397 research outputs found
Interpolating point spread function anisotropy
Planned wide-field weak lensing surveys are expected to reduce the
statistical errors on the shear field to unprecedented levels. In contrast,
systematic errors like those induced by the convolution with the point spread
function (PSF) will not benefit from that scaling effect and will require very
accurate modeling and correction. While numerous methods have been devised to
carry out the PSF correction itself, modeling of the PSF shape and its spatial
variations across the instrument field of view has, so far, attracted much less
attention. This step is nevertheless crucial because the PSF is only known at
star positions while the correction has to be performed at any position on the
sky. A reliable interpolation scheme is therefore mandatory and a popular
approach has been to use low-order bivariate polynomials. In the present paper,
we evaluate four other classical spatial interpolation methods based on splines
(B-splines), inverse distance weighting (IDW), radial basis functions (RBF) and
ordinary Kriging (OK). These methods are tested on the Star-challenge part of
the GRavitational lEnsing Accuracy Testing 2010 (GREAT10) simulated data and
are compared with the classical polynomial fitting (Polyfit). We also test all
our interpolation methods independently of the way the PSF is modeled, by
interpolating the GREAT10 star fields themselves (i.e., the PSF parameters are
known exactly at star positions). We find in that case RBF to be the clear
winner, closely followed by the other local methods, IDW and OK. The global
methods, Polyfit and B-splines, are largely behind, especially in fields with
(ground-based) turbulent PSFs. In fields with non-turbulent PSFs, all
interpolators reach a variance on PSF systematics better than
the upper bound expected by future space-based surveys, with
the local interpolators performing better than the global ones
Weighted Quasi Interpolant Spline Approximations: Properties and Applications
Continuous representations are fundamental for modeling sampled data and
performing computations and numerical simulations directly on the model or its
elements. To effectively and efficiently address the approximation of point
clouds we propose the Weighted Quasi Interpolant Spline Approximation method
(wQISA). We provide global and local bounds of the method and discuss how it
still preserves the shape properties of the classical quasi-interpolation
scheme. This approach is particularly useful when the data noise can be
represented as a probabilistic distribution: from the point of view of
nonparametric regression, the wQISA estimator is robust to random
perturbations, such as noise and outliers. Finally, we show the effectiveness
of the method with several numerical simulations on real data, including curve
fitting on images, surface approximation and simulation of rainfall
precipitations
Memetic electromagnetism algorithm for surface reconstruction with rational bivariate Bernstein basis functions
Surface reconstruction is a very important issue with outstanding applications in fields such as medical imaging (computer tomography, magnetic resonance), biomedical engineering (customized prosthesis and medical implants), computer-aided design and manufacturing (reverse engineering for the automotive, aerospace and shipbuilding industries), rapid prototyping (scale models of physical parts from CAD data), computer animation and film industry (motion capture, character modeling), archaeology (digital representation and storage of archaeological sites and assets), virtual/augmented reality, and many others. In this paper we address the surface reconstruction problem by using rational Bézier surfaces. This problem is by far more complex than the case for curves we solved in a previous paper. In addition, we deal with data points subjected to measurement noise and irregular sampling, replicating the usual conditions of real-world applications. Our method is based on a memetic approach combining a powerful metaheuristic method for global optimization (the electromagnetism algorithm) with a local search method. This method is applied to a benchmark of five illustrative examples exhibiting challenging features. Our experimental results show that the method performs very well, and it can recover the underlying shape of surfaces with very good accuracy.This research is kindly supported by the Computer Science National Program of the Spanish Ministry of Economy and Competitiveness, Project #TIN2012-30768, Toho University, and the University of Cantabria. The authors are particularly grateful to the Department of Information Science of Toho University for all the facilities given to carry out this work. We also thank the Editor and the two anonymous reviewers who helped us to improve our paper with several constructive comments and suggestions
Hybrid Functional-Neural Approach for Surface Reconstruction
ABSTRACT. This paper introduces a new hybrid functional-neural approach for surface reconstruction. Our approach is based on the combination of two powerful artificial intelligence paradigms: on one hand, we apply the popular Kohonen neural network to address the data parameterization problem. On the other hand, we introduce a new functional network, called NURBS functional network, whose topology is aimed at reproducing faithfully the functional structure of the NURBS surfaces. These neural and functional networks are applied in an iterative fashion for further surface refinement. The hybridization of these two networks provides us with a powerful computational approach to obtain a NURBS fitting surface to a set of irregularly sampled noisy data points within a prescribed error threshold. The method has been applied to two illustrative examples. The experimental results confirm the good performance of our approach.This research has been kindly supported by the Computer
Science National Program of the Spanish Ministry of Economy
and Competitiveness, Project ref. no. TIN2012-30768,
Toho University (Funabashi, Japan), and the University of
Cantabria (Santander, Spain)
Study of weighted fusion methods for the measurement of surface geometry
Four types of weighted fusion methods, including pixel-level, least-squares, parametrical and non-parametrical, have been classified and theoretically analysed in this study. In particular, the uncertainty propagation of the weighted least-squares fusion was analysed and its relation to the Kalman filter was studied. In cooperation with different fitting models, these four weighted fusion methods can be applied to a range of measurement challenges. The experimental results of this study show that the four weighted fusion methods compose a computationally efficient and reliable system for multi-sensor measurement problems, especially for freeform surface measurement. A comparison of weighted fusion with residual approximation-based fusion has also been conducted by providing the input datasets with different noise levels and sample sizes. The results demonstrated that weighted fusion and residual approximation-based fusion are complementary approaches applicable to most fusion scenarios
Research issues in data modeling for scientific visualization
This article summarizes some topics of modeling as they impinge on the future development of scientific data visualization. The benefits from visualization techniques in analyzing data are well established, but to build on these pioneering efforts, one must recognize modeling as a distinct structural component in the larger context of visualization and problem-solving systems. Volume modeling is the entry way to this arena of future development, and model-based rendering describes how scientists will view the results. Important side developments such as multiresolution modeling and model-based segmentation will contribute structural capability to these systems. All of these components ultimately depend on the mathematical foundations of scattered data modeling and on model validation and standards to incorporate this modeling methodology into effective tools for scientific inquiry.Postprint (published version
- …