Variational Geometry-aware Neural Network based Method for Solving High-dimensional Diffeomorphic Mapping Problems

• URL: http://arxiv.org/abs/2511.01911v1
• Date: Fri, 31 Oct 2025 20:39:08 GMT
• Title: Variational Geometry-aware Neural Network based Method for Solving High-dimensional Diffeomorphic Mapping Problems
• Authors: Zhiwen Li, Cheuk Hin Ho, Lok Ming Lui,
• Abstract summary: We propose a mesh-free learning framework designed for $n$-dimensional mapping problems.<n>We regulate conformality distortion and volume distortion, enabling robust control over deformation quality.
• Score: 1.2955718209635254
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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