Variational Geometry-aware Neural Network based Method for Solving High-dimensional Diffeomorphic Mapping Problems
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908626015223808 |
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| author | Li, Zhiwen Ho, Cheuk Hin Lui, Lok Ming |
| author_facet | Li, Zhiwen Ho, Cheuk Hin Lui, Lok Ming |
| contents | Traditional methods for high-dimensional diffeomorphic mapping often struggle with the curse of dimensionality. We propose a mesh-free learning framework designed for $n$-dimensional mapping problems, seamlessly combining variational principles with quasi-conformal theory. Our approach ensures accurate, bijective mappings by regulating conformality distortion and volume distortion, enabling robust control over deformation quality. The framework is inherently compatible with gradient-based optimization and neural network architectures, making it highly flexible and scalable to higher-dimensional settings. Numerical experiments on both synthetic and real-world medical image data validate the accuracy, robustness, and effectiveness of the proposed method in complex registration scenarios. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_01911 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Variational Geometry-aware Neural Network based Method for Solving High-dimensional Diffeomorphic Mapping Problems Li, Zhiwen Ho, Cheuk Hin Lui, Lok Ming Machine Learning Artificial Intelligence Numerical Analysis Differential Geometry Traditional methods for high-dimensional diffeomorphic mapping often struggle with the curse of dimensionality. We propose a mesh-free learning framework designed for $n$-dimensional mapping problems, seamlessly combining variational principles with quasi-conformal theory. Our approach ensures accurate, bijective mappings by regulating conformality distortion and volume distortion, enabling robust control over deformation quality. The framework is inherently compatible with gradient-based optimization and neural network architectures, making it highly flexible and scalable to higher-dimensional settings. Numerical experiments on both synthetic and real-world medical image data validate the accuracy, robustness, and effectiveness of the proposed method in complex registration scenarios. |
| title | Variational Geometry-aware Neural Network based Method for Solving High-dimensional Diffeomorphic Mapping Problems |
| topic | Machine Learning Artificial Intelligence Numerical Analysis Differential Geometry |
| url | https://arxiv.org/abs/2511.01911 |