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‣ Development and Implementation of Nagata Patches Interpolation Algorithms

Neto, Diogo Mariano Simões
Fonte: Universidade de Coimbra Publicador: Universidade de Coimbra
Tipo: Dissertação de Mestrado
Português
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The main objective of this work is the development and implementation of Nagata patches interpolation algorithms to be used in the description of tools for the numerical simulation of sheet metal forming. Surface description accuracy is of paramount importance when modelling contact problems. However, most FEM researchers still resort to polyhedral models to describe contact surfaces, which can oversimplify the original system by neglecting the curvature. A simple algorithm for interpolating discretized surfaces and recover the original geometry was recently proposed by Nagata (2005). The main idea behind this parametric surface description is the quadratic interpolation of a curved segment, from the position and normal vectors at the end points. In this work, Nagata patches algorithms are first applied to interpolate polyhedral meshes of simple geometries (cylinder, sphere and torus) where the normal vectors in each node are provided by analytical functions. The use of triangular or quadrilateral Nagata patches is compared, both in terms of efficiency and robustness of the local interpolation algorithm. Afterwards, the interpolation algorithms are applied using different normal vectors approximations, to analyse the influence of the normal vector accuracy in the Nagata interpolation accuracy. Several methods for estimating the normal vector from polyhedral models are analyzed and their efficiency is studied...

‣ Desenvolvimento de uma base de funções paramétricas para interpolação de imagens médicas; Development of parametric basis function for interpolation of medical images

Soares, Isaias José Amaral
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Publicado em 03/07/2013 Português
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O uso de imagens é crucial na medicina, e seu uso no diagnóstico de doenças é uma das principais ferramentas clínicas da atualidade. Porém, frequentemente necessitam de pós-processamento para serem úteis. Embora ferramentas clássicas sejam utilizadas para esse fim, elas não dão tratamento específico a certas características de imagens fractais, como as provindas de sistemas biológicos. Nesse enfoque, este trabalho objetivou a criação de novas bases de interpolação utilizando a Q-Estatística para verificar se seriam estas seriam adequadas à representação de objetos com características fractais que as bases clássicas. Foram criados dois tipos de splines: uma unidimensional e outra bidimensional, que permitiram um tipo diferente de interpolação, fundamentado na q-Estatística. Os testes demonstraram a potencialidade dessas ferramentas para uso em sinais e imagens médicas, com acentuada redução do erro de interpolação no caso unidimensional (em até 351,876%) e uma redução sutil no caso bidimensional (0,3%). Como resultado adicional, foram criados filtros de imagens e avaliados seus resultados em imagens médicas, que resultaram em melhorias de até 1.340% de ganho efetivo na remoção de ruídos de natureza fractal (marrom). Os resultados sugerem que as q-bases desenvolvidas foram capazes de representar melhor imagens e sinais médicos...

‣ Evaluation of Spatial interpolation techniques for mapping climate variables with low sample density: a case study using a new gridded dataset of Bangladesh

Bhowmik, Avit Kumar
Fonte: Universidade Nova de Lisboa Publicador: Universidade Nova de Lisboa
Tipo: Dissertação de Mestrado
Publicado em 01/03/2012 Português
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Dissertation submitted in partial fulfillment of the requirements for the Degree of Master of Science in Geospatial Technologies.; This study explores and analyses the impact of sample density on the performances of the spatial interpolation techniques. It evaluates the performances of two alternative deterministic techniques – Thin Plate Spline and Inverse Distance Weighting, and two alternative stochastic techniques – Ordinary Kriging and Universal Kriging; to interpolate two climate indices - Annual Total Precipitation in Wet Days and the Yearly Maximum Value of the Daily Maximum Temperature, in a low sample density region - Bangladesh, for 60 years – 1948 to 2007. It implies the approach of Spatially Shifted Years to create mean variograms with respect to the low sample density. Seven different performance measurements - Mean Absolute Error, Root Mean Square Errors, Systematic Root Mean Square Errors, Unsystematic Root Mean Square Errors, Index of Agreement, Coefficient of Variation of Prediction and Confidence of Prediction, have been applied to evaluate the performance of the spatial interpolation techniques. The resulted performance measurements indicate that for most of the years the Universal Kriging method performs better to interpolate total precipitation...

