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Convergence of cascade algorithms by frequency approach

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2006年第1期314卷 335-344页

作者： Chen, DR Beijing Univ Aeronaut & Astronaut Dept Appl Math Beijing 100083 Peoples R China

Starting with an initial function phi(0), the cascade algorithm generates a sequence {Q(a)(n)phi(0)}(infinity)(n=1) by a cascade operator Q(a) defined by Qa f = Sigma(alpha is an element of Zd) a(alpha) f (M (.)-alpha). A function phi is refinable if it satisfies Q(a)phi = phi. The refinable functions play an important role in wavelet analysis and computer graphics. The cascade algorithm is the main approach to approximate the refinable functions and to study their properties. This note establishes a sufficient condition, in terms of Fourier transforms of the initial function phi(0) and the refinable function phi, for the convergence of cascade algorithm. Our results apply to the case where neither the initial function is compactly supported nor the refinement mask is finitely supported. As a byproduct, we prove that any compactly supported refinable function has a positive Sobolev regularity exponent provided it is in L-2. (c) 2005 Published by Elsevier Inc.

关键词： refinable function cascade algorithm stability transition operator

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Convergence and error estimate of cascade algorithms with infinitely supported masks in L_p(R^s)

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Science China Mathematics 2012年第3期55卷 577-592页

作者： YANG JianBin LI Song Department of Mathematics College of Sciences Hohai University Nanjing 210098 China Department of Mathematics College of Sciences Zhejiang University Hangzhou 310027 China

The cascade algorithm plays an important role in computer graphics and wavelet *** this paper,we first investigate the convergence of cascade algorithms associated with a polynomially decaying mask and a general dilation matrix in L p (R s) (1 p ∞) spaces,and then we give an error estimate of the cascade algorithms associated with truncated *** is proved that under some appropriate conditions if the cascade algorithm associated with a polynomially decaying mask converges in the L p-norm,then the cascade algorithms associated with the truncated masks also converge in the L ***,the error between the two resulting limit functions is estimated in terms of the masks.

关键词： cascade algorithm polynomially decaying masks error estimate

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Convergence rates of vector cascade algorithms in L_p

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JOURNAL OF APPROXIMATION THEORY 2005年第1期137卷 123-142页

作者： Li, S Zhejiang Univ Dept Math Hangzhou 310027 Zhejiang Peoples R China

We investigate the solutions of vector refinement equations of the form phi = Sigma(alpha is an element of Z alpha) a(alpha)phi(M (.) -alpha), where the vector of functions phi = (phi(1),..., phi(r))(T) is in (L-p(R-s))(r). 1 <= p <= infinity. a =: (a(alpha))(alpha is an element of Zs) is a finitely supported sequence of r x r matrices called the refinement mask, and M is an s x s integer matrix such that lim(n ->infinity) M-n = 0. Associated with the mask a and M is a linear operator Q(a) defined on (L-p(R-s))(r) by Q(a psi) := Sigma(beta is an element of Zs) a(beta)psi(M (.) -beta). The iteration scheme (Q(a)(n)psi)(n=1,2....) is called a cascade algorithm (see [D.R. Chen, R.Q. Jia. S.D. Riemenschneider, Convergence or vector subdivision schemes in Sobolev spaces, Appl. Comput. Harmon. Anal. 12 (2002) 128-149;B. Han, The initial functions in a cascade algorithm, in: D.X. Zhou (Ed.), Proceeding of International Conference of Computational Harmonic Analysis in Hong Kong. 2002;B. Han, R.Q. Jia, Multivariate refinement equations and convergence of subdivision schemes. SIAM J. Math. Anal. 29 (1998) 1177-1199: R.Q. Jia, Subdivision schemes in L-p spaces, Adv. Comput. Math. 3 (1995) 309-341;R.Q. Jia, S.D. Riemenschneider. D.X. Zhou. Vector subdivision schemes and multiple wavelets, Math. Comp. 67 (1998) 1533-1363: S. Li, Characterization of smoothness of multivariate refinable functions and convergence of cascade algorithms associated with nonhomogeneous refinement equations. Adv. Comput. Math. 20 (2004) 311-331;Q. Sun, Convergence and boundedness of cascade algorithm in Besov space and Triebel-Lizorkin space 1, Adv. Math. (China) 29 (2000) 507-526]). cascade algorithm is an important issue to wavelets analysis and computer graphics. Main results of this paper are related to the convergence and convergence rates of vector cascade algorithm in (L-p(R-s))(r)(1 <= p <= infinity). We give some characterizations on convergence of cascade algorithm and also give estimates on c

关键词： refinement equation cascade algorithm multiple refinable functions convergence rates smoothness

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Characterization of smoothness of multivariate refinable functions and convergence of cascade algorithms of nonhomogeneous refinement equations

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ADVANCES IN COMPUTATIONAL MATHEMATICS 2004年第4期20卷 311-331页

