Sparse Scale-Space Decomposition of Volume Changes in Deformations Fields

Abstract

Anatomical changes like brain atrophy or growth are usually not homogeneous in space and across spatial scales, since they map differently depending on the anatomical structures. Thus, the accurate analysis of volume changes from medical images requires to reliably localize and distinguish the spatial changes occurring at different scales, from voxel to regional level. We propose here a framework for the sparse probabilistic scale-space analysis of volume changes encoded by deformations. Our framework is based on the Helmoltz decomposition of vector fields. By scale-space analysis of the scalar pressure map associated to the irrotational component of the deformation, we robustly identify the areas of maximal volume changes, and we define a consistent sparse decomposition of the irrotational component. We show the effectiveness of our framework in the challenging problem of detecting the progression of tumor growth, and in the group-wise analysis of the longitudinal atrophy in Alzheimer’s disease.