‣ Ground truth determination for segmentation of tomographic volumes using interpolation

Rodolpho, Beatriz Leão
Fonte: Faculdade de Ciências e Tecnologia Publicador: Faculdade de Ciências e Tecnologia
Tipo: Dissertação de Mestrado
Publicado em //2013 Português
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Dissertação para obtenção do Grau de Mestre em Engenharia Biomédica; Optical projection tomographic microscopy allows for a 3D analysis of individual cells, making it possible to study its morphology. The 3D imagining technique used in this thesis uses white light excitation to image stained cells, and is referred to as single-cell optical computed tomography (cell CT). Studies have shown that morphological characteristics of the cell and its nucleus are deterministic in cancer diagnoses. For a more complete and accurate analysis of these characteristics, a fully-automated analysis of the single-cell 3D tomographic images can be done. The first step is segmenting the image into the different cell components. To assess how accurate the segmentation is, there is a need to determine ground truth of the automated segmentation. This dissertation intends to expose a method of obtaining ground truth for 3D segmentation of single cells. This was achieved by developing a software in CSharp. The software allows the user to input a visual segmentation of each 2D slice of a 3D volume by using a pen to trace the visually identified boundary of a cell component on a tablet. With this information, the software creates a segmentation of a 3D tomographic image that is a result of human visual segmentation. To increase the speed of this process...

‣ A new approach for regularized image interpolation

El-Khamy,S. E.; Hadhoud,M. M.; Dessouky,M. I.; Salam,B. M.; Abd El-Samie,F. E.
Fonte: Sociedade Brasileira de Computação Publicador: Sociedade Brasileira de Computação
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/04/2006 Português
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This paper presents a non-iterative regularized inverse solution to the image interpolation problem. This solution is based on the segmentation of the image to be interpolated into overlapping blocks and the interpolation of each block, separately. The purpose of the overlapping blocks is to avoid edge effects. A global regularization parameter is used in interpolating each block. In this solution, a single matrix inversion process of moderate dimensions is required in the whole interpolation process. Thus, it avoids the large computational cost due to the matrices of large dimensions involved in the interpolation process. The performance of this approach is compared to the standard iterative regularized interpolation scheme and to polynomial based interpolation schemes such as the bicubic and cubic spline techniques. A comparison of the suggested approach with some algorithms implemented in the commercial ACDSee software has been performend in the paper. The obtained results reveal that the suggested solution has a better performance as compared to other algorithms from the MSE and the edges preservation points of view. Its computation time is relatively large as compared to traditional algorithms but this is acceptable when image quality is the main concern.

‣ Interpolation and Denoising of Nonuniformly Sampled Data using Wavelet-domain Processing

Choi, Hyeokho; Baraniuk, Richard G.; Choi, Hyeokho; Baraniuk, Richard G.
Fonte: Universidade Rice Publicador: Universidade Rice
Tipo: Conference paper
Português
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Conference Paper; In this paper, we link concepts from nonuniform sampling, smoothness function spaces, interpolation, and denoising to derive a suite of multiscale, maximum-smoothness interpolation algorithms. We formulate the interpolation problem as the optimization of finding the signal that matches the given samples with smallest norm in a function smoothness space. For signals in the Besov space B," (Lp)t,h e optimization corresponds to convex programming in the wavelet domain; for signals in the Sobolev space We(&), the optimization reduces to a simple weighted least-squares problem. An optional wavelet shrinkage regularization step makes the algorithm suitable for even noisy sample data, unlike classical approaches such as bandlimited and spline interpolation.

‣ Lagrange rational interpolation and its applications to approximation of large-scale dynamical systems

Ionita, Antonio
Fonte: Universidade Rice Publicador: Universidade Rice
Português
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We present several new, efficient algorithms that extract low complexity models from frequency response measurements of large-scale dynamical systems. Our work is motivated by the fact that, in many applications, analytical models of a dynamical system are seldom available. Instead, we may only have access to its frequency response measurements. For example, for a system with multiple inputs and outputs, we may only have access to data sets of S-parameters. In this setting, our new approach extracts models that interpolate the given measurements. The extracted models have low complexity (or reduced order) and, thus, lead to short simulation times and low data storage requirements. The main tool used by our approach is Lagrange rational interpolation -- a generalization of the classic result of Lagrange polynomial interpolation. We present an in-depth look at Lagrange rational interpolation and provide several new insights and simplified proofs. This analysis leads to new algorithms that rely on the singular value decomposition (SVD) of the Loewner matrix pencil formed directly from the measurements. We show several new results on rational interpolation for measurements of linear, bi-linear and quadratic-linear systems. Furthermore...

