Poisson Flow and Wasserstein Registration of Trees

Abstract

Tree-like structures arise in numerous imaging applications, including vascular networks, neuronal arbors, airway trees, and cortical sulcal--gyral folding. We present a nonlinear registration framework based on screened Poisson flow and Wasserstein distance. The screened Poisson equation transforms geometric features into smooth multiscale probability distributions. Registration is formulated by minimizing the Wasserstein distance between these distributions, producing anatomically meaningful correspondences without explicit landmark or branch matching. The framework is demonstrated on the nonlinear registration of cortical sulcal--gyral folding patterns from structural MRI.