Segmentation of 3D Tubular Structures by a PDE-Based Anisotropic Diffusion Model

Many different approaches have been proposed for segmenting vessels, or more generally tubular-like structures from 2D/3D images. In this work we propose to reconstruct the boundaries of 2D/3D tubular structures 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 non-linear curvature motion model. An anisotropic variant is provided which includes a diffusion tensor aimed to follow the tube geometry. Space discretization of the PDE model is obtained by finite volume schemes and semi-implicit approach is used in time/scale. The use of an efficient strategy to apply the linear system iterative solver allows us to reduce significantly the numerical effort by limiting the computation near the structure boundaries. We illustrate how the proposed method works to segment 2D/3D images of synthetic and medical real data representing branching tubular structures.