Multi-Material Mesh Representation of Anatomical Structures for Deep Brain Stimulation Planning

The Dual Contouring algorithm (DC) is a grid-based process used to generate surface meshes from volumetric data. However, DC is unable to guarantee 2-manifold and watertight meshes due to the fact that it produces only one vertex for each grid cube. We present a modified Dual Contouring algorithm that is capable of overcoming this limitation. The proposed method decomposes an ambiguous grid cube into a set of tetrahedral cells and uses novel polygon generation rules that produce 2-manifold and watertight surface meshes with good-quality triangles. These meshes, being watertight and 2-manifold, are geometrically correct, and therefore can be used to initialize tetrahedral meshes. The 2-manifold DC method has been extended into the multi-material domain. Due to its multi-material nature, multi-material surface meshes will contain non-manifold elements along material interfaces or shared boundaries. The proposed multi-material DC algorithm can (1) generate multi-material surface meshes where each material sub-mesh is a 2-manifold and watertight mesh, (2) preserve the non-manifold elements along the material interfaces, and (3) ensure that the material interface or shared boundary between materials is consistent. The proposed method is used to generate multi-material surface meshes of deep brain anatomical structures from a digital atlas of the basal ganglia and thalamus. Although deep brain anatomical structures can be labeled as functionally separate, they are in fact continuous tracts of soft tissue in close proximity to each other. The multi-material meshes generated by the proposed DC algorithm can accurately represent the closely-packed deep brain structures as a single mesh consisting of multiple material sub-meshes. Each sub-mesh represents a distinct functional structure of the brain. Printed and/or digital atlases are important tools for medical research and surgical intervention. While these atlases can provide guidance in identifying anatomical structures, they do not take into account the wide variations in the shape and size of anatomical structures that occur from patient to patient. Accurate, patient-specific representations are especially important for surgical interventions like deep brain stimulation, where even small inaccuracies can result in dangerous complications. The last part of this research effort extends the discrete deformable 2-simplex mesh into the multi-material domain where geometry-based internal forces and image-based external forces are used in the deformation process. This multi-material deformable framework is used to segment anatomical structures of the deep brain region from Magnetic Resonance (MR) data

Doctor of Philosophy

dissertationComputational simulation has become an indispensable tool in the study of both basic mechanisms and pathophysiology of all forms of cardiac electrical activity. Because the heart is comprised of approximately 4 billion electrically active cells, it is not possible to geometrically model or computationally simulate each individual cell. As a result computational models of the heart are, of necessity, abstractions that approximate electrical behavior at the cell, tissue, and whole body level. The goal of this PhD dissertation was to evaluate several aspects of these abstractions by exploring a set of modeling approaches in the field of cardiac electrophysiology and to develop means to evaluate both the amplitude of these errors from a purely technical perspective as well as the impacts of those errors in terms of physiological parameters. The first project used subject specific models and experiments with acute myocardial ischemia to show that one common simplification used to model myocardial ischemia-the simplest form of the border zone between healthy and ischemic tissue-was not supported by the experimental results. We propose a alternative approximation of the border zone that better simulates the experimental results. The second study examined the impact of simplifications in geometric models on simulations of cardiac electrophysiology. Such models consist of a connected mesh of polygonal elements and must often capture complex external and internal boundaries. A conforming mesh contains elements that follow closely the shapes of boundaries; nonconforming meshes fit the boundaries only approximately and are easier to construct but their impact on simulation accuracy has, to our knowledge, remained unknown. We evaluated the impact of this simplification on a set of three different forms of bioelectric field simulations. The third project evaluated the impact of an additional geometric modeling error; positional uncertainty of the heart in simulations of the ECG. We applied a relatively novel and highly efficient statistical approach, the generalized Polynomial Chaos-Stochastic Collocation method (gPC-SC), to a boundary element formulation of the electrocardiographic forward problem to carry out the necessary comprehensive sensitivity analysis. We found variations large enough to mask or to mimic signs of ischemia in the ECG

