UM
Integral Equation-Wavelet Collocation Method for Geometric Transformation and Application to Image Processing
Lina Yang1,2; Yuan Yan Tang1,3; Xiang Chu Feng4; Lu Sun5
2014-04-01
Source PublicationAbstract and Applied Analysis
ISSN1085-3375
Volume2014
Other Abstract

Geometric (or shape) distortion may occur in the data acquisition phase in information systems, and it can be characterized by geometric transformation model. Once the distorted image is approximated by a certain geometric transformation model, we can apply its inverse transformation to remove the distortion for the geometric restoration. Consequently, finding a mathematical form to approximate the distorted image plays a key role in the restoration. A harmonic transformation cannot be described by any fixed functions in mathematics. In fact, it is represented by partial differential equation (PDE) with boundary conditions. Therefore, to develop an efficient method to solve such a PDE is extremely significant in the geometric restoration. In this paper, a novel wavelet-based method is presented, which consists of three phases. In phase 1, the partial differential equation is converted into boundary integral equation and representation by an indirect method. In phase 2, the boundary integral equation and representation are changed to plane integral equation and representation by boundary measure formula. In phase 3, the plane integral equation and representation are then solved by a method we call wavelet collocation. The performance of our method is evaluated by numerical experiments.

DOIhttp://dx.doi.org/10.1155/2014/798080
URLView the original
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000334205000001
PublisherHINDAWI PUBLISHING CORPORATION, 410 PARK AVENUE, 15TH FLOOR, #287 PMB, NEW YORK, NY 10022 USA
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Document TypeJournal article
CollectionUniversity of Macau
Corresponding AuthorYuan Yan Tang
Affiliation1.Department of Computer and Information Science, Faculty of Science and Technology, University of Macau, Macau
2.Department of Mathematics and Computer Science, Guangxi Normal University of Nationalities, Chongzuo 532200, China
3.College of Computer Science, Chongqing University, Chongging 40030, China
4.Department of Mathematics, Xidian University, Xi’an 710126, China
5.Sichuan Sunray Machinery Co., Ltd., Deyang 618000, China
First Author AffilicationFaculty of Science and Technology
Corresponding Author AffilicationFaculty of Science and Technology
Recommended Citation
GB/T 7714
Lina Yang,Yuan Yan Tang,Xiang Chu Feng,et al. Integral Equation-Wavelet Collocation Method for Geometric Transformation and Application to Image Processing[J]. Abstract and Applied Analysis,2014,2014.
APA Lina Yang,Yuan Yan Tang,Xiang Chu Feng,&Lu Sun.(2014).Integral Equation-Wavelet Collocation Method for Geometric Transformation and Application to Image Processing.Abstract and Applied Analysis,2014.
MLA Lina Yang,et al."Integral Equation-Wavelet Collocation Method for Geometric Transformation and Application to Image Processing".Abstract and Applied Analysis 2014(2014).
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