Contribution to structural parameters computation: volume models and methods

Bio-CAD and in-silico experimentation are getting a growing interest in biomedical applications where scientific data coming from real samples are used to compute structural parameters that allow to evaluate physical properties. Non-invasive imaging acquisition technologies such as CT, mCT or MRI, plus the constant growth of computer capabilities, allow the acquisition, processing and visualization of scientific data with increasing degree of complexity. Structural parameters computation is based on the existence of two phases (or spaces) in the sample: the solid, which may correspond to the bone or material, and the empty or porous phase and, therefore, they are represented as binary volumes. The most common representation model for these datasets is the voxel model, which is the natural extension to 3D of 2D bitmaps. In this thesis, the Extreme Vertices Model (EVM) and a new proposed model, the Compact Union of Disjoint Boxes (CUDB), are used to represent binary volumes in a much more compact way. EVM stores only a sorted subset of vertices of the object¿s boundary whereas CUDB keeps a compact list of boxes. In this thesis, methods to compute the next structural parameters are proposed: pore-size distribution, connectivity, orientation, sphericity and roundness. The pore-size distribution helps to interpret the characteristics of porous samples by allowing users to observe most common pore diameter ranges as peaks in a graph. Connectivity is a topological property related to the genus of the solid space, measures the level of interconnectivity among elements, and is an indicator of the biomechanical characteristics of bone or other materials. The orientation of a shape can be defined by rotation angles around a set of orthogonal axes. Sphericity is a measure of how spherical is a particle, whereas roundness is the measure of the sharpness of a particle's edges and corners. The study of these parameters requires dealing with real samples scanned at high resolution, which usually generate huge datasets that require a lot of memory and large processing time to analyze them. For this reason, a new method to simplify binary volumes in a progressive and lossless way is presented. This method generates a level-of-detail sequence of objects, where each object is a bounding volume of the previous objects. Besides being used as support in the structural parameter computation, this method can be practical for task such as progressive transmission, collision detection and volume of interest computation. As part of multidisciplinary research, two practical applications have been developed to compute structural parameters of real samples. A software for automatic detection of characteristic viscosity points of basalt rocks and glasses samples, and another to compute sphericity and roundness of complex forms in a silica dataset.El Bio-Diseño Asistido por Computadora (Bio-CAD), y la experimentacion in-silico est an teniendo un creciente interes en aplicaciones biomedicas, en donde se utilizan datos cientificos provenientes de muestras reales para calcular par ametros estructurales que permiten evaluar propiedades físicas. Las tecnologías de adquisicion de imagen no invasivas como la TC, TC o IRM, y el crecimiento constante de las prestaciones de las computadoras, permiten la adquisicion, procesamiento y visualizacion de datos científicos con creciente grado de complejidad. El calculo de parametros estructurales esta basado en la existencia de dos fases (o espacios) en la muestra: la solida, que puede corresponder al hueso o material, y la fase porosa o vacía, por tanto, tales muestras son representadas como volumenes binarios. El modelo de representacion mas comun para estos conjuntos de datos es el modelo de voxeles, el cual es una extension natural a 3D de los mapas de bits 2D. En esta tesis se utilizan el modelo Extreme Verrtices Model (EVM) y un nuevo modelo propuesto, the Compact Union of Disjoint Boxes (CUDB), para representar los volumenes binarios en una forma mucho mas compacta. El modelo EVM almacena solo un subconjunto ordenado de vertices de la frontera del objeto mientras que el modelo CUDB mantiene una lista compacta de cajas. En esta tesis se proponen metodos para calcular los siguientes parametros estructurales: distribucion del tamaño de los poros, conectividad, orientacion, esfericidad y redondez. La distribucion del tamaño de los poros ayuda a interpretar las características de las muestras porosas permitiendo a los usuarios observar los rangos de diametro mas comunes de los poros mediante picos en un grafica. La conectividad es una propiedad topologica relacionada con el genero del espacio solido, mide el nivel de interconectividad entre los elementos, y es un indicador de las características biomecanicas del hueso o de otros materiales. La orientacion de un objeto puede ser definida por medio de angulos de rotacion alrededor de un conjunto de ejes ortogonales. La esfericidad es una medida de que tan esferica es una partícula, mientras que la redondez es la medida de la nitidez de sus aristas y esquinas. En el estudio de estos parametros se trabaja con muestras reales escaneadas a alta resolucion que suelen generar conjuntos de datos enormes, los cuales requieren una gran cantidad de memoria y mucho tiempo de procesamiento para ser analizados. Por esta razon, se presenta un nuevo metodo para simpli car vol umenes binarios de una manera progresiva y sin perdidas. Este metodo genera una secuencia de niveles de detalle de los objetos, en donde cada objeto es un volumen englobante de los objetos previos. Ademas de ser utilizado como apoyo en el calculo de parametros estructurales, este metodo puede ser de utilizado en otras tareas como transmision progresiva, deteccion de colisiones y calculo de volumen de interes. Como parte de una investigacion multidisciplinaria, se han desarrollado dos aplicaciones practicas para calcular parametros estructurales de muestras reales. Un software para la deteccion automatica de puntos de viscosidad característicos en muestras de rocas de basalto y vidrios, y una aplicacion para calcular la esfericidad y redondez de formas complejas en un conjunto de datos de sílice

