Orientation, sphericity and roundness evaluation of particles using alternative 3D representations

Sphericity and roundness indices have been used mainly in geology to analyze the shape of particles. In this paper, geometric methods are proposed as an alternative to evaluate the orientation, sphericity and roundness indices of 3D objects. In contrast to previous works based on digital images, which use the voxel model, we represent the particles with the Extreme Vertices Model, a very concise representation for binary volumes. We define the orientation with three mutually orthogonal unit vectors. Then, some sphericity indices based on length measurement of the three representative axes of the particle can be computed. In addition, we propose a ray-casting-like approach to evaluate a 3D roundness index. This method provides roundness measurements that are highly correlated with those provided by the Krumbein's chart and other previous approach. Finally, as an example we apply the presented methods to analyze the sphericity and roundness of a real silica nano dataset.Postprint (published version

Compact union of disjoint boxes: An efficient decomposition model for binary volumes

This paper presents in detail the CompactUnion of Disjoint Boxes (CUDB), a decomposition modelfor binary volumes that has been recently but brieflyintroduced. This model is an improved version of aprevious model called Ordered Union of Disjoint Boxes(OUDB). We show here, several desirable features thatthis model has versus OUDB, such as less unitary basicelements (boxes) and thus, a better efficiency in someneighborhood operations. We present algorithms forconversion to and from other models, and for basiccomputations as area (2D) or volume (3D). We alsopresent an efficient algorithm for connected-componentlabeling (CCL) that does not follow the classical two-passstrategy. Finally we present an algorithm for collision (oradjacency) detection in static environments. We test theefficiency of CUDB versus existing models with severaldatasets.Peer ReviewedPostprint (published version

CUDB: An improved decomposition model for orthogonal pseudo-polyhedra

We present a new decomposition model for Orthogonal Pseudo-Polyhedra (OPP): the Compact Union of Disjoint Boxes. This model is an improved version of the Ordered Union of Disjoint Boxes model. Our model has many desirable features versus the OUDB, such as less storage size and a better efficiency in the connected-component labeling (CCL) process. CCL is a very important operation for manipulating volume data where multiple disconnected components that compose a volume need to be identify. We present the algorithms for conversion to and from the Extreme Vertices Model, which is closely related to the OUDB, and for CCL. The performance of the CUDB is experimentally analyzed with 2D and 3D datasets.Postprint (published version

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

Skeletonless porosimeter simulation

We introduce a new approach to simulate a virtual mercury intrusion porosimetry (MIP) using neither skeleton computing nor seed-growing methods. Most of the existing methods to determine local pore sizes in a porous medium require to compute the skeleton of the pore space. However, the skeleton computation is a very time consuming process. Instead, our approach uses a particular spatial enumeration encoding of the porous media, a set of disjoint boxes, and an algorithm able to determine the set of boxes invaded by the mercury at each iteration without any need of a previous skeleton computation. The algorithm detects all the pores which must be lled for a given mercury intrusion pressure, which is related to a diameter by the Washburn equation. The presented method is able to detect narrow throats and one-dimensional transitions between pores in order to prevent incorrect full uid invasion of the whole sample. The particular encoding used in this work is a new compact version of an existing model, the Ordered Union of Disjoint Boxes (OUDB). Finally, the pore size distribution of the porous medium and the corresponding pore graph can be obtained from the analyzed sample.Postprint (published version

Sphericity and roundness computation for particles using the extreme vertices model

Shape is a property studied for many kinds of particles. Among shape parameters, sphericity and roundness indices had been largely studied to understand several processes. Some of these indices are based on length measurements of the particle obtained from its oriented bounding box (OBB). In this paper we follow a discrete approach based on Extreme Vertices Model and devise new methods to compute the OBB and the mentioned indices. We apply these methods to synthetic sedimentary rocks and to a real dataset of silicon nanocrystals (Si NC) to analyze the obtained results and compare them with those obtained with a classical voxel model.Peer ReviewedPostprint (author's final draft

Determination of shape and sphericity of silicon quantum dots imaged by EFTEM-tomography

The shape of size-controlled silicon nanocrystals (Si NCs) embedded in SiO2 is investigated by tomographic energy-filtered transmission electron microscopy (EFTEM). The sphericity of the quantum dots is determined by computational analyses. In contrast to other fabrication methods, we demonstrate that the NCs in superlattices are non-agglomerated, individual clusters with slightly oblate spheroidal shape. This allows for low surface-to-volume ratios and thereby low non-radiative defect densities as required by optoelectronic or sensing applications. A near-spherical shape is also a prerequisite for the direct comparison of Si quantum dots (QDs) with theoretical simulationsPeer ReviewedPostprint (author's final draft

CUDB: An improved decomposition model for orthogonal pseudo-polyhedra

We present a new decomposition model for Orthogonal Pseudo-Polyhedra (OPP): the Compact Union of Disjoint Boxes. This model is an improved version of the Ordered Union of Disjoint Boxes model. Our model has many desirable features versus the OUDB, such as less storage size and a better efficiency in the connected-component labeling (CCL) process. CCL is a very important operation for manipulating volume data where multiple disconnected components that compose a volume need to be identify. We present the algorithms for conversion to and from the Extreme Vertices Model, which is closely related to the OUDB, and for CCL. The performance of the CUDB is experimentally analyzed with 2D and 3D datasets

Compact union of disjoint boxes: An efficient decomposition model for binary volumes

This paper presents in detail the CompactUnion of Disjoint Boxes (CUDB), a decomposition modelfor binary volumes that has been recently but brieflyintroduced. This model is an improved version of aprevious model called Ordered Union of Disjoint Boxes(OUDB). We show here, several desirable features thatthis model has versus OUDB, such as less unitary basicelements (boxes) and thus, a better efficiency in someneighborhood operations. We present algorithms forconversion to and from other models, and for basiccomputations as area (2D) or volume (3D). We alsopresent an efficient algorithm for connected-componentlabeling (CCL) that does not follow the classical two-passstrategy. Finally we present an algorithm for collision (oradjacency) detection in static environments. We test theefficiency of CUDB versus existing models with severaldatasets.Peer Reviewe