Direct cortical mapping via solving partial differential equations on implicit surfaces

摘要: In this paper, we propose a novel approach for cortical mapping that computes direct map between two surfaces while satisfying constraints on sulcal landmark curves. By computing the directly, can avoid conventional intermediate parameterizations and help simplify process. The in our method is formulated as minimizer of flexible variational energy under constraints. include both harmonic term to ensure smoothness general data terms matching geometric features. Starting from properly designed initial map, compute iteratively by solving partial differential equation (PDE) defined source surface. For numerical implementation, set adaptive schemes are developed extend technique PDEs implicit such enforced. experiments, show flexibility smooth maps following different energies. We also quantitatively compare metric preserving property with parametric group 30 subjects. Finally, demonstrate brain applications atlas construction variability analysis.