@Article{EAJAM-5-361,
author = {Sopida Jewprasert, Noppadol Chumchob and Chantana Chantrapornchai},
title = {A Fourth-Order Compact Finite Difference Scheme for Higher-Order PDE-Based Image Registration},
journal = {East Asian Journal on Applied Mathematics},
year = {2018},
volume = {5},
number = {4},
pages = {361--386},
abstract = {<p style="text-align: justify;">Image registration is an ill-posed problem that has been studied widely in recent
years. The so-called curvature-based image registration method is one of the most
effective and well-known approaches, as it produces smooth solutions and allows an
automatic rigid alignment. An important outstanding issue is the accurate and efficient
numerical solution of the Euler-Lagrange system of two coupled nonlinear biharmonic
equations, addressed in this article. We propose a fourth-order compact (FOC) finite
difference scheme using a splitting operator on a 9-point stencil, and discuss how the
resulting nonlinear discrete system can be solved efficiently by a nonlinear multi-grid
(NMG) method. Thus after measuring the h-ellipticity of the nonlinear discrete operator
involved by a local Fourier analysis (LFA), we show that our FOC finite difference method
is amenable to multi-grid (MG) methods and an appropriate point-wise smoothing procedure.
A high potential point-wise smoother using an outer-inner iteration method is
shown to be effective by the LFA and numerical experiments. Real medical images are
used to compare the accuracy and efficiency of our approach and the standard second-order
central (SSOC) finite difference scheme in the same NMG framework. As expected
for a higher-order finite difference scheme, the images generated by our FOC finite difference
scheme prove significantly more accurate than those computed using the SSOC
finite difference scheme. Our numerical results are consistent with the LFA analysis, and
also demonstrate that the NMG method converges within a few steps.</p>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.270415.280915a},
url = {http://global-sci.org/intro/article_detail/eajam/10821.html}
}