A bi-variant variational model for diffeomorphic image registration with relaxed Jacobian determinant constraints
Li, Yanyan and Chen, Ken and Chen, Chong and Zhang, Jianping (2024) A bi-variant variational model for diffeomorphic image registration with relaxed Jacobian determinant constraints. Applied Mathematical Modelling, 130. pp. 66-93. ISSN 0307-904X (https://doi.org/10.1016/j.apm.2024.02.033)
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Abstract
Diffeomorphic registration is a widely used technique for finding a smooth and invertible transformation between two coordinate systems, which are measured using template and reference images. The point-wise volume-preserving constraint det(∇()) = 1 is effective in some cases, but may be too restrictive in others, especially when local deformations are relatively large. This can result in poor matching when enforcing large local deformations. In this paper, we propose a new bi-variant diffeomorphic image registration model that introduces a soft constraint on the Jacobian equation det(∇()) = () > 0. This allows local deformations to shrink and grow within a flexible range 0 < < det(∇()) < . The Jacobian determinant of transformation is explicitly controlled by optimizing the relaxation function (). To prevent deformation folding and improve the smoothness of the transformation, a positive constraint is imposed on the optimization of the relaxation function (), and a regularizer is used to ensure the smoothness of (). Furthermore, the positivity constraint ensures that () is as close to one as possible, which helps to achieve a volume preserving transformation on average. We also analyze the existence of the minimizer for the variational model and propose a penalty-splitting algorithm with a multilevel strategy to solve this model. Numerical experiments demonstrate the convergence of the proposed algorithm and show that the positivity constraint can effectively control the range of relative volume without compromising the accuracy of the registration. Moreover, the proposed model generates diffeomorphic maps for large local deformations and outperforms several existing registration models in terms of performance.
ORCID iDs
Li, Yanyan, Chen, Ken ORCID: https://orcid.org/0000-0002-6093-6623, Chen, Chong and Zhang, Jianping;-
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Item type: Article ID code: 90798 Dates: DateEvent15 March 2024Published5 March 2024Published Online29 February 2024Accepted5 August 2023SubmittedSubjects: Science > Mathematics Department: Faculty of Science > Mathematics and Statistics Depositing user: Pure Administrator Date deposited: 09 Oct 2024 10:59 Last modified: 06 Nov 2024 02:00 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/90798