Tree-based adaptive finite element methods for deformable image registration
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911013384749056 |
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| author | Barnafi, Nicolás A. Martın, Alberto F. Ruiz-Baier, Ricardo |
| author_facet | Barnafi, Nicolás A. Martın, Alberto F. Ruiz-Baier, Ricardo |
| contents | In this work we propose an adaptive Finite Element Method (FEM) formulation for the Deformable Image Registration problem (DIR) together with a residual-based a posteriori error estimator, whose efficiency and reliability are theoretically established. This estimator is used to guide Adaptive Mesh Refinement and coarsening (AMR). The nonlinear Euler-Lagrange equations associated with the minimisation of the relevant functional are solved with a pseudo time-stepping fixed-point scheme which is further accelerated using Anderson Acceleration (AA). The efficient implementation of these solvers relies on an efficient adaptive mesh data structure based on forests-of-octrees endowed with space-filling-curves. Several numerical results illustrate the performance of the proposed methods applied to adaptive DIR in application-oriented problems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_15876 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tree-based adaptive finite element methods for deformable image registration Barnafi, Nicolás A. Martın, Alberto F. Ruiz-Baier, Ricardo Numerical Analysis 65N50, 65N15, 74B20, 74N25 In this work we propose an adaptive Finite Element Method (FEM) formulation for the Deformable Image Registration problem (DIR) together with a residual-based a posteriori error estimator, whose efficiency and reliability are theoretically established. This estimator is used to guide Adaptive Mesh Refinement and coarsening (AMR). The nonlinear Euler-Lagrange equations associated with the minimisation of the relevant functional are solved with a pseudo time-stepping fixed-point scheme which is further accelerated using Anderson Acceleration (AA). The efficient implementation of these solvers relies on an efficient adaptive mesh data structure based on forests-of-octrees endowed with space-filling-curves. Several numerical results illustrate the performance of the proposed methods applied to adaptive DIR in application-oriented problems. |
| title | Tree-based adaptive finite element methods for deformable image registration |
| topic | Numerical Analysis 65N50, 65N15, 74B20, 74N25 |
| url | https://arxiv.org/abs/2506.15876 |