Diffeomorphic Transformation

Diffeomorphic transformations, smooth and invertible mappings, are increasingly used in various fields to model continuous deformations of data, primarily focusing on achieving efficient and accurate transformations. Current research emphasizes developing trainable diffeomorphic models, often leveraging ordinary differential equations or reproducing kernel Hilbert spaces, for applications such as data augmentation, topological optimization, and generative modeling. These advancements improve the expressiveness and efficiency of algorithms across diverse domains, including medical image analysis, time series alignment, and machine learning model interpretability, by enabling more sophisticated data manipulation and analysis.