49 research outputs found

    Two hierarchies of spline interpolations. Practical algorithms for multivariate higher order splines

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    A systematic construction of higher order splines using two hierarchies of polynomials is presented. Explicit instructions on how to implement one of these hierarchies are given. The results are limited to interpolations on regular, rectangular grids, but an approach to other types of grids is also discussed

    Insect phenology: a geographical perspective

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    Motion enriching using humanoide captured motions

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    Animated humanoid characters are a delight to watch. Nowadays they are extensively used in simulators. In military applications animated characters are used for training soldiers, in medical they are used for studying to detect the problems in the joints of a patient, moreover they can be used for instructing people for an event(such as weather forecasts or giving a lecture in virtual environment). In addition to these environments computer games and 3D animation movies are taking the benefit of animated characters to be more realistic. For all of these mediums motion capture data has a great impact because of its speed and robustness and the ability to capture various motions. Motion capture method can be reused to blend various motion styles. Furthermore we can generate more motions from a single motion data by processing each joint data individually if a motion is cyclic. If the motion is cyclic it is highly probable that each joint is defined by combinations of different signals. On the other hand, irrespective of method selected, creating animation by hand is a time consuming and costly process for people who are working in the art side. For these reasons we can use the databases which are open to everyone such as Computer Graphics Laboratory of Carnegie Mellon University.Creating a new motion from scratch by hand by using some spatial tools (such as 3DS Max, Maya, Natural Motion Endorphin or Blender) or by reusing motion captured data has some difficulties. Irrespective of the motion type selected to be animated (cartoonish, caricaturist or very realistic) human beings are natural experts on any kind of motion. Since we are experienced with other peoples’ motions, and comparing each motion to the others, we can easily judge one individual’s mood from his/her body language. As being a natural master of human motions it is very difficult to convince people by a humanoid character’s animation since the recreated motions can include some unnatural artifacts (such as foot-skating, flickering of a joint)

    Bayesian Nonparametric Differential Equation Models for Functions

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    Bayesian nonparametric methods develop priors over a large class of functions that essentially allow any continuous function to be modeled. Though these methods are flexible, they are black box approaches that do not explicitly incorporate additional information on the shape of the curve. In many contexts, though the exact parametric form of the curve is unknown, additional scientific information is available in the form of differential operators. This dissertation develops nonparametric priors over function spaces that are specified by differential operators. Here two novel approaches to nonparametric function estimation are considered. In the first approach the prior is specified by a linear differential equation. The Mechanistic Hierarchical Gaussian process defines a prior over functions consistent with a differential operator. The method is applied to muscle force tracings in a functional ANOVA context, and is shown to adequately describe the between subject variability often seen in such tracings. In the second case a novel spline based approach is considered. Here prior information is specifies the maximum number of extrema (changepoints) for an arbitrary function located on an open set in R. The Local Extrema (LX) spline models the first derivative of the curve and puts a prior over the maximum number of changepoints. This method is applied to animal toxicology studies, human health surveys, and seasonal data; and it is shown to remove artifactual bumps common to other nonparametric methods. It is further shown to superior in terms of estimated squared error loss in simulation studies.Doctor of Philosoph

    Computations of Delaunay and Higher Order Triangulations, with Applications to Splines

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    Digital data that consist of discrete points are frequently captured and processed by scientific and engineering applications. Due to the rapid advance of new data gathering technologies, data set sizes are increasing, and the data distributions are becoming more irregular. These trends call for new computational tools that are both efficient enough to handle large data sets and flexible enough to accommodate irregularity. A mathematical foundation that is well-suited for developing such tools is triangulation, which can be defined for discrete point sets with little assumption about their distribution. The potential benefits from using triangulation are not fully exploited. The challenges fundamentally stem from the complexity of the triangulation structure, which generally takes more space to represent than the input points. This complexity makes developing a triangulation program a delicate task, particularly when it is important that the program runs fast and robustly over large data. This thesis addresses these challenges in two parts. The first part concentrates on techniques designed for efficiently and robustly computing Delaunay triangulations of three kinds of practical data: the terrain data from LIDAR sensors commonly found in GIS, the atom coordinate data used for biological applications, and the time varying volume data generated from from scientific simulations. The second part addresses the problem of defining spline spaces over triangulations in two dimensions. It does so by generalizing Delaunay configurations, defined as follows. For a given point set P in two dimensions, a Delaunay configuration is a pair of subsets (T, I) from P, where T, called the boundary set, is a triplet and I, called the interior set, is the set of points that fall in the circumcircle through T. The size of the interior set is the degree of the configuration. As recently discovered by Neamtu (2004), for a chosen point set, the set of all degree k Delaunay configurations can be associated with a set of degree k plus 1 splines that form the basis of a spline space. In particular, for the trivial case of k equals 0, the spline space coincides with the PL interpolation functions over the Delaunay triangulation. Neamtu’s definition of the spline space relies only on a few structural properties of the Delaunay configurations. This raises the question whether there exist other sets of configurations with identical structural properties. If there are, then these sets of configurations—let us call them generalized configurations from hereon—can be substituted for Delaunay configurations in Neamtu’s definition of spline space thereby yielding a family of splines over the same point set

