Metamorphoses and optimal transport for the multimodal registration of brain tumor images

Project Summary

Medical imaging often involves nonlinear space-valued images, where pixel or voxel values belong to more complex spaces than simple real numbers. For example, diffusion tensor imaging encodes data in a space of symmetric positive definite matrices, providing information about the orientation of water diffusion in tissues, while soft segmentation maps use probability vectors to label different tissue types and account for uncertainty. My project aims to develop new theoretical and computational tools to analyze variability in these complex images. Specifically, I focus on separating changes in shape or structure, such as tumor growth, from changes in tissue properties, like necrosis, by using a method that combines deformations and intensity variations.