The rapid development in acquiring multimodal neuroimaging data provides opportunities to systematically characterize human brain structures and functions. For example, in the brain magnetic resonance imaging (MRI), a typical non-invasive imaging technique, different acquisition sequences (modalities) lead to the different descriptions of brain functional activities, or anatomical biomarkers. Nowadays, in addition to the traditional voxel-level analysis of images, there is a trend to process and investigate the cross-modality relationship in a high dimensional level of images, e.g. surfaces and networks.

In this study, I aim to achieve multimodal brain image fusion by referring to some intrinsic properties of data, e.g. geometry of embedding structures where the commonly used image features reside. Since the image features investigated in this study share an identical embedding space, i.e. either defined on a brain surface or brain atlas, where a graph structure is easy to define, it is straightforward to consider the mathematically meaningful properties of the shared structures from the geometry perspective.

I first introduce the background of multimodal fusion of brain image data and insights of geometric properties playing a potential role to link different modalities. Then, several proposed computational frameworks either using the solid and efficient geometric algorithms or current geometric deep learning models are be fully discussed. I show how these designed frameworks deal with distinct geometric properties respectively, and their applications in the real healthcare scenarios, e.g. to enhanced detections of fetal brain diseases or abnormal brain development.