Dois métodos distintos são descritos e implementados. O primeiro método, proposto por Ruppert, possui garantias teóricas de qualidade quando a fronteira do domínio obedece certas restrições. O segundo método, proposto por Persson, possibilita um maior controle na densidade dos elementos que discretizam o domínio. As vantagens, desvantagens e particularidades de cada um dos métodos são descritas e detalhadas / Two distinct methods are described and implemented. The first method, proposed by Ruppert, has theoretical guarantees on the quality of elements when the domain boundaries respect certain restrictions. The second method, proposed by Persson, makes it possible to have greater control over the density of the elements that make up the domain. The advantages, disadvantages and specific points about each method are described and detailed

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The presented research summarizes (1) the development of a rapid prototyping framework, (2) the application of advance meshing algorithms, data structures, programming languages and libraries toward the field of numerical surface-water modeling (NSWM), (3) the application of (2) in (1), and (4) a real world application. The result of the research was the development of a prototype grid generator tool, the Mesh Generation and Refinement Tool (MGRT). MGRT supports a customizable interface and plug-and-play functionality through the use of plug-ins and incorporates a plug-in based topology/geometry system. A detailed explanation of the data structures, algorithms, and tools used to construct the MGRT are presented. Additionally, the construction of a mesh of Mobile Bay is presented. This represents a real world application of the MGRT. This tool provides many benefits over current tools in NSWM, which include faster meshing and the ability the use any grid generator that can be plugged-in.

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Aortic stenosis (AS) is a critical valvular disease often treated by Transcatheter Aortic Valve Replacement (TAVR). This thesis introduces several novel approaches for improving the assessment and management of AS and the associated TAVR procedure. The research presents new indices for characterizing AS progression, including the False Positive Rate (FPR) method for detecting and quantifying calcification in contrast-enhanced computed tomography (CT) images. This method adapts dynamically to the variability in calcium density and offers precise estimates of calcific burden. Additionally, a Minimal Variation Geometry Invariant Parametric Reconstruction (MVGIPR) method was developed to reconstruct the full geometry of the aortic valve complex (AVC). This approach enhances the accuracy of geometric models from routine CT scans, providing detailed 3D models of the aortic valve, including patient-specific anatomical and pathological features. Moreover, the Virtual Transcatheter Aortic Valve Replacement (VTAVR) framework is introduced for TAVR optimization and intervention planning using developments from both previous techniques. This novel simulation-based system incorporates kinematic modeling within a patient-specific parametric geometry to predict device deployment outcomes, including complications such as paravalvular leakage, patient-prosthesis mismatch, and left bundle branch block. By simulating patient-specific device deployment, the VTAVR framework may potentially enhance pre-procedural planning, leading to better surgical outcomes and reduced risks in TAVR procedures. / Thesis / Doctor of Philosophy (PhD) / Aortic stenosis (AS) is a condition where the heart’s aortic valve becomes narrowed due to calcification, restricting blood flow and leading to severe health risks, especially in older adults. This research introduces new ways to measure the progression of this disease and predict complications from the commonly used treatment called Transcatheter Aortic Valve Replacement (TAVR). Using advanced computational models, the study develops personalized aortic valve shape and structure assessment frameworks using routine clinical computed tomography (CT) imaging. Moreover, we introduce a virtual interventional simulation framework that can predict how a patient’s valve may respond to TAVR. This "Virtual TAVR" system may help treating physicians to plan surgeries more accurately by simulating different approaches, allowing them to identify the best treatment strategy for each patient. By improving our ability to predict complications, the system ultimately aims to increase the success rate of these life-saving procedures.

