Globally Optimal Pixel Labeling Algorithms for Tree Metrics

We consider pixel labeling problems where the label set forms a tree, and where the observations are also labels. Such problems arise in feature-space analysis with a very large label set, for instance in color image segmentation. In this case a tree of labels can be constructed via hierarchical clustering of the observations. This leads to an obvious distance function between two labels, namely their distance within the tree; such tree metrics have been extensively studied outside of computer vision [14]. We provide fast algorithms that use graph cuts to exactly minimize the energy function for pixel labeling problems with tree metrics. Our work substantially improves a facility location algorithm of Kolen [18], which is impractical for large label sets L since it requires O(jLj) min cuts on large graphs. Our main technical contribution is a new ordering of swap moves that reduces the running time to the equivalent of O(log jLj) min cuts; as a result, we can handle rea...

• Type: Conference
• Year: 2010
• Where: CVPR
• Authors: Pedro Felzenszwalb, Gyula Pap, Eva Tardos, Ramin Zabih
• Keywords: Computer Vision, CVPR 2010, Globally Optimal Pixel Labeling Algorithms, Tree Metrics