GEM se parece mucho a los enfoques de ondículas, pero ofrece algunas ventajas en el caso de condiciones de contorno periódicas. Al principio de la tesis se expone un breve repaso del GEM y, cuando es necesario, se aborda su reformulación para un problema particular en el capítulo correspondiente.
Acoustic black holes (ABHs) in mechanics usually consist of geometrical indentations on beams and plates having a power-law decreasing thickness profile. An ABH slows down the phase and group velocity of incident flexural waves in such a way that, ideally, it would take an infinite amount of time for them to reach the ABH center, if the latter had an exact zero thickness. Though this is not possible in practice, strong wave dissipation can be achieved by placing a damping layer at the central region of the ABH, where most vibration energy concentrates. In recent years, ABHs have been not only exploited as a passive means for structural vibration and noise reduction, but its potential for other applications like wave manipulation or energy harvesting have been also explored. The objective of this thesis is threefold. Therefore, after an initial overview the work is divided into three main parts. The first one deals with ABH applications on straight beams and flat plates. To start with, an ABH piezoelectric bimorph cantilever for energy harvesting is proposed and analyzed. Then, ring-shaped ABH indentations are suggested as a means of isolating external excitation points in flat plates and prevent vibration transmission. Finally, periodic ABH array configurations are contemplated to collimate flexural wave beams and focus energy at desired plate locations. The second part of the thesis proposes new ABH designs for curved structures. The latter are very common in the naval, aeronautical and industrial sectors so it is worth investigating if ABHs could function for them. The section starts analyzing the embedding of ABHs on circular beams and how this results in the appearance of typical phenomena of periodic systems. After that, an annular ABH is proposed to reduce vibrations in cylindrical shells. The cases of a simply supported shell with an annular ABH indentation and of a periodic simply supported ABH shell with stiffeners are considered. To finish the section, the effects of annular ABHs on sound radiation are investigated in terms of sound power level, radiation efficiency and supersonic intensity. The third part of the thesis is shorter than the previous ones and is devoted to analyzing the transmission loss of a plate with multiple ABH indentations, in the mid-high frequency range. Statistical modal energy distribution analysis is used for that purpose. Here, the ABH plate is not taken as an individual structure but coupled to two air cavities, thus being part of a more complex mechanical system. Throughout the thesis repeated use is made of the Gaussian expansion method (GEM). The GEM refers to taking Gaussian functions as the basis for solving partial differential equations in the framework of the Rayleigh-Ritz method. The GEM closely resembles wavelet approaches but offers some advantages in the case of periodic boundary conditions. A brief overview of the GEM is exposed at the beginning of the thesis and, when necessary, its reformulation for a particular problem is tackled in its corresponding chapter.

L’articolazione dell'anca è un'articolazione sinoviale sferica che costituisce la connessione primaria tra gli arti inferiori e lo scheletro della parte superiore del corpo. Durante le attività quotidiane di routine, carichi anormali ripetuti sull'anca possono portare alla danneggiamento della cartilagine articolare e conseguentemente , all’osteoartrite (OA). L'OA dell'anca è una condizione muscolo-scheletrica cronica e progressiva, il cui trattamento per i pazienti severi è l'artroplastica totale dell'anca (THA). Il centro dell'articolazione dell'anca (HJC) ha grande importanza nell’analisi della biomeccanica dell’anca, così come il suo spostamento, che puo’ essere dovuto a patologie, come OA, o alla chirurgia, THA. Per valutare la biomeccanica del bacino in questa tesi sono stati implementati un modello muscoloscheletrico (NMS) personalizzato statistical shape e modelli ad elementi finiti (FE) di un paziente con grave OA mono-laterale dell'anca. Viene discussa l'accuratezza relativamente al modello scalato generico nella predizione delle grandezze biomeccaniche piu’ importanti, durante la deambulazione. Attraverso i modelli FE, è stato studiato l'effetto di una cattiva stima e/o dello spostamento del centro dell'articolazione dell'anca nelle direzioni antero-posteriore, mediolaterale o infero-superiore per valutare lo stato di sollecitazione della pelvi. Infine sono presentati i risultati di un approccio multiscala integrato, per valutare le caratteristiche biomeccaniche del suddetto paziente, passando dalla modellazione NMS, all’analisi del modello FE della pelvi, per effettuare un’analisi comparativa dell’arto osteoartritico con il modello dall’arto controlaterale prima dell’intervento e dopo lo stesso

