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Circular Slit Maps of Multiply Connected Regions with Application to Brain Image Processing.

Authors :
Sangawi, Ali W. K.
Murid, Ali H. M.
Lee, Khiy Wei
Source :
Bulletin of the Malaysian Mathematical Sciences Society; Jan2021, Vol. 44 Issue 1, p171-202, 32p
Publication Year :
2021

Abstract

In this paper, we present a fast boundary integral equation method for the numerical conformal mapping and its inverse of bounded multiply connected regions onto a disk and annulus with circular slits regions. The method is based on two uniquely solvable boundary integral equations with Neumann-type and generalized Neumann kernels. The integral equations related to the mappings are solved numerically using combination of Nyström method, GMRES method, and fast multipole method. The complexity of this new algorithm is O ((M + 1) n) , where M + 1 stands for the multiplicity of the multiply connected region and n refers to the number of nodes on each boundary component. Previous algorithms require O ((M + 1) 3 n 3) operations. The numerical results of some test calculations demonstrate that our method is capable of handling regions with complex geometry and very high connectivity. An application of the method on medical human brain image processing is also presented. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
01266705
Volume :
44
Issue :
1
Database :
Complementary Index
Journal :
Bulletin of the Malaysian Mathematical Sciences Society
Publication Type :
Academic Journal
Accession number :
147703508
Full Text :
https://doi.org/10.1007/s40840-020-00942-7