A robust multigrid approach for variational image registration models

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:236

Article; Proceedings Paper

Chumchob, Noppadol^1,2  Chen, Ke¹ 

[1] Univ Liverpool, Dept Math Sci, Ctr Math Imaging Tech, Liverpool L69 7ZL, Merseyside, England

[2] Silpakorn Univ, Fac Sci, Dept Math, Nakhon Pathom 73000, Thailand

关键词: Variational models;    Deformable registration;    Diffusion and curvature image models;    Smoothing analysis;    Nonlinear multigrid;    Inverse problems;   

DOI  :  10.1016/j.cam.2011.06.026

来源: Elsevier

【 摘 要 】

Variational registration models are non-rigid and deformable imaging techniques for accurate registration of two images. As with other models for inverse problems using the Tikhonov regularization, they must have a suitably chosen regularization term as well as a data fitting term. One distinct feature of registration models is that their fitting term is always highly nonlinear and this nonlinearity restricts the class of numerical methods that are applicable. This paper first reviews the current state-of-the-art numerical methods for such models and observes that the nonlinear fitting term is mostly 'avoided' in developing fast multigrid methods. It then proposes a unified approach for designing fixed point type smoothers for multigrid methods. The diffusion registration model (second-order equations) and a curvature model (fourth-order equations) are used to illustrate our robust methodology. Analysis of the proposed smoothers and comparisons to other methods are given. As expected of a multigrid method, being many orders of magnitude faster than the unilevel gradient descent approach, the proposed numerical approach delivers fast and accurate results for a range of synthetic and real test images. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free