Shortest Enclosing Walks with a Non-zero Winding Number in Directed Weighted Planar Graphs: A Technique for Image Segmentation

This paper presents an efficient graph-based image segmentation algorithm based on finding the shortest closed directed walks surrounding a given point in the image. Our work is motivated by the Intelligent Scissors algorithm, which finds open contours using the shortestpath algorithm, and the Corridor Scissors algorithm, which is able to find closed contours. Both of these algorithms focus on undirected, nonnegatively weighted graphs. We generalize these results to directed planar graphs (not necessary with nonnegative weights), which allows our approach to utilize knowledge of the object’s appearance. The running time of our algorithm is approximately the same as that of a standard shortest-path algorithm.