Unsupervised multimodal surface registration with geometric deep learning.

This paper introduces GeoMorph, a novel geometric deep-learning framework designed for image registration of cortical surfaces. The registration process consists of two main steps. First, independent feature extraction is performed on each input surface using graph convolutions, generating low-dimensional feature representations that capture important cortical surface characteristics. Subsequently, features are registered in a deep-discrete manner to optimize the overlap of common structures across surfaces by learning displacements of a set of control points. To ensure smooth and biologically plausible deformations, we implement regularization through a deep conditional random field implemented with a recurrent neural network. Experimental results demonstrate that GeoMorph surpasses existing deep-learning methods by achieving improved alignment with smoother deformations. Furthermore, GeoMorph exhibits competitive performance compared to classical frameworks. Such versatility and robustness suggest strong potential for various neuroscience applications. Code is made available at https://github.com/mohamedasuliman/GeoMorph.