Contour cut: Identifying salient contours in images by solving a Hermitian eigenvalue problem

The problem of finding one-dimensional structures in images and videos can be formulated as a problem of searching for cycles in graphs. In, an untangling-cycle cost function was proposed for identifying persistent cycles in a weighted graph, corresponding to salient contours in an image. We have analyzed their method and give two significant improvements. First, we generalize their cost function to a contour cut criterion and give a computational solution by solving a family of Hermitian eigenvalue problems. Second, we use the idea of a graph circulation, which ensures that each node has a balanced in- and out-flow and permits a natural random-walk interpretation of our cost function. We show that our method finds far more accurate contours in images than. Furthermore, we show that our method is robust to graph compression which allows us to accelerate the computation without loss of accuracy.