作者： Li, S Zhejiang Univ Dept Math Hangzhou 310027 Zhejiang Peoples R China

This paper concerns multivariate homogeneous refinement equations of the form (GRAPHICS) This paper concerns multivariate homogeneous refinement equations of the form (GRAPHICS) where phi=(phi(1),...,phi(r))(T) is the unknown, M is an s x s dilation matrix with m = \detM\, g = (g(1),...,g(r))(T) is a given compactly supported vector-valued function on R-s, and a is a finitely supported refinement mask such that each a(alpha) is an r x r (complex) matrix. In this paper, we characterize the optimal smoothness of a multiple refinable function associated with homogeneous refinement equations in terms of the spectral radius of the corresponding transition operator restricted to a suitable finite-dimensional invariant subspace when M is an isotropic dilation matrix. Nonhomogeneous refinement equations naturally occur in multi-wavelets constructions. Let phi(0) be an initial vector of functions in the Sobolev space (W-2(k)(R-s))(r) (kis an element ofN). The corresponding cascade algorithm is given by (GRAPHICS) We also provide necessary and sufficient conditions for the strong convergence of the cascade algorithm in the Sobolev space (W-2(K) (R-s))(r) (kis an element ofN)) for the case in which M is isotropic.

关键词： refinement equation refinable function smoothness cascade algorithm Sobolev space Lipschitz space transition operator self-affine tile

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ENHANCEMENT OF FAST FACE DETECTION algorithm BASED ON A cascade OF DECISION TREES 2

ENHANCEMENT OF FAST FACE DETECTION ALGORITHM BASED ON A CASC...

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International Workshop on Photogrammetric and Computer Vision Techniques for Video Surveillance, Biometrics and Biomedicine

作者： Khryashchev, V. V. Lebedev, A. A. Priorov, A. L. YSU Yaroslavl Russia

Face detection algorithm based on a cascade of ensembles of decision trees (CEDT) is presented. The new approach allows detecting faces other than the front position through the use of multiple classifiers. Each classifier is trained for a specific range of angles of the rotation head. The results showed a high rate of productivity for CEDT on images with standard size. The algorithm increases the area under the ROC-curve of 13% compared to a standard Viola-Jones face detection algorithm. Final realization of given algorithm consist of 5 different cascades for frontal/non-frontal faces. One more thing which we take from the simulation results is a low computational complexity of CEDT algorithm in comparison with standard Viola-Jones approach. This could prove important in the embedded system and mobile device industries because it can reduce the cost of hardware and make battery life longer.

关键词： Face Detection cascade algorithm Decision Trees

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A cascade optimization methodology for automatic parameter identification and shape/process optimization in metal forming simulation

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2006年第41-43期195卷 5472-5508页

作者： Ponthot, J-P. Kleinermann, J-P. Univ Liege LTAS MC&T B-4000 Liege Belgium

Computer simulations of metal forming processes using the finite element method (FEM) are, today, well established. This form of simulation uses an increasing number of sophisticated geometrical and material models, relying on a certain number of input data, which are not always readily available. The aim of inverse problems, which will be considered here, is to determine one or more of the input data relating to these forming process simulations, thereby leading to a desired result. In this paper, we will focus on two categories of such inverse problems. The first category consists of parameter identification inverse problems. These involve evaluating the material parameters for material constitutive models that would lead to the most accurate results with respect to physical experiments, i.e. minimizing the difference between experimental results and FEM simulations. The second category consists of shape/process optimization inverse problems. These involve determining the initial geometry of the specimen and/or the shape of the forming tools, as well as some parameters of the process itself, in order to provide the desired final geometry after the forming process. These two categories of inverse problems can be formulated as optimization problems in a similar way, i.e. by using identical optimization algorithms. In this paper, we intend firstly to solve these two types of optimization problems by using different non-linear gradient based optimization methods and secondly to compare their efficiency and robustness in a variety of numerical applications. (c) 2005 Elsevier B.V. All rights reserved.

关键词： finite element method (FEM) large strains inverse problems parameter identification forming processes optimization methods cascade algorithm

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LabVIEW based robust cascade predictive model for evaluating cancer prognosis

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PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 2020年 549卷 123978-123978页

作者： Kaya, Duygu Turk, Mustafa Firat Univ Fac Engn Dept Elect & Elect Engn Elazig Turkey

