Shortest Paths with Curvature and Torsion

Paper in proceeding, 2013

This paper describes a method of finding thin, elongated structures in images and volumes. We use shortest paths to minimize very general functionals of higher-order curve properties, such as curvature and torsion. Our globally op- timal method uses line graphs and its runtime is polynomial in the size of the discretization, often in the order of seconds on a single computer. To our knowledge, we are the first to perform experiments in three dimensions with cur- vature and torsion regularization. The largest graphs we process have almost one hundred billion arcs. Experiments on medical images and in multi-view reconstruction show the significance and practical usefulness of regularization based on curvature while torsion is still only tractable for small-scale problems.