Програмні засоби процедурної генерації ландшафту

Актуальність теми. В сучасному світі, особливої актуальності набуває індустрія розваг. Послуги цієї індустрії здатні задовільнити потреби людини і не рідко сприяють її розвитку. Вагоме місце в індустрії розваг посідають відеоігри. Основним етапом розробки ігрових програм є створення навколишнього середовища. Для певних ігрових програм це може бути фонове зображення, а для деяких це може бути повноцінний ландшафт. Існує безліч програмних засобів, які дозволяють створювати ландшафти, щоб потім використовувати їх в ігрових програмах. Здебільшого алгоритми генерації ландшафту націлені на вирішення певної задачі, тому не завжди можна отримати бажаний результат. Ще однією, важливою проблемою є залежність від програмної архітектури застосунків, які використовуються, тому досить часто виникає проблема не раціонального використання пам’яті та інших обмежень. Не менш важливим, є можливість модифікації згенерованого ландшафту, тому можна спостерігати суттєве підвищення інтересу до воксельної графіки. Зважаючи на підвищення інтересу до воксельної графіки, виникає необхідність в розробці ефективних алгоритмів опису воксельних даних. Об’єктом дослідження є методи та алгоритми процедурної генерації ландшафту. Предметом дослідження є програмна реалізація розробленого алгоритму процедурної генерації ландшафту. Мета роботи: підвищення ефективності процедурної генерації ландшафту використовуючи модифіковане розріджене воксельне октодерево Методи дослідження. В роботі використовуються системного аналізу, графічної візуалізації, оптимізації. Наукова новизна полягає в запропонованому алгоритмі оптимізації процедурної генерації ландшафту, що дозволяє зменшити вимоги до пам’яті. Практична цінність отриманих в роботі результатів полягає в тому, що запропонований алгоритм дозволяє зменшити необхідний обсяг пам’яті, який потрібний для опису згенерованого ландшафту. Це дозволить створювати більш складне навколишнє середовище, що значно підвищить візуальне сприйняття. Структура та обсяг роботи. Магістерська дисертація складається з вступу, чотирьох розділів, висновків та додатків. У вступі представлена загальна характеристика проблеми, обґрунтована необхідність розробки нового алгоритму, сформульована задача роботи. У першому розділі розглянуто основні методи створення ландшафтів. Проведено порівняльний аналіз методів процедурної генерації ландшафту. У другому розділі описується воксельна технологія, проаналізовані способи опису воксельних даних. У третьому розділі описано алгоритми для генерації ландшафту в ігрових програмах; розроблено та описано етапи алгоритму генерації з використанням модифікованого розрідженого воксельного октодерева. У четвертому розділі реалізовано розроблений алгоритм процедурної генерації ландшафту з використанням модифікованого розрідженого воксельного октодерева; описано структуру розробленого програмного продукту. У висновках проаналізовано отримані результати. У додатках наведено презентацію, лістинг розробленого програмного продукту, а також копії публікацій. Магістерська дисертація виконана на 69 аркушах, містить 3 додатки та посилання на список використаних літературних джерел з 16 найменувань. У роботі наведено 72 рисунків та 1 таблиць.Actuality of theme. In today's world, the entertainment industry is especially relevant. The services of this industry are able to meet human needs and often contribute to its development. Video games play an important role in the entertainment industry. The main stage of game development is the creation of the environment. For some game programs it may be a background image, and for some it may be a full- fledged landscape. There are many software tools that allow you to create landscapes and then use them in gaming applications. For the most part, landscape generation algorithms are aimed at solving a specific problem, so it is not always possible to obtain the desired result. Another important problem is the dependence on the software architecture of the applications used, so quite often there is a problem of irrational use of memory and other limitations. No less important is the ability to modify the generated landscape, so you can see a significant increase in interest in voxel graphics. Due to the growing interest in voxel graphics, there is a need to develop effective algorithms for describing voxel data. The object of research is the methods and algorithms of procedural generation of the landscape. The subject of research is the software implementation of the developed algorithm of procedural generation of the landscape. Purpose: to increase the efficiency of procedural generation of the landscape using a modified sparse voxel octopus Research methods. The work uses system analysis, graphical visualization, optimization. The scientific novelty lies in the proposed algorithm for optimizing the procedural generation of the landscape, which reduces memory requirements. The practical value of the results obtained in this work is that the proposed algorithm reduces the required amount of memory required to describe the generated landscape. This will create a more complex environment that will greatly enhance visual perception. Structure and scope of work. The master's dissertation consists of an introduction, four chapters, conclusions and appendices. The introduction presents the general characteristics of the problem, substantiates the need to develop a new algorithm, formulates the task. The first section discusses the main methods of creating landscapes. The comparative analysis of methods of procedural generation of a landscape is carried out. The second section describes the voxel technology, analyzes the methods of describing voxel data. The third section describes algorithms for generating landscape in game programs; the stages of the generation algorithm using a modified sparse voxel octodree are developed and described. In the fourth section the developed algorithm of procedural generation of a landscape with use of the modified rarefied voxel octodree is realized; describes the structure of the developed software product. The results analyze the results. The appendices provide a presentation, listing of the developed software product, as well as copies of publications. The master's dissertation is made on 69 sheets, contains 3 appendices and links to the list of used literature sources from 16 titles. The paper contains 72 figures and 1 table

