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Decomposition of mixed pixels in MODIS data using bernstein basis functions

JOURNAL OF APPLIED REMOTE SENSING 2019年第4期13卷

作者： Qin, Yi Guo, Feng Ren, Yupeng Wang, Xin Gu, Juan Ma, Jingyu Zou, Lejun Shen, Xiaohua Zhejiang Univ Sch Earth Sci Hangzhou Peoples R China Geomat Ctr Zhejiang Third Tech Serv Dept Hangzhou Peoples R China

The decomposition of mixed pixels in Moderate Resolution Imaging Spectroradiometer (MODIS) images is essential for the application of MODIS data in many fields. Many existing methods for unmixing mixed pixels use principal component analysis to reduce the dimensionality of the image data and require the extraction of endmember spectra. We propose the pixel spectral unmixing index (PSUI) method for unmixing mixed pixels in MODIS images. In this method, a set of third-order bernstein basis functions is applied to reduce the dimensionality of the image data and characterize the spectral curves of the mixed pixels in a MODIS image, and then the derived PSUIs (i.e., the coefficients of the basis functions) are calibrated by means of the abundance values of the ground features from the Landsat Enhanced Thematic Mapper Plus (ETM+)/Operational Land Imager (OLI) classification images corresponding to the date and region of the MODIS image. The proposed method was tested on MODIS and ETM+/OLI images, and it obtained satisfying unmixing results. We compared the PSUI method with conventional methods, including the pixel purity index, the N-finder algorithm, the sequential maximum angle convex cone, and vertex component analysis and found that the PSUI method outperformed the other four methods. (C) The Authors. Published by SPIE under a Creative Commons Attribution 4.0 Unported License.

关键词： bernstein basis functions mixed pixels Moderate Resolution Imaging Spectroradiometer image pixel spectral unmixing index

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8-node quasi-conforming plane element by using bernstein basis functions

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EUROPEAN JOURNAL OF MECHANICS A-SOLIDS 2018年 70卷 127-140页

作者： Wang, Changsheng Lu, Xingtong Zhang, Xiangkui Hu, Ping Dalian Univ Technol State Key Lab Struct Anal Ind Equipment Sch Automot Engn Dalian 116023 Peoples R China

bernstein basis functions are used extensively in geometric modeling for their excellent merits. In this paper, a new 8-node assumed stress quasi-conforming plane element is proposed by using bernstein basis functions. Firstly, the fundamental analytical solutions, which satisfy both the equilibrium and the compatibility relations of plane stress problem are used as the initial assumed stress of the element. Then the stress-function matrix is adopted as the weighted function to weaken the strain-displacement equations. Finally, the bernstein polynomials are chosen as string-net functions on the boundary of the element for the process of strain integration. The formulations of the element are simple and concise, and the element is immune to the distorted mesh, which can be used to the mesh shape degenerates into a triangle or concave quadrangle and curved-side element. The characteristics of bernstein polynomials to approximate models' geometry accuracy make the element competitive when compared with other solutions, especially for the curved-edge structures, which is proven by the numerical tests.

关键词： Quasi-conforming bernstein basis functions Fundamental analytical solutions

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A New Set of bernstein basis functions with Multiparameter and Applications

A New Set of Bernstein Basis Functions with Multiparameter a...

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2016 2nd International Conference on Mechanical,Electronic and Information Technology Engineering(ICMITE 2016)

作者： Caiyong Wang Ying Zeng Xiaoming Zeng School of Mathematical Sciences Xiamen University Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing Xiamen University

In this paper, a new set of bernstein type basis functions with 3 parameters is introduced. The properties of these basis functions are studied. A new kind of Bézier like curves with 3 parameters is defined based on the new basis functions. The new curve not only holds many practical geometrical properties of Bézier curve, but also its shape can be adjusted totally or locally by changing values of the parameters. Finally, some application examples of the new curve are presented.

关键词： Bézier curve shape parameter bernstein basis functions

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Analysis of the bernstein basis functions: an approach to combinatorial sums involving binomial coefficients and Catalan numbers

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MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2015年第14期38卷 3007-3021页

作者： Simsek, Yilmaz Akdeniz Univ Fac Sci Dept Math TR-07058 Antalya Turkey

We give some alternative forms of the generating functions for the bernstein basis functions. Using these forms, we derive a collection of functional equations for the generating functions. By applying these equations, we prove some identities for the bernstein basis functions. Integrating these identities, we derive a variety of identities and formulas, some old and some new, for combinatorial sums involving binomial coefficients, Pascal's rule, Vandermonde's type of convolution, the Bernoulli polynomials, and the Catalan numbers. Copyright (C) 2014 John Wiley & Sons, Ltd.

关键词： bernstein basis functions generating function functional equations Catalan numbers Bernoulli numbers Bernoulli polynomials combinatorial identity combinatorial sum binomial coefficients gamma function beta function

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Conversion from NURBS to Bézier representation

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COMPUTER AIDED GEOMETRIC DESIGN 2024年 113卷

作者： Yan, Lanlan East China Univ Technol Coll Sci Nanchang 330013 Jiangxi Peoples R China

With the help of the Cox-de Boor recursion formula and the recurrence relation of the bernstein polynomials, two categories of recursive algorithms for calculating the conversion matrix from an arbitrary non-uniform B-spline basis to a bernstein polynomial basis of the same degree are presented. One is to calculate the elements of the matrix one by one, and the other is to calculate the elements of the matrix in two blocks. Interestingly, the weights in the two most basic recursion formulas are directly related to the weights in the recursion definition of the B-spline basis functions. The conversion matrix is exactly the B & eacute;zier extraction operator in isogeometric analysis, and we obtain the local extraction operator directly. With the aid of the conversion matrix, it is very convenient to determine the B & eacute;zier representation of NURBS curves and surfaces on any specified domain, that is, the isogeometric B & eacute;zier elements of these curves and surfaces.

