Minimum ratio contours for meshes

We present a novel minimum ratio contour (MRC) algorithm, for discretely optimizing contours on the surface of triangle meshes. We compute the contour having the minimal ratio between a numerator and a denominator energy. The numerator energy measures the bending and salience (feature adaptation) of a contour, while the denominator energy measures contour length. Given an initial contour, the optimal contour within a prescribed search domain is sought. The search domain is modeled by a weighted acyclic edge graph, where nodes in the graph correspond to directed edges in the mesh. The acyclicity of this graph allows for an efficient computation of the MRC. To further improve the result, the algorithm may be run on a refined mesh to allow for smoother contours that can cut across mesh faces. Results are demonstrated for postprocessing in mesh segmentation. We also speculate on possible global optimization methods for computing a MRC.