126 research outputs found

    Faster ASV decomposition for orthogonal polyhedra using the Extreme Vertices Model (EVM)

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    The alternating sum of volumes (ASV) decomposition is a widely used technique for converting a B-Rep into a CSG model. The obtained CSG tree has convex primitives at its leaf nodes, while the contents of its internal nodes alternate between the set union and difference operators. This work first shows that the obtained CSG tree T can also be expressed as the regularized Exclusive-OR operation among all the convex primitives at the leaf nodes of T, regardless the structure and internal nodes of T. This is an important result in the case in which EVM represented orthogonal polyhedra are used because in this model the Exclusive-OR operation runs much faster than set union and difference operations. Therefore this work applies this result to EVM represented orthogonal polyhedra. It also presents experimental results that corroborate the theoretical results and includes some practical uses for the ASV decomposition of orthogonal polyhedra.Postprint (published version

    CUDB: An improved decomposition model for orthogonal pseudo-polyhedra

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    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

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

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    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

    Contribution to structural parameters computation: volume models and methods

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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

    Skeletal representations of orthogonal shapes

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    Skeletal representations are important shape descriptors which encode topological and geometrical properties of shapes and reduce their dimension. Skeletons are used in several fields of science and attract the attention of many researchers. In the biocad field, the analysis of structural properties such as porosity of biomaterials requires the previous computation of a skeleton. As the size of three-dimensional images become larger, efficient and robust algorithms that extract simple skeletal structures are required. The most popular and prominent skeletal representation is the medial axis, defined as the shape points which have at least two closest points on the shape boundary. Unfortunately, the medial axis is highly sensitive to noise and perturbations of the shape boundary. That is, a small change of the shape boundary may involve a considerable change of its medial axis. Moreover, the exact computation of the medial axis is only possible for a few classes of shapes. For example, the medial axis of polyhedra is composed of non planar surfaces, and its accurate and robust computation is difficult. These problems led to the emergence of approximate medial axis representations. There exists two main approximation methods: the shape is approximated with another shape class or the Euclidean metric is approximated with another metric. The main contribution of this thesis is the combination of a specific shape and metric simplification. The input shape is approximated with an orthogonal shape, which are polygons or polyhedra enclosed by axis-aligned edges or faces, respectively. In the same vein, the Euclidean metric is replaced by the L infinity or Chebyshev metric. Despite the simpler structure of orthogonal shapes, there are few works on skeletal representations applied to orthogonal shapes. Much of the efforts have been devoted to binary images and volumes, which are a subset of orthogonal shapes. Two new skeletal representations based on this paradigm are introduced: the cube skeleton and the scale cube skeleton. The cube skeleton is shown to be composed of straight line segments or planar faces and to be homotopical equivalent to the input shape. The scale cube skeleton is based upon the cube skeleton, and introduces a family of skeletons that are more stable to shape noise and perturbations. In addition, the necessary algorithms to compute the cube skeleton of polygons and polyhedra and the scale cube skeleton of polygons are presented. Several experimental results confirm the efficiency, robustness and practical use of all the presented methods

    ISSUES IN THE CONTROL OF HALFSPACE SYSTEMS

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    By the name HALFSPACE SYSTEMS, this dissertation refers to systems whose dynamics are modeled by linear constraints of the form Exk+1 \u3c= Fxk + Buk (where E, F 2 andlt;mn, B 2 andlt;mp). This dissertation explores the concepts of BOUNDEDNESS, STABILITY, IRREDUNDANCY, and MAINTAINABILITY (which is the same as REACHABILITY OF A TARGET TUBE) that are related to the control of halfspace systems. Given that a halfspace system is bounded, and that a given static target tube is reachable for this system, this dissertation presents algorithms to MAINTAIN the system in this target tube. A DIFFERENCE INCLUSION has the form xk+1 = Axk + Buuk, where xk, xk+1 2 andlt;n, uk 2 andlt;p, A 2 andlt;nn, Bu 2 andlt;np, Ai 2 andlt;nn, Bj 2 andlt;np, and A and Bu belong to the convex hulls of (A1,A2, . . . ,Aq) and (B1, B2, . . . , Br) respectively. This dissertation investigates the possibility that halfspace systems have equivalent difference inclusion representation for the case of uk = 0. An affirmitive result in this direction may make it possible to apply to halfspace systems the control theory that exists for difference inclusions

    Automatic creation of boundary-representation models from single line drawings

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    This thesis presents methods for the automatic creation of boundary-representation models of polyhedral objects from single line drawings depicting the objects. This topic is important in that automated interpretation of freehand sketches would remove a bottleneck in current engineering design methods. The thesis does not consider conversion of freehand sketches to line drawings or methods which require manual intervention or multiple drawings. The thesis contains a number of novel contributions to the art of machine interpretation of line drawings. Line labelling has been extended by cataloguing the possible tetrahedral junctions and by development of heuristics aimed at selecting a preferred labelling from many possible. The ”bundling” method of grouping probably-parallel lines, and the use of feature detection to detect and classify hole loops, are both believed to be original. The junction-line-pair formalisation which translates the problem of depth estimation into a system of linear equations is new. Treating topological reconstruction as a tree-search is not only a new approach but tackles a problem which has not been fully investigated in previous work

    Iterative Schedule Optimization for Parallelization in the Polyhedron Model

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    In high-performance computing, one primary objective is to exploit the performance that the given target hardware can deliver to the fullest. Compilers that have the ability to automatically optimize programs for a specific target hardware can be highly useful in this context. Iterative (or search-based) compilation requires little or no prior knowledge and can adapt more easily to concrete programs and target hardware than static cost models and heuristics. Thereby, iterative compilation helps in situations in which static heuristics do not reflect the combination of input program and target hardware well. Moreover, iterative compilation may enable the derivation of more accurate cost models and heuristics for optimizing compilers. In this context, the polyhedron model is of help as it provides not only a mathematical representation of programs but, more importantly, a uniform representation of complex sequences of program transformations by schedule functions. The latter facilitates the systematic exploration of the set of legal transformations of a given program. Early approaches to purely iterative schedule optimization in the polyhedron model do not limit their search to schedules that preserve program semantics and, thereby, suffer from the need to explore numbers of illegal schedules. More recent research ensures the legality of program transformations but presumes a sequential rather than a parallel execution of the transformed program. Other approaches do not perform a purely iterative optimization. We propose an approach to iterative schedule optimization for parallelization and tiling in the polyhedron model. Our approach targets loop programs that profit from data locality optimization and coarse-grained loop parallelization. The schedule search space can be explored either randomly or by means of a genetic algorithm. To determine a schedule's profitability, we rely primarily on measuring the transformed code's execution time. While benchmarking is accurate, it increases the time and resource consumption of program optimization tremendously and can even make it impractical. We address this limitation by proposing to learn surrogate models from schedules generated and evaluated in previous runs of the iterative optimization and to replace benchmarking by performance prediction to the extent possible. Our evaluation on the PolyBench 4.1 benchmark set reveals that, in a given setting, iterative schedule optimization yields significantly higher speedups in the execution of the program to be optimized. Surrogate performance models learned from training data that was generated during previous iterative optimizations can reduce the benchmarking effort without strongly impairing the optimization result. A prerequisite for this approach is a sufficient similarity between the training programs and the program to be optimized
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