Time Continuous Diffeomorphisms

Time-continuous diffeomorphisms, topology-preserving transformations, are increasingly studied for their applications in areas like image registration and neural network analysis. Current research focuses on developing efficient algorithms, often leveraging neural networks like UNets or coupling flows, to learn and represent these transformations, particularly emphasizing continuous-time solutions and minimizing the need for extensive regularization. This work is significant because it improves the accuracy and efficiency of image analysis techniques and provides new insights into the underlying mathematical structure of deep learning models, potentially leading to more robust and interpretable architectures.