PDEs level sets on weighted graphs

In this paper we propose an adaptation of PDEs level sets over weighted graphs of arbitrary structure, based on PdEs and using a framework of discrete operators. A general PDEs level sets formulation is presented and an algorithm to solve such equation is described. Some transcriptions of well-known models under this formalism, as the mean-curvature-motion or active contours, are also provided. Then, we present several applications of our formalism, including image segmentation with active contours, using weighted graphs of arbitrary topologies.