‣ A Critical Comparison of Some Methods for Interpolation of Scattered Data

Franke, Richard
Fonte: Monterey, California: Naval Postgraduate School. Publicador: Monterey, California: Naval Postgraduate School.
Tipo: Relatório
Português
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Reproduction of all or part of this report authorized.; This report is concerned with methods for solving the scattered data interpolation problem: Given points x (subscript k), y (subscript k), f (subscript) k, k =1, ..., N, construct a smooth function, F (x,y), so that Fxk, ryk = fk, k -1, ...,N. A comparison of 29 methods for solution of this problem has been made. Each of the methods is discussed and the results of extensive testing for their properties and appropriate values of their parameters is given. Both local and global methods are considered. Comparisons of timing, storage, accuracy, visual pleasantness of the surface, and ease of implementation are made. A large number (over 200) of pages of perspective plots of surfaces are given. Suggestions for improvement of some methods are made, and methods which have poor approximation properties are identified.

‣ Nonuniform Interpolation of Noisy Signals Using Support Vector Machines

Rojo-Álvarez, José Luis; Figuera, Carlos; Martínez-Cruz, Carlos E.; Camps-Valls, Gustavo; Alonso-Atienza, Felipe; Martínez-Ramón, Manel
Fonte: The IEEE Publicador: The IEEE
Tipo: info:eu-repo/semantics/publishedVersion; info:eu-repo/semantics/article
Publicado em /08/2007 Português
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The problem of signal interpolation has been intensively studied in the information theory literature, in conditions such as unlimited band, nonuniform sampling, and presence of noise. During the last decade, support vector machines (SVM) have been widely used for approximation problems, including function and signal interpolation. However, the signal structure has not always been taken into account in SVM interpolation. We propose the statement of two novel SVM algorithms for signal interpolation, specifically, the primal and the dual signal model based algorithms. Shift-invariant Mercer's kernels are used as building blocks, according to the requirement of bandlimited signal. The sine kernel, which has received little attention in the SVM literature, is used for bandlimited reconstruction. Well-known properties of general SVM algorithms (sparseness of the solution, robustness, and regularization) are explored with simulation examples, yielding improved results with respect to standard algorithms, and revealing good characteristics in nonuniform interpolation of noisy signals.

‣ Study of interpolation methods for high-accuracy computations on overlapping grids

CHICHEPORTICHE, Jérémie; GLOERFELT, Xavier
Fonte: Elsevier Publicador: Elsevier
Português
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Overset strategy can be an efficient way to keep high-accuracy discretization by decomposing a complex geometry in topologically simple subdomains. Apart from the grid assembly algorithm, the key point of overset technique lies in the interpolation processes which ensure the communications between the overlapping grids. The family of explicit Lagrange and optimized interpolation schemes is studied. The a priori interpolation error is analyzed in the Fourier space, and combined with the error of the chosen discretization to highlight the modification of the numerical error. When high-accuracy algorithms are used an optimization of the interpolation coefficients can enhance the resolvality, which can be useful when high-frequency waves or small turbulent scales need to be supported by a grid. For general curvilinear grids in more than one space dimension, a mapping in a computational space followed by a tensorization of 1-D interpolations is preferred to a direct evaluation of the coefficient in the physical domain. A high-order extension of the isoparametric mapping is accurate and robust since it avoids the inversion of a matrix which may be ill-conditioned. A posteriori error analyses indicate that the interpolation stencil size must be tailored to the accuracy of the discretization scheme. For well discretized wavelengthes...

‣ Um estudo sobre algoritmos de interpolação de sequencias numericas; A study of algorithms for interpolation of numerical sequences

Eric Magalhães Delgado
Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 28/08/2009 Português
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Esta dissertação apresenta um estudo sobre algoritmos de interpolação e dizimação de sequências numéricas, cujos filtros são derivados do filtro de reconstrução ideal. É proposto um algoritmo adaptativo de interpolação cúbica e avaliado os ganhos deste algoritmo quando comparado aos algoritmos clássicos. A idéia é explorar o compromisso entre qualidade e complexidade dos filtros de interpolação. A adaptação do filtro, obtida através de estimativas espaciais e espectrais da sequência a ser interpolada, é útil já que proporciona um uso eficiente de filtros complexos em regiões criticas como, por exemplo, regiões de borda de uma imagem. Simulações em imagens típicas mostram um ganho quantitativo significativo do algoritmo adaptativo quando comparado aos algoritmos clássicos. Além disso, é analisado o algoritmo de interpolação quando existe informação do processo de aquisição da sequência a ser interpolada; This dissertation presents a study on interpolation and decimation algorithms of numerical sequences, whose filters are derived from the ideal reconstruction filter. An adaptive algorithm of cubic interpolation is proposed and the gains of this algorithm is analized by comparing with the classic algorithms. The idea is to explore the trade-off between quality and complexity of the interpolation filters. The adaptation of the filter...

