A Survey on Deep Learning-Based Diffeomorphic Mapping

Diffeomorphic mapping is a specific type of registration methods that can be used to align biomedical structures for subsequent analyses. Diffeomorphism not only provides a smooth transformation that is desirable between a pair of biomedical template and target structures but also offers a set of statistical metrics that can be used to quantify characteristics of the pair of structures of interest. However, traditional one-to-one numerical optimization is time-consuming, especially for 3D images of large volumes and 3D meshes of numerous vertices. To address this computationally expensive problem while still holding desirable properties, deep learning-based diffeomorphic mapping has been extensively explored, which learns a mapping function to perform registration in an end-to-end fashion with high computational efficiency on GPU. Learning-based approaches can be categorized into two types, namely, unsupervised and supervised. In this chapter, recent progresses on these two major categories will be covered. We will review the general frameworks of diffeomorphic mapping as well as the loss functions, regularizations, and network architectures of deep learning-based diffeomorphic mapping. Specifically, unsupervised ones can be further subdivided into convolutional neural network (CNN)-based methods and variational autoencoder-based methods, according to the network architectures, the corresponding loss functions, as well as the optimization strategies, while supervised ones mostly employ CNN. After summarizing recent achievements and challenges, we will also provide an outlook of future directions to fully exploit deep learning-based diffeomorphic mapping and its potential roles in biomedical applications such as segmentation, detection, and diagnosis.