M.Sc (Computer Science) / Facial modelling and animation is considered one of the most challenging areas in the animation world. Since Parke and Waters’s (1996) comprehensive book, no major work encompassing the entire field of facial animation has been published. This thesis covers Parke and Waters’s work, while also providing a survey of the developments in the field since 1996. The thesis describes, analyses, and compares (where applicable) the existing techniques and practices used to produce the facial animation. Where applicable, the related techniques are grouped in the same chapter and described in a chronological fashion, outlining their differences, as well as their advantages and disadvantages. The thesis is concluded by exploratory work towards a talking head for Northern Sotho. Facial animation and lip synchronisation of a fragment of Northern Sotho is done by using software tools primarily designed for English. / Computing

This large body of work is entirely centered around dual-tree algorithms, a class of algorithm based on spatial indexing structures that often provide large amounts of acceleration for various problems. This work focuses on understanding dual-tree algorithms using a new, tree-independent abstraction, and using this abstraction to develop new algorithms. Stated more clearly, the thesis of this entire work is that we may improve and expand the class of dual-tree algorithms by focusing on and providing improvements for each of the three independent components of a dual-tree algorithm: the type of space tree, the type of pruning dual-tree traversal, and the problem-specific BaseCase() and Score() functions. This is demonstrated by expressing many existing dual-tree algorithms in the tree-independent framework, and focusing on improving each of these three pieces. The result is a formidable set of generic components that can be used to assemble dual-tree algorithms, including faster traversals, improved tree theory, and new algorithms to solve the problems of max-kernel search and k-means clustering.

Les modèles virtuels de plantes sont visuellement de plus en plus réalistes dans les applications infographiques. Cependant, dans le contexte de la biologie et l'agronomie, l'acquisition de modèles précis de plantes réelles reste un problème majeur pour la construction de modèles quantitatifs du développement des plantes.Récemment, des scanners laser 3D permettent d'acquérir des images 3D avec pour chaque pixel une profondeur correspondant à la distance entre le scanner et la surface de l'objet visé. Cependant, une plante est généralement un ensemble important de petites surfaces sur lesquelles les méthodes classiques de reconstruction échouent. Dans cette thèse, nous présentons une méthode pour reconstruire des modèles virtuels de plantes à partir de scans laser. Mesurer des plantes avec un scanner laser produit des données avec différents niveaux de précision. Les scans sont généralement denses sur la surface des branches principales mais recouvrent avec peu de points les branches fines. Le cœur de notre méthode est de créer itérativement un squelette de la structure de la plante en fonction de la densité locale de points. Pour cela, une méthode localement adaptative a été développée qui combine une phase de contraction et un algorithme de suivi de points.Nous présentons également une procédure d'évaluation quantitative pour comparer nos reconstructions avec des structures reconstruites par des experts de plantes réelles. Pour cela, nous explorons d'abord l'utilisation d'une distance d'édition entre arborescence. Finalement, nous formalisons la comparaison sous forme d'un problème d'assignation pour trouver le meilleur appariement entre deux structures et quantifier leurs différences.

The dissertation introduces Sphere Support Vector Machines (SphereSVM) and Minimal Norm Support Vector Machines (MNSVM) as the new fast classification algorithms that use geometrical properties of the underlying classification problems to efficiently obtain models describing training data. SphereSVM is based on combining minimal enclosing ball approach, state of the art nearest point problem solvers and probabilistic techniques. The blending of the three speeds up the training phase of SVMs significantly and reaches similar (i.e., practically the same) accuracy as the other classification models over several big and large real data sets within the strict validation frame of a double (nested) cross-validation (CV). MNSVM is further simplification of SphereSVM algorithm. Here, relatively complex classification task was converted into one of the simplest geometrical problems -- minimal norm problem. This resulted in additional speedup compared to SphereSVM. The results shown are promoting both SphereSVM and MNSVM as outstanding alternatives for handling large and ultra-large datasets in a reasonable time without switching to various parallelization schemes for SVMs algorithms proposed recently. The variants of both algorithms, which work without explicit bias term, are also presented. In addition, other techniques aiming to improve the time efficiency are discussed (such as over-relaxation and improved support vector selection scheme). Finally, the accuracy and performance of all these modifications are carefully analyzed and results based on nested cross-validation procedure are shown.