We describe coordinate systems adapted for the space between two surfaces, such as those delineating the highly folded cortex in mammalian brains. These systems are estimated in order to satisfy geometric priors, including streamline normality or equivolumetric conditions on layers. We give a precise mathematical formulation of these problems, and present numerical simulations based on diffeomorphic registration methods, comparing them with recent approaches. Our method involves•Diffeomorphic registration of inner and outer folded folded surfaces.•Followed by equivolumetric reparametrization of layers to yield coordinate system.
Keywords: Bok's hypothesis; Cortical thickness; Equivolumetric coordinates; Medical imaging; Normal Equivolumetric Coordinate System; Shape analysis.
© 2024 The Authors. Published by Elsevier B.V.