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A fast approach of nonparametric elastic image registration problem
Author(s) -
Alahyane Mohamed,
Hakim Abdelilah,
Laghrib Amine,
Raghay Said
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5810
Subject(s) - mathematics , tridiagonal matrix , image registration , speedup , block (permutation group theory) , uniqueness , linear elasticity , image (mathematics) , matrix (chemical analysis) , algorithm , simple (philosophy) , range (aeronautics) , linear system , mathematical analysis , finite element method , computer science , computer vision , geometry , eigenvalues and eigenvectors , parallel computing , philosophy , physics , materials science , epistemology , composite material , quantum mechanics , thermodynamics
In this paper, we present a fast algorithm of the nonparametric elastic image registration using a simple implementation of the Range Restricted GMRES (RRGMRES) method. This approach differs from the others in the fact that it is specified to the tridiagonal block matrix type to resolve a nonsymmetric linear system. In what follows, we prove existence and uniqueness of minimizer of the elastic registration problem and present the corresponding discrete problem by employing a finite difference scheme. The accuracy of the proposed method is demonstrated on different image registration examples; we also show the speedup of the proposed approach by calculating the corresponding CPU time and compared it with the classical elastic registration method.