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 [11], 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 [11]. Furthermore, we show that our method is robust to graph compression which allows us to accelerate the computation without loss of accuracy.

• Type: Journal
• Year: 2011
• Where: CVPR
• Authors: Ryan Kennedy, Jean Gallier, Jianbo Shi
• Keywords: Computer Vision, Cost Function, CVPR 2011, Images, Untangling-cycle Cost Function