A High-Order Scheme for Image Segmentation via a modified Level-Set method

The method is based on an adaptive "filtered" scheme recently introduced by the authors. The main feature of the scheme is the possibility to stabilize an a priori unstable high-order scheme via a filter function which allows to combine a high-order scheme in the regularity regions and a monotone scheme elsewhere, in presence of singularities. The filtered scheme considered in this paper uses the local Lax-Friedrichs scheme as monotone scheme and the Lax-Wendroff scheme as high-order scheme but other couplings are possible. Moreover, we introduce also a modified velocity function for the level-set model used in segmentation, this velocity allows to obtain more accurate results with respect to other velocities proposed in the literature. Some numerical tests on synthetic and real images confirm the accuracy of the proposed method and the advantages given by the new velocity.