Scene Reconstruction from Multi-Scale Input Data

Geometry acquisition of real-world objects by means of 3D scanning or stereo reconstruction constitutes a very important and challenging problem in computer vision. 3D scanners and stereo algorithms usually provide geometry from one viewpoint only, and several of the these scans need to be merged into one consistent representation. Scanner data generally has lower noise levels than stereo methods and the scanning scenario is more controlled. In image-based stereo approaches, the aim is to reconstruct the 3D surface of an object solely from multiple photos of the object. In many cases, the stereo geometry is contaminated with noise and outliers, and exhibits large variations in scale. Approaches that fuse such data into one consistent surface must be resilient to such imperfections. In this thesis, we take a closer look at geometry reconstruction using both scanner data and the more challenging image-based scene reconstruction approaches. In particular, this work focuses on the uncontrolled setting where the input images are not constrained, may be taken with different camera models, under different lighting and weather conditions, and from vastly different points of view. A typical dataset contains many views that observe the scene from an overview perspective, and relatively few views capture small details of the geometry. What results from these datasets are surface samples of the scene with vastly different resolution. As we will show in this thesis, the multi-resolution, or, "multi-scale" nature of the input is a relevant aspect for surface reconstruction, which has rarely been considered in literature yet. Integrating scale as additional information in the reconstruction process can make a substantial difference in surface quality. We develop and study two different approaches for surface reconstruction that are able to cope with the challenges resulting from uncontrolled images. The first approach implements surface reconstruction by fusion of depth maps using a multi-scale hierarchical signed distance function. The hierarchical representation allows fusion of multi-resolution depth maps without mixing geometric information at incompatible scales, which preserves detail in high-resolution regions. An incomplete octree is constructed by incrementally adding triangulated depth maps to the hierarchy, which leads to scattered samples of the multi-resolution signed distance function. A continuous representation of the scattered data is defined by constructing a tetrahedral complex, and a final, highly-adaptive surface is extracted by applying the Marching Tetrahedra algorithm. A second, point-based approach is based on a more abstract, multi-scale implicit function defined as a sum of basis functions. Each input sample contributes a single basis function which is parameterized solely by the sample's attributes, effectively yielding a parameter-free method. Because the scale of each sample controls the size of the basis function, the method automatically adapts to data redundancy for noise reduction and is highly resilient to the quality-degrading effects of low-resolution samples, thus favoring high-resolution surfaces. Furthermore, we present a robust, image-based reconstruction system for surface modeling: MVE, the Multi-View Environment. The implementation provides all steps involved in the pipeline: Calibration and registration of the input images, dense geometry reconstruction by means of stereo, a surface reconstruction step and post-processing, such as remeshing and texturing. In contrast to other software solutions for image-based reconstruction, MVE handles large, uncontrolled, multi-scale datasets as well as input from more controlled capture scenarios. The reason lies in the particular choice of the multi-view stereo and surface reconstruction algorithms. The resulting surfaces are represented using a triangular mesh, which is a piecewise linear approximation to the real surface. The individual triangles are often so small that they barely contribute any geometric information and can be ill-shaped, which can cause numerical problems. A surface remeshing approach is introduced which changes the surface discretization such that more favorable triangles are created. It distributes the vertices of the mesh according to a density function, which is derived from the curvature of the geometry. Such a mesh is better suited for further processing and has reduced storage requirements. We thoroughly compare the developed methods against the state-of-the art and also perform a qualitative evaluation of the two surface reconstruction methods on a wide range of datasets with different properties. The usefulness of the remeshing approach is demonstrated on both scanner and multi-view stereo data