    New Techniques for the Modeling, Processing and Visualization of Surfaces and Volumes

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    With the advent of powerful 3D acquisition technology, there is a growing demand for the modeling, processing, and visualization of surfaces and volumes. The proposed methods must be efficient and robust, and they must be able to extract the essential structure of the data and to easily and quickly convey the most significant information to a human observer. Independent of the specific nature of the data, the following fundamental problems can be identified: shape reconstruction from discrete samples, data analysis, and data compression. This thesis presents several novel solutions to these problems for surfaces (Part I) and volumes (Part II). For surfaces, we adopt the well-known triangle mesh representation and develop new algorithms for discrete curvature estimation,detection of feature lines, and line-art rendering (Chapter 3), for connectivity encoding (Chapter 4), and for topology preserving compression of 2D vector fields (Chapter 5). For volumes, that are often given as discrete samples, we base our approach for reconstruction and visualization on the use of new trivariate spline spaces on a certain tetrahedral partition. We study the properties of the new spline spaces (Chapter 7) and present efficient algorithms for reconstruction and visualization by iso-surface rendering for both, regularly (Chapter 8) and irregularly (Chapter 9) distributed data samples

    Fast Visualization by Shear-Warp using Spline Models for Data Reconstruction

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    This work concerns oneself with the rendering of huge three-dimensional data sets. The target thereby is the development of fast algorithms by also applying recent and accurate volume reconstruction models to obtain at most artifact-free data visualizations. In part I a comprehensive overview on the state of the art in volume rendering is given. Part II is devoted to the recently developed trivariate (linear,) quadratic and cubic spline models defined on symmetric tetrahedral partitions directly obtained by slicing volumetric partitions of a three-dimensional domain. This spline models define piecewise polynomials of total degree (one,) two and three with respect to a tetrahedron, i.e. the local splines have the lowest possible total degree and are adequate for efficient and accurate volume visualization. The following part III depicts in a step by step manner a fast software-based rendering algorithm, called shear-warp. This algorithm is prominent for its ability to generate projections of volume data at real time. It attains the high rendering speed by using elaborate data structures and extensive pre-computation, but at the expense of data redundancy and visual quality of the finally obtained rendering results. However, to circumvent these disadvantages a further development is specified, where new techniques and sophisticated data structures allow combining the fast shear-warp with the accurate ray-casting approach. This strategy and the new data structures not only grant a unification of the benefits of both methods, they even easily admit for adjustments to trade-off between rendering speed and precision. With this further development also the 3-fold data redundancy known from the original shear-warp approach is removed, allowing the rendering of even larger three-dimensional data sets more quickly. Additionally, real trivariate data reconstruction models, as discussed in part II, are applied together with the new ideas to onward the precision of the new volume rendering method, which also lead to a one order of magnitude faster algorithm compared to traditional approaches using similar reconstruction models. In part IV, a hierarchy-based rendering method is developed which utilizes a wavelet decomposition of the volume data, an octree structure to represent the sparse data set, the splines from part II and a new shear-warp visualization algorithm similar to that presented in part III. This thesis is concluded by the results centralized in part V

    Learning models for intelligent photo editing

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    Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference

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    The 6th ECCOMAS Young Investigators Conference YIC2021 will take place from July 7th through 9th, 2021 at Universitat Politècnica de València, Spain. The main objective is to bring together in a relaxed environment young students, researchers and professors from all areas related with computational science and engineering, as in the previous YIC conferences series organized under the auspices of the European Community on Computational Methods in Applied Sciences (ECCOMAS). Participation of senior scientists sharing their knowledge and experience is thus critical for this event.YIC 2021 is organized at Universitat Politécnica de València by the Sociedad Española de Métodos Numéricos en Ingeniería (SEMNI) and the Sociedad Española de Matemática Aplicada (SEMA). It is promoted by the ECCOMAS.The main goal of the YIC 2021 conference is to provide a forum for presenting and discussing the current state-of-the-art achievements on Computational Methods and Applied Sciences,including theoretical models, numerical methods, algorithmic strategies and challenging engineering applications.Nadal Soriano, E.; Rodrigo Cardiel, C.; Martínez Casas, J. (2022). Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference. Editorial Universitat Politècnica de València. https://doi.org/10.4995/YIC2021.2021.15320EDITORIA
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