Cancer is a disease that is found in many forms. Early diagnosis process significantly affects follow-up of the disease. As in other diseases, it is important to classify the data in cancer cases to determine whether the person belongs to healthy-patient or high-low risk groups. For this purpose, machine learning based on artificial intelligence can be used as a very effective method to follow both the progress and the treatment response process of such diseases and to reveal important features of data sets. In this publication, breast cancer diagnosis was carried out using Principal Component Analysis-Support Vector Machine (PCA-SVM) and proposed parallel Principal Component Analysis-Linear Discriminant Analysis-Support Vector Machine (PCA-LDA-SVM) model classifier algorithms, by LabVIEW. LabVIEW, known as Virtual Instrument (VI), is a graphical programming language. The durableness of the used algorithms is analyzed using accuracy, sensitivity, specificity, rand index, False Positive Rate (FPR), False Discovery Rate (FDR), False Negative Rate (FNR), Negative Predictive Value (NPV), Matthews Correlation Coefficient (MCC) parameters and status detection. The obtained results are compared with each other. After training, of the 140 data used in the test set, 130 were used for the test performance analysis and 10 data were used for the status determination of the newly entered data. Performance analysis has been examined for Polynomial and Gaussian kernel functions. The proposed parallel model provides improvement especially for the Polynomial kernel function. With the proposed model, an increase in classification accuracy was observed in the test phase compared to PCA-SVM, and it was observed that 10 data used for status determination were correctly classified. (C) 2020 Elsevier B.V. All rights reserved.

关键词： LabVIEW Prognosis of disease cascade algorithm Machine learning Support vector machine

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Pointwise convergence of bounded cascade sequences

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PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 2007年第1期135卷 181-189页

作者： Chen, Di-Rong Han, Min Beijing Univ Aeronaut & Astronaut Dept Math Beijing 100083 Peoples R China Beijing Univ Aeronaut & Astronaut LMIB Beijing 100083 Peoples R China

The cascade algorithm plays an important role in computer graphics and wavelet analysis. For an initial function phi(0), a cascade sequence (phi(n))(n=0)(infinity) is constructed by the iteration phi(n) = C-a phi(n-1), n = 1, 2,..., where C-a is defined by C(a)g = Sigma(alpha is an element of Z) a(alpha)g(2 (.) -alpha), g is an element of L-p(R). In this paper, under a condition that the sequence (phi n)(n=0)(infinity) is bounded in L-infinity(R), we prove that the following three statements are equivalent: (i) (phi n)(n=0)(infinity) converges a.e. x is an element of R. (ii) For a.e. x is an element of R, there exist a positive constant c and a constant gamma is an element of (0, 1) such that vertical bar phi(n+1)(x) - phi(n)(x)vertical bar <= c gamma(n) for all n = 1, 2,.... (iii) For some p is an element of [1,8), (phi(n))(n=0)(infinity) converges in L-p(R). An example is presented to illustrate our result.

关键词： refinable function cascade algorithm subdivision scheme pointwise convergence refinable curve joint spectral radius

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Facial Expression Recognition Method Based on cascade Convolution Neural Network 17

Facial Expression Recognition Method Based on Cascade Convol...

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17th IEEE International Wireless Communications and Mobile Computing Conference (IEEE IWCMC)

作者： Liu, Weida Fang, Jian Jilin Engn Normal Univ Dept Elect Engn Jilin Jilin Peoples R China

ISBN: (纸本)9781728186160

In view of the problem that the convolution neural network research of facial expression recognition ignores the internal relevance of the key links, which leads to the low accuracy and speed of facial expression recognition, and can't meet the recognition requirements, a series cascade algorithm model for expression recognition of educational robot is constructed and enables the educational robot to recognize multiple students' facial expressions simultaneously, quickly and accurately in the process of movement, in the balance of the accuracy, rapidity and stability of the algorithm, based on the cascade convolution neural network model. Through the CK+ and Oulu-CASIA expression recognition database, the expression recognition experiments of this algorithm are compared with the commonly used STM-ExpLet and FN2EN cascade network algorithms. The results show that the accuracy of the expression recognition method is more than 90%. Compared with the other two commonly used cascade convolution neural network methods, the accuracy of expression recognition is significantly improved.

关键词： Convolution Neural Network Facial Expression Recognition cascade algorithm

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A cascade Method for TFT-LCD Defect Detection 9

A Cascade Method for TFT-LCD Defect Detection

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9th International Conference on Digital Image Processing (ICDIP)

作者： Yi, Songsong Wu, Xiaojun Yu, Zhiyang Mo, Zhuoya Harbin Inst Technol Sch Mech Engn & Automat Shenzhen 518055 Guangdong Peoples R China Shenzhen Key Lab Adv Mot Control & Modern Automat Shenzhen 518055 Guangdong Peoples R China Guangdong Tianji Ind Intelligent Syst Co Ltd Dongguan 523808 Peoples R China

ISBN: (纸本)9781510613058;9781510613041

In this paper, we propose a novel cascade detection algorithm which focuses on point and line defects on TFT-LCD. At the first step of the algorithm, we use the gray level difference of su-bimage to segment the abnormal area. The second step is based on phase only transform (POT) which corresponds to the Discrete Fourier Transform (DFT), normalized by the magnitude. It can remove regularities like texture and noise. After that, we improve the method of setting regions of interest (ROI) with the method of edge segmentation and polar transformation. The algorithm has outstanding performance in both computation speed and accuracy. It can solve most of the defect detections including dark point, light point, dark line, etc.

关键词： TFT-LCD defect detection cascade algorithm

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