Variational Geometry-aware Neural Network based Method for Solving High-dimensional Diffeomorphic Mapping Problems
This work addresses diffeomorphic mapping for applications like medical image registration, but it appears incremental as it builds on existing variational and quasi-conformal methods with neural network integration.
The paper tackled the problem of high-dimensional diffeomorphic mapping, which traditional methods struggle with due to the curse of dimensionality, by proposing a mesh-free learning framework that combines variational principles with quasi-conformal theory, resulting in accurate, bijective mappings validated on synthetic and real-world medical image data.
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.