Composed Segmentation of Tubular Structures by an Anisotropic PDE Model

In this work we introduce the composed segmentation (C- segmentation), that is a priori composition of sources to obtain a sin- gle one segmentation result according to speci¯c Boolean operations. The approach and the segmentation model are general but we apply the C-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 Di®erential Equation (PDE)-based di®usion model derived from a minimal volume- like variational formulation. The gradient °ow for this functional leads to a nonlinear curvature motion model. An anisotropic variant is provided which includes a di®usion 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.