Processing of Bolu-Himmetoglu (Type I Kerogen) and Ankara-Beypazari (Type II Kerogen) oil shales by flotation techniques were investigated for achieving clean solid fuel substitutes. Materials characterization was done through mineralogical, XRD and FTIR analyses. Flotation responses of the samples were tested with non-ionizing and ionizing collectors of cationic and anionic types. The effects of the collector dosage and pulp pH on cleaning were determined. Other important flotation parameters, conditioning time, flotation time, pulp density, particle size and frother dosage were encountered using a statistical approach, through a full two level factorial experimental design. An advanced flotation procedure, assisted by ultrasonic application, was developed for further improvement in flotation performance. The effects of cleaning on thermal characterstics and combustion kinetics were evaluated with Differential Scanning Calorimetry and ASTM methods while the changes in the emission profiles were assessed using Effluent Gas Analysis. Himmetoglu sample was characterized as a carbonate and organic rich humic oil shale with XRD and FTIR analyses while Beypazari oil shale involved significant carbonate and clay minerals and exhibited a fulvic character with a poor organics content. Reverse flotation with amine acetates provided the most effective means of cleaning with Himmetoglu oil shale. Ash was decreased from 34.76 % to 23.52 % with a combustible recovery of 83.57 % using 800 g/ton Flotigam CA at natural pH and the calorific value increased from 4312 kcal/kg to 5010 kcal/kg. Direct flotation with amines was most effective for Beypazari oil shale cleaning. Using Armoflote 17, ash was reduced from 69.88 % to 53.10 % with 58.64 % combustible recovery using 800 g/ton Armoflote 17 at natural pulp pH and the calorific value of the sample increased from 876 kcal/kg to 2046 kcal/kg. Following optimization, ash of Himmetoglu oil shale decreased to 16.81 % with 84.10 % combustible recovery and calorific value increased to 5564 kcal/kg. For Beypazari oil shale ash decreased to % 48.42 with 59.17 % combustible recovery and the calorific value increased to 2364 kcal/kg. Ultrasonic pre-treatment before flotation further decreased the ash of Himmetoglu sample to 11.82 % with 82.66 % combustible recovery at 15 minutes pre-conditioning time and 50 % power level. For Beypazari oil shale, ash decreased to 34.76 % with 64.78 % combustible recovery after 15 minutes pre-treatment time at 70 % power level. Comparative XRD spectra and SEM analyses revealed that the extent of mineral matter removal relied on the flotation performance. The thermal indicators considerably improved after cleaning and the extent of improvement increased with a decrease in the ash of the concentrates. Kinetic analysis showed the favorable effect of inorganics removal on the effectiveness and easiness of combustion and activation energies decreased after cleaning for both oil shales. The contributions of cleaning on the effectiveness of combustion were also revealed by the increases in the emission rates and total CO2 and CO emission amounts. CO2 emissions due to mineral matter decomposition and harmful SO2 emissions apparently decreased as a consequence of the cleaning of the undesired inorganic contituents and potentially cleaning components. Results of the cleaning and thermal analysis sudies revealed that it was possible to achieve a clean energy source alternative from oil shales through flotation and a significant potential can be anticipated for future use of oil shales as a cost effective and environmental friendly solid fuel substitute in view of Turkey&
#8217
s great oil shale reserves.

This biomedical engineering thesis explores the opportunities and challenges of 2D+t contrast echocardiography for left ventricle functional analysis, both clinically and within a computer vision atlas-based deformable template model framework. A database was created for the experiments in this thesis, with 21 studies of contrast Dobutamine Stress Echo, in all 4 principal planes. The database includes clinical variables, human expert hand-traced myocardial contours and visual scoring. First the problem is studied from a clinical perspective. Quantification of endocardial global and local function using standard measures shows expected values and agreement with human expert visual scoring, but the results are less reliable for myocardial thickening. Next, the problem of segmenting the endocardium with a computer is posed in a standard landmark and atlas-based deformable template model framework. The underlying assumption is that these models can emulate human experts in terms of integrating previous knowledge about the anatomy and physiology with three sources of information from the image: texture, geometry and kinetics. Probabilistic atlases of contrast echocardiography are computed, while noting from histograms at selected anatomical locations that modelling texture with just mean intensity values may be too naive. Intensity analysis together with the clinical results above suggest that lack of external boundary definition may preclude this imaging technique for appropriate measuring of myocardial thickening, while endocardial boundary definition is appropriate for evaluation of wall motion. Geometry is presented in a Principal Component Analysis (PCA) context, highlighting issues about Gaussianity, the correlation and covariance matrices with respect to physiology, and analysing different measures of dimensionality. A popular extension of deformable models ---Active Appearance Models (AAMs)--- is then studied in depth. Contrary to common wisdom, it is contended that using a PCA texture space instead of a fixed atlas is detrimental to segmentation, and that PCA models are not convenient for texture modelling. To integrate kinetics, a novel spatio-temporal model of cardiac contours is proposed. The new explicit model does not require frame interpolation, and it is compared to previous implicit models in terms of approximation error when the shape vector changes from frame to frame or remains constant throughout the cardiac cycle. Finally, the 2D+t atlas-based deformable model segmentation problem is formulated and solved with a gradient descent approach. Experiments using the similarity transformation suggest that segmentation of the whole cardiac volume outperforms segmentation of individual frames. A relatively new approach ---the inverse compositional algorithm--- is shown to decrease running times of the classic Lucas-Kanade algorithm by a factor of 20 to 25, to values that are within real-time processing reach.

