A fuzzy edge-weighted centroidal Voronoi tessellation model for image segmentation

The centroidal Voronoi tessellation (CVT) is a special Voronoi tessellation whose generators are also the centers of mass of the corresponding Voronoi regions. The edge-weighted centroidal Voronoi tessellation (EWCVT) greatly improves the classic CVT model by adding an edge energy term in the energy functional, and has been proven to be very effective and efficient for image segmentation. In this paper, we propose a fuzzy edge-weighted centroidal Voronoi tessellation (FEWCVT) model which generalizes the EWCVT clustering with fuzzy membership information. The FEWCVT model novelly introduces an edge energy based on fuzzy clustering and naturally combines it into the EWCVT model, and thus appropriately combines the image intensity information with the length of cluster boundaries in a fuzzy form. In its simplest form, FEWCVT model reduces to the classic EWCVT model. An iterative algorithm is proposed for the FEWCVT model based on energy minimization. In the experiments, we apply the FEWCVT method to segment various types of images and also compare it with several existing fuzzy clustering methods to demonstrate its performance.