EVM: A Complete Solid Model for Surface Rendering

Rodríguez, Jorge; Ayala, Dolors; Aguilera, Antonio

doi:10.1007/978-3-662-07443-5_16

Cited by 5 publications

(7 citation statements)

References 17 publications

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“…We have tested merging faces with and without shape preservation in several 3D datasets with different shape features, obtained from public repositories and our own collection. All of them have been converted to EVM using existing algorithms [17]. The presented algorithms have been written in C++ and executed on a PC Intel R Core i7 CPU 870 at 2.93GHz with 16Gb of RAM under Linux.…”

Section: Resultsmentioning

confidence: 99%

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Merging Faces: A New Orthogonal Simplification of Solid Models

Cruz-Matías

Ayala

2013

Discrete Geometry for Computer Imagery

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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.

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Section: Resultsmentioning

confidence: 99%

“…The ⊗ * is even faster, EV M (P ⊗ * Q) = EV M (P )⊗ * EV M (Q), i.e, it is a simple point-wise xor, without section computation. For more details concerning EVM see [1] and [17].…”

Section: Extreme Vertices Model (Evm)mentioning

confidence: 99%

Merging Faces: A New Orthogonal Simplification of Solid Models

Cruz-Matías

Ayala

2013

Discrete Geometry for Computer Imagery

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“…This together with the fact that sections can be computed from cuts allows to prove the completeness of this codification as a boundary model [3], [4]. Moreover, its efficiency in terms of memory requirements, compared to that of the semiboundary representation [16], which is usually considered as the most efficient block-form representation, has been shown to be clearly favorable [1]. Arbitrary boolean operations between OPPs can be carried out by applying recursively the same operation over the corresponding OPP sections which can be reduced to XOR operations between the extreme vertex encodings of both operands [2].…”

Section: Extreme Vertex Encodingmentioning

confidence: 99%

Efficient Computation of 3D Skeletons by Extreme Vertex Encoding

Rodríguez

Thomas²,

Ayala

et al. 2003

Discrete Geometry for Computer Imagery

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Abstract. Many skeletonisation algorithms for discrete volumes have been proposed. Despite its simplicity, the one given here still has many theoretically favorable properties. Actually, it provides a connected surface skeleton that allows shapes to be reconstructed with bounded error. It is based on the application of directional erosions, while retaining those voxels that introduce disconnections. This strategy is proved to be specially well-suited for extreme vertex encoded volumes, leading to a fast thinning algorithm.

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“…This representation scheme stores only the boundary voxels of the volume keeping the information of the interior voxels in an implicit way. It requires seven to eight times less storage space and achieves three to five times faster computation than the voxel model [164], and allows fast visualization and manipulation operations with a set of ad-hoc operations specially designed to exploit the conciseness of the model [127]. Shell representation [165] has the same indexing scheme used in the SB representation, but the set of voxels, which belongs to the list that contains all the boundary voxels of the volume, was redefined in order to represent objects with fuzzy boundaries.…”

Section: Boundary Representationsmentioning

confidence: 99%

“…EVM [1,3] is a very concise representation scheme in which any OPP can be described using a subset of its vertices: the extreme vertices. EVM is actually a complete solid model, it is an implicit B-Rep model, i.e., all the geometry and topological relations concerning faces, edges and vertices of the represented OPP can be obtained from the EVM [125]. This representation model has been used to prove the suitability of OPP as geometric bounds in CSG [2].…”

Section: Boundary Representationsmentioning

confidence: 99%

Contribution to structural parameters computation: volume models and methods

Cruz Matías

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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.

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EVM: A Complete Solid Model for Surface Rendering

Cited by 5 publications

References 17 publications

Merging Faces: A New Orthogonal Simplification of Solid Models

Merging Faces: A New Orthogonal Simplification of Solid Models

Efficient Computation of 3D Skeletons by Extreme Vertex Encoding

Contribution to structural parameters computation: volume models and methods

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