Exploring 3D Shapes through Real Functions

This thesis lays in the context of research on representation, modelling and coding knowledge related to digital shapes, where by shape it is meant any individual object having a visual appareance which exists in some two-, three- or higher dimensional space. Digital shapes are digital representations of either physically existing or virtual objects that can be processed by computer applications. While the technological advances in terms of hardware and software have made available plenty of tools for using and interacting with the geometry of shapes, to manipulate and retrieve huge amount of data it is necessary to define methods able to effectively code them. In this thesis a conceptual model is proposed which represents a given 3D object through the coding of its salient features and defines an abstraction of the object, discarding irrelevant details. The approach is based on the shape descriptors defined with respect to real functions, which provide a very useful shape abstraction method for the analysis and structuring of the information contained in the discrete shape model. A distinctive feature of these shape descriptors is their capability of combining topological and geometrical information properties of the shape, giving an abstraction of the main shape features. To fully develop this conceptual model, both theoretical and computational aspects have been considered, related to the definition and the extension of the different shape descriptors to the computational domain. Main emphasis is devoted to the application of these shape descriptors in computational settings; to this aim we display a number of application domains that span from shape retrieval, to shape classification and to best view selection.Questa tesi si colloca nell\u27ambito di ricerca riguardante la rappresentazione, la modellazione e la codifica della conoscenza connessa a forme digitali, dove per forma si intende l\u27aspetto visuale di ogni oggetto che esiste in due, tre o pi? dimensioni. Le forme digitali sono rappresentazioni di oggetti sia reali che virtuali, che possono essere manipolate da un calcolatore. Lo sviluppo tecnologico degli ultimi anni in materia di hardware e software ha messo a disposizione una grande quantit? di strumenti per acquisire, rappresentare e processare la geometria degli oggetti; tuttavia per gestire questa grande mole di dati ? necessario sviluppare metodi in grado di fornirne una codifica efficiente. In questa tesi si propone un modello concettuale che descrive un oggetto 3D attraverso la codifica delle caratteristiche salienti e ne definisce una bozza ad alto livello, tralasciando dettagli irrilevanti. Alla base di questo approccio ? l\u27utilizzo di descrittori basati su funzioni reali in quanto forniscono un\u27astrazione della forma molto utile per analizzare e strutturare l\u27informazione contenuta nel modello discreto della forma. Una peculiarit? di tali descrittori di forma ? la capacit? di combinare propriet? topologiche e geometriche consentendo di astrarne le principali caratteristiche. Per sviluppare questo modello concettuale, ? stato necessario considerare gli aspetti sia teorici che computazionali relativi alla definizione e all\u27estensione in ambito discreto di vari descrittori di forma. Particolare attenzione ? stata rivolta all\u27applicazione dei descrittori studiati in ambito computazionale; a questo scopo sono stati considerati numerosi contesti applicativi, che variano dal riconoscimento alla classificazione di forme, all\u27individuazione della posizione pi? significativa di un oggetto

Part decomposition of 3D surfaces

This dissertation describes a general algorithm that automatically decomposes realworld scenes and objects into visual parts. The input to the algorithm is a 3 D triangle mesh that approximates the surfaces of a scene or object. This geometric mesh completely specifies the shape of interest. The output of the algorithm is a set of boundary contours that dissect the mesh into parts where these parts agree with human perception. In this algorithm, shape alone defines the location of a bom1dary contour for a part. The algorithm leverages a human vision theory known as the minima rule that states that human visual perception tends to decompose shapes into parts along lines of negative curvature minima. Specifically, the minima rule governs the location of part boundaries, and as a result the algorithm is known as the Minima Rule Algorithm. Previous computer vision methods have attempted to implement this rule but have used pseudo measures of surface curvature. Thus, these prior methods are not true implementations of the rule. The Minima Rule Algorithm is a three step process that consists of curvature estimation, mesh segmentation, and quality evaluation. These steps have led to three novel algorithms known as Normal Vector Voting, Fast Marching Watersheds, and Part Saliency Metric, respectively. For each algorithm, this dissertation presents both the supporting theory and experimental results. The results demonstrate the effectiveness of the algorithm using both synthetic and real data and include comparisons with previous methods from the research literature. Finally, the dissertation concludes with a summary of the contributions to the state of the art