关键词： NURBS B-spline basis functions bernstein basis functions Conversion matrix B & eacute zier extraction operator Recurrence relation

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On the generating functions and special functions associated with superoscillations

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DISCRETE APPLIED MATHEMATICS 2023年第1期340卷 215-227页

作者： Colombo, F. Krausshar, R. S. Sabadini, I. Simsek, Y. Politecn Milan Dipartimento Matemat Via E Bonardi 9 I-20133 Milan Italy Univ Erfurt Chair Math Nordhauser Str 63 D-99089 Erfurt Germany Akdeniz Univ Fac Sci Dept Math TR-07058 Antalya Turkiye

The aim of this paper is to study generating functions for the coefficients of the classical superoscillatory function associated with weak measurements. We also establish some new relations between the superoscillatory coefficients and many well-known families of special polynomials, numbers, and functions such as bernstein basis functions, the Hermite polynomials, the Stirling numbers of second kind, and also the confluent hypergeometric functions. Moreover, by using generating functions, we are able to develop a recurrence relation and a derivative formula for the superoscillatory coefficients.& COPY;2023 Elsevier B.V. All rights reserved.

关键词： Superoscillating functions Stirling numbers bernstein basis functions Hermite polynomials Generating functions for superoscillations

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Development of a direct time integration method based on Bezier curve and 5th-order bernstein basis function

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COMPUTERS & STRUCTURES 2018年 194卷 15-31页

作者： Malakiyeh, Mohammad Mandi Shojaee, Saeed Javaran, Saleh Hamzehei Kerman Azad Univ Dept Civil Engn Kerman Iran Shahid Bahonar Univ Dept Civil Engn Kerman Iran

In this study, a robust unconditionally stable method for linear analysis of structures based on Bezier curves and bernstein polynomials is proposed. The Bezier curve is used as interpolation function and bernstein basis functions are applied for interpolation. The spectral radius, period elongation and amplitude decay are investigated for stability analysis, numerical dispersion and dissipation of proposed method, and results are compared with other methods that are the best in these properties. It is also shown that the behavior of the proposed method in analysis of finite element system is effective and reliable. To show the robustness and features of proposed method, a challenging problem with a very stiff and flexible response, a Howe truss under impact load, a frame under harmonic loading and a rectangular domain in plane strain condition are considered, and derived results are compared with references solutions and other results reported in the literature. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Time integration methods Structural dynamics Unconditional stability bernstein basis functions Bezier curves

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Further Insights Into Time-Integration Method Based on bernstein Polynomials and Bezier Curve for Structural Dynamics

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INTERNATIONAL JOURNAL OF STRUCTURAL STABILITY AND DYNAMICS 2019年第10期19卷

作者： Malakiyeh, Mohammad Mahdi Shojaee, Saeed Hamzehei-Javaran, Saleh Tadayon, Behrooz Shahid Bahonar Univ Kerman Dept Civil Engn Kerman Iran

In [M. M. Malakiyeh, S. Shojaee and S. Hamzehei-Javaran, Development of a direct time integration method based on Bezier curve and 5th-order Berstein basis function, Comput. Struct. 194 (2108) 15-31] an unconditionally stable implicit time-integration method using the Bezier curve was proposed for solving structural dynamic problems. In this study, a new class of the previous algorithm is presented by using the bernstein polynomials and the Bezier curve as the interpolation functions for solving the equations of motion with the possibility of using large time steps. The spectral radius, period elongation, amplitude decay and overshooting of the present method are investigated and compared with some other methods. To show the high-performance, robustness and validity of this method, five numerical examples are presented. The theoretical analysis and numerical examples show that the proposed method has low dissipation in the lower modes and high dissipation in the higher modes in comparison with the other methods reported in the literature.

关键词： Direct time-integration methods unconditional stability bernstein basis functions Bezier curve spectral radius numerical dissipation overshooting

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A novel Bezier curve with a shape parameter of the same degree

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RESULTS IN MATHEMATICS 2018年第4期73卷 1-11页

作者： Li, Juncheng Hunan Univ Humanities Sci & Technol Coll Math & Finances Loudi 417000 Peoples R China

In this paper, we construct a class of bernstein basis functions with a shape parameter of the same degree by extending definition interval of the classical bernstein basis functions to be dynamic. Then, we define the corresponding Bezier curve based on the introduced basis functions. The new curve not only has most properties of the classical Bezier curve, but also can be adjusted in shape by altering the value of the shape parameter when the control points are remained unchanged. The proposed curve is simpler than some existing similar models, which is a novel extension of the Bezier curve.

关键词： bernstein basis functions Bezier curve the same degree shape adjustment

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Insight into an implicit time integration method based on Bezier curve and third-order bernstein basis function for structural dynamics

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Asian Journal of Civil Engineering 2018年第1期19卷 1-11页

作者： Malakiyeh, Mohammad Mahdi Shojaee, Saeed Hamzehei Javaran, Saleh Department of Civil Engineering Kerman Azad University Kerman Iran Department of Civil Engineering Shahid Bahonar University Kerman Iran

In this paper, an implicit time integration method based on Bezier curves and bernstein polynomials for analysis of structures is presented. Unconditional stability and accuracy comparable to other methods such as Newmark with high numerical damping to suppress spurious participation of the higher modes are the features of the proposed method that are demonstrated in stability and accuracy analyses. To show the efficiency and validity of presented method, three numerical examples are considered. A simple step-by-step algorithm is also provided for the proposed method. © 2017, Springer International Publishing AG.

关键词： bernstein basis functions Bezier curves Structural dynamics Time integration methods Unconditional stability

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