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In this paper we present a new framework for the solution of active contourmodels on graphs. With the use of the Finite Element Method we generalizeactive contour models on graphs and reduce the problem from a partialdifferential equation to the solution of a sparse non-linear system.Additionally, we extend the proposed framework to solve models where the curveevolution is locally constrained around its current location. Based on theprevious extension, we propose a fast algorithm for the solution of a widerange active contour models. Last, we present a supervised extension ofGeodesic Active Contours for image segmentation and provide experimentalevidence for the effectiveness of our framework.

A Finite Element Computational Framework for Active Contours on Graphs