Optimal Separable Algorithms to Compute the Reverse Euclidean Distance Transformation and Discrete Medial Axis in Arbitrary Dimension

In binary images, the distance transformation (DT) and the geometrical skeleton extraction are classic tools for shape analysis. In this paper, we present time optimal algorithms to solve the reverse Euclidean distance transformation and the reversible medial axis extraction problems for $d$-dimensional images. We also present a $d$-dimensional medial axis filtering process that allows us to control the quality of the reconstructed shape

Segmentation And Spatial Depth Ridge Detection Of Unorganized Point Cloud Data

Visual 3D data are of interest to a number of fields: medical professionals, game designers, graphic designers, and (in the interest of this paper) ichthyologists interested in the taxonomy of fish. Since the release of the Kinect for the Microsoft XBox, game designers have been interested in using the 3D data returned by the device to understand human movement and translate that movement into an interface with which to interact with game systems. In the medical field, researchers must use computer vision tools to navigate through the data found in CT scans and MRI scans. These tools must segment images into the parts that are relevant to researchers and account for noise related to the scanning process all while ignoring other types of noise such as foreign elements in the body that might indicate signs of illness. 3D point cloud data represents some unique challenges. Consider an object scanned with a laser scanner. The scanner returns the surface points of the object, but nothing more. Using the tool Qhull, a researcher can quickly compute the convex hull of an object (which is an interesting challenge in itself), but the convex hull (obviously) leaves out any description of an object\u27s concave features. Several algorithms have been proposed to illustrate an object\u27s complete features based on unorganized 3D point cloud data as accurately as possible, most notably Boissonnat\u27s tetrahedral culling algorithm and The Power Crust algorithm. We introduce a new approach to the area partitioning problem that takes into consideration these algorithms\u27 strengths and weaknesses. In this paper we propose a methodology for approximating a shape\u27s solid geometry using the unorganized 3D point cloud data of that shape primarily by utilizing localized principal component analysis information. Our model accounts for three comissues that arise in the scanning of 3D objects: noise in surface points, poorly sampled surface area, and narrow corners. We explore each of these areas of concern and outline our approach to each. Our technique uses a growing algorithm that labels points as it progresses and uses those labels with a simple priority queue. We found that our approach works especially well for approximating surfaces under the condition where a local surface is poorly sampled (i.e a significant hole is present in the point cloud). We then turn to study the medial axis of a shape for the purposes of `unfolding\u27 that structure. Our approach uses a ridge formulation based on the spatial depth statistic to create the medial axis. We conclude the paper with visual results of our technique

Caracterização de rochas reservatório de petróleo a partir da modelagem do sistema poroso em rede de poros

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia Mecânica, Florianópolis, 2016.Os métodos de análise de imagem vêm se tornando um poderoso aliado na caracterização de rochas reservatórios, com vantagens como uniformidade e repetitividade das análises assim como redução em tempo e custos de operação. A partir de uma imagem tridimensional, propriedades petrofísicas podem ser estimadas utilizando um modelo matemático que capture a física do escoamento de fluidos no interior do meio poroso. Este trabalho utiliza uma metodologia chamada de ?extração de rede de poros e ligações?, o que essencialmente consiste em criar uma estrutura topologicamente equivalente ao meio poroso original, mas com uma geometria simplificada e conhecida. Esta transformação é realizada de modo a imitar a natureza das estruturas porosas, que contém espaços maiores entre a matriz sólida, compondo as estruturas chamadas de poros na rede, e aberturas alongadas conectando dois ou mais poros, chamadas de ligações ou gargantas. A vantagem deste método é utilizar a geometria simplificada dos elementos da rede para expressar a vazão de um poro a outro através da equação generalizada de Poiseulle para escoamento no interior de dutos prismáticos. Com o emprego destas expressões na conservação de massa, é formado um sistema linear de equações para pressão em cada poro. Esta abordagem necessita, portanto, de menos recursos computacionais que as alternativas existentes (e.g. método Lattice Boltzmann). Possibilitando análises mais rápidas e a caracterização de volumes maiores de dados que seriam proibitivos com o uso de outros métodos. Neste trabalho são apresentadas de forma detalhada todas as etapas do processo de extração da rede a partir de uma imagem tridimensional binarizada. Redes de poros e ligações são extraídas a partir de imagens de arenitos, e utilizadas para calcular porosidade, permeabilidade absoluta e pressão capilar por intrusão de mercúrio, apresentando boa concordância com dados experimentais.Abstract : Methods based on image analysis are proving to be a powerful ally for reservoir rock characterization with advantages such as analysis uniformity and repeatability as well as reduction of operational costs and time. Once a three-dimensional image is obtained, petrophysical properties can be estimated using a mathematical model that captures the physics of fluid flow through porous media. This work uses the Pore network extraction methodology, which in essence consists in creating a topologically equivalent structure of the porous system but with a simplified geometry, trying to mimic the rock in its nature, which contains larger spaces between grains (pores) and elongated apertures connecting two or more pores (throats).The main advantage of this method is to make use of the simplified geometry of the network elements to express flow between pores using generalized Poiseulle equation for flow inside prismatic ducts. Applying these expressions in mass conservation equation, a linear equation system is formed for pressure on each pore. This approach requires less computational resources than the existing numeric alternatives (e.g. Lattice Boltzmann method), therefore obtaining faster responses and allowing larger image analysis which would be prohibitive when using other methods. An in-depth description of the complete process of network extraction from three dimensional binarized images is presented. Pore networks are extracted from siliciclastic rock samples, and used to calculate porosity, absolute permeability and capillary pressure curve for mercury intrusion, showing good accordance with experimental data

Real-Time High-Quality Image to Mesh Conversion for Finite Element Simulations

Technological Advances in Medical Imaging have enabled the acquisition of images accurately describing biological tissues. Finite Element (FE) methods on these images provide the means to simulate biological phenomena such as brain shift registration, respiratory organ motion, blood flow pressure in vessels, etc. FE methods require the domain of tissues be discretized by simpler geometric elements, such as triangles in two dimensions, tetrahedra in three, and pentatopes in four. This exact discretization is called a mesh . The accuracy and speed of FE methods depend on the quality and fidelity of the mesh used to describe the biological object. Elements with bad quality introduce numerical errors and slower solver convergence. Also, analysis based on poor fidelity meshes do not yield accurate results specially near the surface. In this dissertation, we present the theory and the implementation of both a sequential and a parallel Delaunay meshing technique for 3D and ---for the first time--- 4D space-time domains. Our method provably guarantees that the mesh is a faithful representation of the multi-tissue domain in topological and geometric sense. Moreover, we show that our method generates graded elements of bounded radius-edge and aspect ratio, which renders our technique suitable for Finite Element analysis. A notable feature of our implementation is speed and scalability. The single-threaded performance of our 3D code is faster than the state of the art open source meshing tools. Experimental evaluation shows a more than 82% weak scaling efficiency for up to 144 cores, reaching a rate of more than 14.3 million elements per second. This is the first 3D parallel Delaunay refinement method to achieve such a performance, on either distributed or shared-memory architectures. Lastly, this dissertation is the first to develop and examine the sequential and parallel high-quality and fidelity meshing of general space-time 4D multi-tissue domains