Segmentation of 3D tubular structures by a PDE-based anisotropic diffusion model

In this work we introduce the segmentation of 3D tubular structures by a PDE-based anisotropic diffusion model. The approach and the segmentation model are general but we apply the segmentation technique to the challenging problem of segmenting tubular-like structures. The reconstruction is obtained by continuously deforming an initial distance function following the Partial Differential Equation (PDE)-based diffusion model derived from a minimal volume-like variational formulation. The gradient flow for this functional leads to a nonlinear curvature motion model. An anisotropic variant is provided which includes a diffusion tensor aimed to follow the tube geometry. Numerical examples demonstrate the ability of the proposed method to produce high quality 2D/3D segmentations of complex and eventually incomplete synthetic and real data.