A new lossless orthogonal simplification method for 3D objects based on bounding structures

This paper presents a new approach to simplify 3D binary images and general orthogonal pseudo-polyhedra (OPP). The method is incremental and produces a level-of-detail sequence of OPP, where any object of this sequence bounds the previous objects and, therefore, is a bounding orthogonal approximation of them. The sequence finishes with the axis-aligned bounding box. OPP are encoded using the Extreme Vertices Model, a complete model that stores a subset of their vertices and performs fast Boolean operations. Simplification is achieved by using a new strategy, which relies on the application of 2D Boolean operations. We also present a technique, based on model continuity, for better shape preservation. Finally, we present a data structure to encode in a progressive and lossless way the generated sequence. Tests with several datasets show that the proposed method produces smaller storage sizes and good quality approximations compared with other methods that also produce bounding objects.Peer ReviewedPostprint (published version

Merging faces: A new orthogonal simplification of solid models

A new approach to simplify orthogonal pseudo-polyhedra (OPP) and binary volumes is presented. The method is incremental and produces a level-of-detail (LOD) sequence of OPP. Any object of this sequence contains the previous objects and, therefore, it is a bounding orthogonal approximation of them. The sequence finishes with the minimum axis-aligned bounding box (AABB). OPP are represented by the Extreme Vertices Model, a complete model that stores a subset of their vertices and performs fast Boolean operations. Simplification is achieved using a new approach called merging faces, which relies on the application of 2D Boolean operations. We also present a technique, based on the model continuity, for a better shape preservation. The method has been tested with several datasets and compared with two similar methods

A connected-component-labeling-based approach to virtual porosimetry

Analyzing the pore-size distribution of porous materials, made up of an aggregation of interconnected pores, is a demanding task. Mercury intrusion porosimetry (MIP) is a physical method that intrudes mercury into a sample at increasing pressures to obtain a poresize histogram. This method has been simulated in-silice with several approaches requiring prior computation of a skeleton. We present a new approach to simulate MIP that does not require skeleton computation. Our method is an iterative process that considers the diameters corresponding to pressures. At each iteration, geometric tests detect throats for the corresponding diameter and a CCL process collects the region invaded by the mercury. Additionally, a new decomposition model called CUDB, is used. This is suitable for computing the throats and performs better with the CCL algorithm than a voxel model. Our approach obtains the pore-size distribution of the porous medium, and the corresponding pore graph.Peer Reviewe

A connected-component-labeling-based approach to virtual porosimetry

Analyzing the pore-size distribution of porous materials, made up of an aggregation of interconnected pores, is a demanding task. Mercury intrusion porosimetry (MIP) is a physical method that intrudes mercury into a sample at increasing pressures to obtain a poresize histogram. This method has been simulated in-silice with several approaches requiring prior computation of a skeleton. We present a new approach to simulate MIP that does not require skeleton computation. Our method is an iterative process that considers the diameters corresponding to pressures. At each iteration, geometric tests detect throats for the corresponding diameter and a CCL process collects the region invaded by the mercury. Additionally, a new decomposition model called CUDB, is used. This is suitable for computing the throats and performs better with the CCL algorithm than a voxel model. Our approach obtains the pore-size distribution of the porous medium, and the corresponding pore graph.Peer Reviewe