‣ The real interpolation method on couples of intersections

Astashkin, S.V.; Sunehag, Peter
Fonte: Springer Publicador: Springer
Tipo: Artigo de Revista Científica
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Suppose that (X 0, X 1) is a Banach couple, X 0 ∩ X 1 is dense in X 0 and X 1, (X0,X1)θq (0 < θ < 1, 1 ≤ q < ∞) are the spaces of the real interpolation method, ψ ∈ (X 0 ∩ X 1)*, ψ ≠ 0, is a linear functional, N = Ker ψ, and N i stands fo

‣ Optimal interpolation grids for accurate numerical solutions of singular ordinary differential equations

Margitus, Michael
Fonte: Rochester Instituto de Tecnologia Publicador: Rochester Instituto de Tecnologia
Tipo: Tese de Doutorado
Português
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Researchers are interested in three types of error: experimental error, truncation error, and interpolation error. This thesis will study the last. Given a differential equation g"(x) = f(x) and a fixed number of interpolation grid points, an optimation problem is formulated to minimize the difference between f(x) and its interpolating function, thus reducing the error between the actual solution and the approximated solution of the ODE. Using the Nelder-Mead Simplex Method, the optimal distribution of grid points that will minimize the error between the solution g and its approximated solution will be found. This technique will then be applied to the one dimensional light scattering equation gxx = E²x/R. Using the Nelder-Mead Method, the optimal interpolation grid for a given number of grid points will be found. These numerical computations will ultimately be used to give guidance to experimenters on where to take measurements for the Rayleigh Ratio R.

‣ Spatial interpolation of monthly mean climate data for China

Hong, Yan; Nix, Henry A; Hutchinson, Michael; Booth, Trevor
Fonte: John Wiley & Sons Inc Publicador: John Wiley & Sons Inc
Tipo: Artigo de Revista Científica
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Spline interpolation techniques are used to develop a gridded climate database for China at a resolution of 0.01° in latitude and longitude. A digital elevation model (DEM) was developed at the same resolution to improve the accuracy of interpolation bas

‣ Exponential Spline Interpolation in Characteristic Based Scheme for Solving the Advective-Diffusion Equation

Zoppou, Christopher; Roberts, Stephen; Renka, R J
Fonte: John Wiley & Sons Inc Publicador: John Wiley & Sons Inc
Tipo: Artigo de Revista Científica
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This paper demonstrates the use of shape-preserving exponential spline interpolation in a characteristic based numerical scheme for the solution of the linear advective-diffusion equation. The results from this scheme are compared with results from a number of numerical schemes in current use using test problems in one and two dimensions. These test cases are used to assess the merits of using shape-preserving interpolation in a characteristic based scheme. The evaluation of the schemes is based on accuracy, efficiency, and complexity. The use of the shape-preserving interpolation in a characteristic based scheme is accurate, captures discontinuities, does not introduce spurious oscillations, and preserves the monotonicity and positivity properties of the exact solution. However, fitting exponential spline interpolants to the nodal concentrations is computationally expensive. Exponential spline interpolants were also fitted to the integral of the concentration profile. The integral of the concentration profile is a smoother function than the concentration profile. It requires less computational effort to fit an exponential spline interpolant to the integral than the nodal concentrations. By differentiating the interpolant, the nodal concentrations are obtained. This results in a more efficient and more accurate numerical scheme.

‣ Application of the modified Shepard interpolation method to the determination of the potential energy surface for a molecule�surface reaction: H 2 + Pt(111)

Crespos, C; Collins, Michael; Pijper, E; Kroes, G
Fonte: American Institute of Physics (AIP) Publicador: American Institute of Physics (AIP)
Tipo: Artigo de Revista Científica
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The technique to determine the potential energy surface (PES) for a molecule-surface reaction was presented using modified Shepard (MS) interpolation method. The efficiency and accuracy of the interpolation method for an activated multidimensional molecule-surface reactive problem was also analyzed. The efficiency of the interpolation method was tested by using an already existing PES to provide the input data required for the concentration of the new PES. It was shown that the MS interpolation method could be used efficiently to yield accurate PES for activated molecule-surface reactions.