This thesis enters on the development of a point-based statistical shape model relying on correspondence probabilities in a sound mathematical framework. Further focus lies on the integration of the model into a segmentation method where a novel approach is taken by combining an explicitly represented shape prior with an implicitly represented segmentation contour. In medical image analysis, the notion of shape is recognized as an important feature to distinguish and analyse anatomical structures. The modeling of shape realized by the concept of statistical shape models constitutes a powerful tool to facilitate the solutions to analysis, segmentation and reconstruction problems. A statistical shape model tries to optimally represent a set of segmented shape observations of any given organ via a mean shape and a variability model. A fundamental challenge in doing statistics on shapes lies in the determination of correspondences between the shape observations. The prevailing assumption of one-to-one point correspondences seems arguable due to uncertainties of the shape surface representations as well as the general di fficulty of pinpointing exact correspondences. In this thesis, the following solution to the point correspondence problem is derived: For all point pairs, a correspondence probability is computed which amounts to representing the shape surfaces by Mixtures of Gaussians. This approach allows to formulate the model computation in a generative framework where the shape observations are interpreted as randomly generated by the model. Based on that, the computation of the model is then treated as an optimization problem. An algorithm is proposed to optimize for model parameters and observation parameters through a single maximum a posteriori criterion which leads to a mathematically sound and unified framework. The method is evaluated and validated in a series of experiments on synthetic and real data. To do so, adequate performance measures and metrics are defined based on which the quality of the new model is compared to the qualities of a classical point-based model and of an established surface-based model that both rely on one-to-one correspondences. A segmentation algorithm is developed which employs the a priori shape knowledge inherent in the statistical shape model to constrain the segmentation contour to probable shapes. An implicit segmentation sheme is chosen instead of an explicit one, which is beneficial regarding topological exibility and implementational issues. The mathematically sound probabilistic shape model enables the challenging integration of an explicit shape prior into an implicit segmentation scheme in an elegant formulation. A maximum a posteriori estimation is developed of a level set function whose zero level set best separates the organ from the background under a shape constraint introduced by the model. This leads to an energy functional which is minimized with respect to the level set using an Euler-Lagrangian equation. Since both the model and the implicitly defined contour are well suited to represent multi-object shapes, an extension of the algorithm to multi-object segmentation is developed which is integrated into the same probabilistic framework. The novel method is evaluated on kidney and hip joint segmentation.

This thesis focuses on the development of semiparametric estimation methods for a class of time series models using shape constraints. Many of the existing time series models assume the noise follows some known parametric distributions. Typical examples are the Gaussian and t distributions. Then the model parameters are estimated by maximizing the resultant likelihood function. As an example, the autoregressive moving average (ARMA) models (Brockwell and Davis, 2009) assume Gaussian noise sequence and are estimated under the causal-invertible constraint by maximizing the Gaussian likelihood. Although the same estimates can also be used in the causal-invertible non-Gaussian case, they are not asymptotically optimal (Rosenblatt, 2012). Moreover, for the noncausal/noninvertible cases, the Gaussian likelihood estimation procedure is not applicable, since any second-order based methods cannot distinguish between causal-invertible and noncausal/noninvertible models (Brockwell and Davis,2009). As a result, many estimation methods for noncausal/noninvertible ARMA models assume the noise follows a known non-Gaussian distribution, like a Laplace distribution or a t distribution. To relax this distributional assumption and allow noncausal/noninvertible models, we borrow ideas from nonparametric shape-constraint density estimation and propose a semiparametric estimation procedure for general ARMA models by projecting the underlying noise distribution onto the space of log-concave measures (Cule and Samworth, 2010; Dümbgen et al., 2011). We show the maximum likelihood estimators in this semiparametric setting are consistent. In fact, the MLE is robust to the misspecification of log-concavity in cases where the true distribution of the noise is close to its log-concave projection. We derive a lower bound for the best asymptotic variance of regular estimators at rate sqrt(n) for AR models and construct a semiparametric efficient estimator. We also consider modeling time series of counts with shape constraints. Many of the formulated models for count time series are expressed via a pair of generalized state-space equations. In this set-up, the observation equation specifies the conditional distribution of the observation Yt at time t given a state-variable Xt. For count time series, this conditional distribution is usually specified as coming from a known parametric family such as the Poisson or the Negative Binomial distribution. To relax this formal parametric framework, we introduce a concave shape constraint into the one-parameter exponential family. This essentially amounts to assuming that the reference measure is log-concave. In this fashion, we are able to extend the class of observation-driven models studied in Davis and Liu (2016). Under this formulation, there exists a stationary and ergodic solution to the state-space model. In this new modeling framework, we consider the inference problem of estimating both the parameters of the mean model and the log-concave function, corresponding to the reference measure. We then compute and maximize the likelihood function over both the parameters associated with the mean function and the reference measure subject to a concavity constraint. The estimator of the mean function and the conditional distribution are shown to be consistent and perform well compared to a full parametric model specification. The finite sample behavior of the estimators are studied via simulation and two empirical examples are provided to illustrate the methodology.

