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.
@article{arxiv.2511.01911,
title = {Variational Geometry-aware Neural Network based Method for Solving High-dimensional Diffeomorphic Mapping Problems},
author = {Zhiwen Li and Cheuk Hin Ho and Lok Ming Lui},
journal= {arXiv preprint arXiv:2511.01911},
year = {2025}
}