Active contours and minimal paths have been extensively studied theoretical tools for image segmentation. The recent geodesically linked active contour model, which basically consists in a set of vertices connected by paths of minimal cost, blend the bene ts of both concepts. This makes up a closed piecewise-smooth curve, over which an edge or region energy functional can be formulated. As an important shortcoming, the geodesically linked active contour model in its initial formulation does not guarantee the curve to be simple, consistent with respect to the purpose of segmentation. In this paper, we propose to extract a relevant contour from a set of possible paths, such that the resulting structure ts the image data and is simple. Toward this goal, we introduce a novel term to favor the simplicity of the generated contour, as well as a local search method to choose the best combination among possible paths.