‣ A Generalized Concept for Fuzzy Rule Interpolation

Baranyi, Peter; Gedeon, Tamas (Tom); Koczy, Lazlo
Fonte: Institute of Electrical and Electronics Engineers (IEEE Inc) Publicador: Institute of Electrical and Electronics Engineers (IEEE Inc)
Tipo: Artigo de Revista Científica
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The concept of fuzzy rule interpolation in sparse rule bases was introduced in 1993. It has become a widely researched topic in recent years because of its unique merits in the topic of fuzzy rule base complexity reduction. The first implemented technique of fuzzy rule interpolation was termed as α-cut distance based fuzzy rule base interpolation. Despite its advantageous properties in various approximation aspects and in complexity reduction, it was shown that it has some essential deficiencies, for instance, it does not always result in immediately interpretable fuzzy membership functions. This fact inspired researchers to develop various kinds of fuzzy rule interpolation techniques in order to alleviate these deficiencies. This paper is an attempt into this direction. It proposes an interpolation methodology, whose key idea is based on the interpolation of relations instead of interpolating α-cut distances, and which offers a way to derive a family of interpolation methods capable of eliminating some typical deficiencies of fuzzy rule interpolation techniques. The proposed concept of interpolating relations is elaborated here using fuzzy- and semantic-relations. This paper presents numerical examples, in comparison with former approaches...

‣ Multilinear interpolation between adjoint operators

Tao, T; Grafakos, Loukas
Fonte: Academic Press Publicador: Academic Press
Tipo: Artigo de Revista Científica
Português
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Multilinear interpolation is a powerful tool used in obtaining strong-type boundedness for a variety of operators assuming only a finite set of restricted weak-type estimates. A typical situation occurs when one knows that a multilinear operator satisfies a weak Lq estimate for a single index q (which may be less than one) and that all the adjoints of the multilinear operator are of similar nature, and thus they also satisfy the same weak Lq estimate. Under this assumption, in this note we give a general multilinear interpolation theorem which allows one to obtain strong-type boundedness for the operator (and all of its adjoints) for a large set of exponents. The key point in the applications we discuss is that the interpolation theorem can handle the case q ≤ 1. When q > 1, weak Lq has a predual, and such strong-type boundedness can be easily obtained by duality and multilinear interpolation (cf. Interpolation Spaces, An Introduction, Springer, New York, 1976; Math. Ann. 319 (2001) 151; in: Function Spaces and Applications (Lund, 1986), Lecture Notes in Mathematics, Vol. 1302, Springer, Berlin, New York, 1988; J. Amer. Math. Soc. 15 (2002) 469; Proc. Amer. Math. Soc. 21 (1969) 441).

‣ Fuzzy Rule Interpolation for Multidimensional Input Spaces With Applications: A Case Study

Wong, Kok Wai; Tikk, Domonkos; Gedeon, Tamas (Tom); Koczy, Lazlo
Fonte: Institute of Electrical and Electronics Engineers (IEEE Inc) Publicador: Institute of Electrical and Electronics Engineers (IEEE Inc)
Tipo: Artigo de Revista Científica
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Fuzzy rule based systems have been very popular in many engineering applications. However, when generating fuzzy rules from the available information, this may result in a sparse fuzzy rule base. Fuzzy rule interpolation techniques have been established to solve the problems encountered in processing sparse fuzzy rule bases. In most engineering applications, the use of more than one input variable is common, however, the majority of the fuzzy rule interpolation techniques only present detailed analysis to one input variable case. This paper investigates characteristics of two selected fuzzy rule interpolation techniques for multidimensional input spaces and proposes an improved fuzzy rule interpolation technique to handle multidimensional input spaces. The three methods are compared by means of application examples in the field of petroleum engineering and mineral processing. The results show that the proposed fuzzy rule interpolation technique for multidimensional input spaces can be used in engineering applications.

‣ Meteorological objective analysis using multiquadric interpolation scheme over India and adjoining region

SINHA,S. K.; MAHAKUR,M.; MAHAJAN,P.N.
Fonte: Centro de Ciencias de la Atmósfera, UNAM Publicador: Centro de Ciencias de la Atmósfera, UNAM
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/01/2002 Português
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This paper is concerned with the development of the multiquadric interpolation scheme to produce gridded fields of meteorological variables. The results of the application of this method to real data is compared with analysis from Gandhi's Optimum Interpolation scheme. Like the optimum interpolation scheme, which uses covariance functions as the basis functions, the multiquadric scheme uses hyperboloid radial basis function to fit the scattered data to a uniform grid. This scheme produces superior analysis compared to optimum interpolation analysis.