This dissertation is devoted to modeling complex data from the

Bayesian perspective via constructing priors with latent structures.

There are three major contexts in which this is done -- strategies for

the analysis of dynamic longitudinal data, estimating

shape-constrained functions, and identifying subgroups. The

methodology is illustrated in three different

interdisciplinary contexts: (1) adaptive measurement testing in

education; (2) emulation of computer models for vehicle crashworthiness; and (3) subgroup analyses based on biomarkers.

Chapter 1 presents an overview of the utilized latent structured

priors and an overview of the remainder of the thesis. Chapter 2 is

motivated by the problem of analyzing dichotomous longitudinal data

observed at variable and irregular time points for adaptive

measurement testing in education. One of its main contributions lies

in developing a new class of Dynamic Item Response (DIR) models via

specifying a novel dynamic structure on the prior of the latent

trait. The Bayesian inference for DIR models is undertaken, which

permits borrowing strength from different individuals, allows the

retrospective analysis of an individual's changing ability, and

allows for online prediction of one's ability changes. Proof of

posterior propriety is presented, ensuring that the objective

Bayesian analysis is rigorous.

Chapter 3 deals with nonparametric function estimation under

shape constraints, such as monotonicity, convexity or concavity. A

motivating illustration is to generate an emulator to approximate a computer

model for vehicle crashworthiness. Although Gaussian processes are

very flexible and widely used in function estimation, they are not

naturally amenable to incorporation of such constraints. Gaussian

processes with the squared exponential correlation function have the

interesting property that their derivative processes are also

Gaussian processes and are jointly Gaussian processes with the

original Gaussian process. This allows one to impose shape constraints

through the derivative process. Two alternative ways of incorporating derivative

information into Gaussian processes priors are proposed, with one

focusing on scenarios (important in emulation of computer

models) in which the function may have flat regions.

Chapter 4 introduces a Bayesian method to control for multiplicity

in subgroup analyses through tree-based models that limit the

subgroups under consideration to those that are a priori plausible.

Once the prior modeling of the tree is accomplished, each tree will

yield a statistical model; Bayesian model selection analyses then

complete the statistical computation for any quantity of interest,

resulting in multiplicity-controlled inferences. This research is

motivated by a problem of biomarker and subgroup identification to

develop tailored therapeutics. Chapter 5 presents conclusions and

some directions for future research.

Dissertation

The dissertation focuses on solving some important theoretical and methodological problems associated with Bayesian modeling of infinite dimensional `objects', popularly called nonparametric Bayes. The term `infinite dimensional object' can refer to a density, a conditional density, a regression surface or even a manifold. Although Bayesian density estimation as well as function estimation are well-justified in the existing literature, there has been little or no theory justifying the estimation of more complex objects (e.g. conditional density, manifold, etc.). Part of this dissertation focuses on exploring the structure of the spaces on which the priors for conditional densities and manifolds are supported while studying how the posterior concentrates as increasing amounts of data are collected.

With the advent of new acquisition devices, there has been a need to model complex objects associated with complex data-types e.g. millions of genes affecting a bio-marker, 2D pixelated images, a cloud of points in the 3D space, etc. A significant portion of this dissertation has been devoted to developing adaptive nonparametric Bayes approaches for learning low-dimensional structures underlying higher-dimensional objects e.g. a high-dimensional regression function supported on a lower dimensional space, closed curves representing the boundaries of shapes in 2D images and closed surfaces located on or near the point cloud data. Characterizing the distribution of these objects has a tremendous impact in several application areas ranging from tumor tracking for targeted radiation therapy, to classifying cells in the brain, to model based methods for 3D animation and so on.

The first three chapters are devoted to Bayesian nonparametric theory and modeling in unconstrained Euclidean spaces e.g. mean regression and density regression, the next two focus on Bayesian modeling of manifolds e.g. closed curves and surfaces, and the final one on nonparametric Bayes spatial point pattern data modeling when the sampling locations are informative of the outcomes.

Dissertation