A more robust multigrid algorithm for diffusion type registration models

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Thompson, Tony and Chen, Ke (2019) A more robust multigrid algorithm for diffusion type registration models. Journal of Computational and Applied Mathematics, 361. pp. 502-527. ISSN 0377-0427 (https://doi.org/10.1016/j.cam.2019.04.006)

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Abstract

Registration refers to the useful process of aligning two similar but different intensity image functions in order to either track changes or combine information. Variational models are capable of finding transform maps containing large and non-uniform deformations between such a pair of images. Since finding a transform map is an inverse problem, as with all models, suitable regularisation is necessary to overcome the non-uniqueness of the problem. In the case of diffusion type models regularisation terms impose smoothness on the transformation by minimising the gradient of the flow field. The diffusion model also coincides with the basic model for optical flow frameworks of Horn and Schunck (1981). The biggest drawback with variational models is the large computational cost required to solve the highly non-linear system of PDEs; Chumchob and Chen (2011) developed a non-linear multigrid (NMG) method to address this cost problem. However, a closer look at the analysis of the NMG scheme highlighted omissions which affected the convergence of the NMG scheme. Moreover, the NMG method proposed by Chumchob and Chen did not impose any control of non-physical folding which invalidates a map. This paper has proposed several key ideas. First we re-evaluate the analysis of the NMG method to show how the omissions in Chumchob and Chen (2011) have a noticeable impact on the convergence of the NMG method. In addition, we also provide a way of estimating the convergence rate of a solver on the coarsest grid in order to estimate the number of iterations that will be required to obtain a solution with appropriate accuracy. Second we propose an extension to the Chumchob–Chen NMG method which controls any folding within the deformation. Experimental results on the proposed multigrid framework demonstrate improvements in convergence and the accuracy of registrations compared with previous methods.

ORCID iDs

Thompson, Tony and Chen, Ke ORCID logoORCID: https://orcid.org/0000-0002-6093-6623;
  • Item type:Article
    ID code:87502
    Dates:
    Date
    Event
    1 December 2019
    Published
    27 May 2019
    Published Online
    14 August 2018
    Accepted
    23 November 2017
    Submitted
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:04 Dec 2023 11:03
    Last modified:11 Nov 2024 14:09
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/87502
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