Topology-preserving image registration with novel multi-dimensional Beltrami regularization

Huang, Chongfei and Chen, Ke and Huang, Meixiang and Kong, Dexing and Yuan, Jing (2024) Topology-preserving image registration with novel multi-dimensional Beltrami regularization. Applied Mathematical Modelling, 125 (Part B). pp. 539-556. ISSN 0307-904X (https://doi.org/10.1016/j.apm.2023.09.033)

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Abstract

Beltrami coefficient provides a proper measure to quantify local distortions for a topology-preserving mapping, a.k.a general quasi-conformal mapping, in 2D. Recent studies managed to extend Beltrami coefficient from 2D to nD, and introduced its corresponding Beltrami-like measures to encode local deformation information in challenging nD topology-preserving image registration tasks. However, all these nD measures are not consistent with the classical 2D Beltrami coefficient. We propose a novel nD measure for evaluating local distortions of an nD diffeomorphic mapping in this work. We show its key mathematical properties, and prove that the new measure coincides with the classical 2D Beltrami coefficient. We further introduce a new nD topology-preserving image registration model by means of regularizing such proposed Beltrami-consistent coefficient, and show the existence of its solution. Meanwhile, a generalized Gauss-Newton scheme is applied to establish a fast multi-level numerical solver. Extensive experiments over different 3D medical image registration tasks, including the challenging multi-modal medical image registration, illustrate that the proposed approach by regularizing the introduced Beltrami-consistent coefficient outperforms the other state-of-the-art topology-preserving methods in both efficiency and accuracy.

ORCID iDs

Chen, Ke ORCID: https://orcid.org/0000-0002-6093-6623

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• Item metadata

  Item type:	Article
  ID code:	87102
  Dates:	Date Event 31 January 2024 Published 16 October 2023 Published Online 27 September 2023 Accepted 4 September 2022 Submitted
  Subjects:	Science > Mathematics
  Department:	Faculty of Science > Mathematics and Statistics
  Depositing user:	Pure Administrator
  Date deposited:	27 Oct 2023 16:06
  Last modified:	12 Dec 2024 15:04
  URI:	https://strathprints.strath.ac.uk/id/eprint/87102