209 research outputs found
Nested Archimedean copulas: a new class of nonparametric tree structure estimators
Any nested Archimedean copula is defined starting from a rooted phylogenetic
tree, for which a new class of nonparametric estimators is presented. An
estimator from this new class relies on a two-step procedure where first a
binary tree is built and second is collapsed if necessary to give an estimate
of the target tree structure. Several examples of estimators from this class
are given and the performance of each of these estimators, as well as of the
only known comparable estimator, is assessed by means of a simulation study
involving target structures in various dimensions, showing that the new
estimators, besides being faster, usually offer better performance as well.
Further, among the given examples of estimators from the new class, one of the
best performing one is applied on three datasets: 482 students and their
results to various examens, 26 European countries in 1979 and the percentage of
workers employed in different economic activities, and 104 countries in 2002
for which various health-related variables are available. The resulting
estimated trees offer valuable insights on the analyzed data. The future of
nested Archimedean copulas in general is also discussed
On C2 cubic quasi-interpolating splines and their computation by subdivision via blossoming
We discuss the construction of C2 cubic spline quasi-interpolation schemes defined on a
refined partition. These schemes are reduced in terms of degrees of freedom compared to
those existing in the literature. Namely, we provide a rule for reducing them by imposing
super-smoothing conditions while preserving full smoothness and cubic precision. In
addition, we provide subdivision rules by means of blossoming. The derived rules are
designed to express the B-spline coefficients associated with a finer partition from those
associated with the former one."Maria de Maeztu" Excellence Unit IMAG (University of Granada, Spain) CEX2020-001105-MICIN/AEI/10.13039/501100011033University of Granada
University of Granada/CBU
New Models for High-Quality Surface Reconstruction and Rendering
The efficient reconstruction and artifact-free visualization of surfaces from measured real-world data is an important issue in various applications, such as medical and scientific visualization, quality control, and the media-related industry. The main contribution of this thesis is the development of the first efficient GPU-based reconstruction and visualization methods using trivariate splines, i.e., splines defined on tetrahedral partitions. Our methods show that these models are very well-suited for real-time reconstruction and high-quality visualizations of surfaces from volume data. We create a new quasi-interpolating operator which for the first time solves the problem of finding a globally C1-smooth quadratic spline approximating data and where no tetrahedra need to be further subdivided. In addition, we devise a new projection method for point sets arising from a sufficiently dense sampling of objects. Compared with existing approaches, high-quality surface triangulations can be generated with guaranteed numerical stability. Keywords. Piecewise polynomials; trivariate splines; quasi-interpolation; volume data; GPU ray casting; surface reconstruction; point set surface
New Models for High-Quality Surface Reconstruction and Rendering
The efficient reconstruction and artifact-free visualization of surfaces from measured real-world data is an important issue in various applications, such as medical and scientific visualization, quality control, and the media-related industry. The main contribution of this thesis is the development of the first efficient GPU-based reconstruction and visualization methods using trivariate splines, i.e., splines defined on tetrahedral partitions. Our methods show that these models are very well-suited for real-time reconstruction and high-quality visualizations of surfaces from volume data. We create a new quasi-interpolating operator which for the first time solves the problem of finding a globally C1-smooth quadratic spline approximating data and where no tetrahedra need to be further subdivided. In addition, we devise a new projection method for point sets arising from a sufficiently dense sampling of objects. Compared with existing approaches, high-quality surface triangulations can be generated with guaranteed numerical stability. Keywords. Piecewise polynomials; trivariate splines; quasi-interpolation; volume data; GPU ray casting; surface reconstruction; point set surface
Generalized Finite Element Systems for smooth differential forms and Stokes problem
We provide both a general framework for discretizing de Rham sequences of
differential forms of high regularity, and some examples of finite element
spaces that fit in the framework. The general framework is an extension of the
previously introduced notion of Finite Element Systems, and the examples
include conforming mixed finite elements for Stokes' equation. In dimension 2
we detail four low order finite element complexes and one infinite family of
highorder finite element complexes. In dimension 3 we define one low order
complex, which may be branched into Whitney forms at a chosen index. Stokes
pairs with continuous or discontinuous pressure are provided in arbitrary
dimension. The finite element spaces all consist of composite polynomials. The
framework guarantees some nice properties of the spaces, in particular the
existence of commuting interpolators. It also shows that some of the examples
are minimal spaces.Comment: v1: 27 pages. v2: 34 pages. Numerous details added. v3: 44 pages. 8
figures and several comments adde
Dynamic Multivariate Simplex Splines For Volume Representation And Modeling
Volume representation and modeling of heterogeneous objects acquired from real world are very challenging research tasks and playing fundamental roles in many potential applications, e.g., volume reconstruction, volume simulation and volume registration. In order to accurately and efficiently represent and model the real-world objects, this dissertation proposes an integrated computational framework based on dynamic multivariate simplex splines (DMSS) that can greatly improve the accuracy and efficacy of modeling and simulation of heterogenous objects. The framework can not only reconstruct with high accuracy geometric, material, and other quantities associated with heterogeneous real-world models, but also simulate the complicated dynamics precisely by tightly coupling these physical properties into simulation. The integration of geometric modeling and material modeling is the key to the success of representation and modeling of real-world objects.
The proposed framework has been successfully applied to multiple research areas, such as volume reconstruction and visualization, nonrigid volume registration, and physically based modeling and simulation
- …