TY - CONF T1 - Entropy rate superpixel segmentation T2 - 2011 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) Y1 - 2011 A1 - Ming-Yu Liu A1 - Tuzel, O. A1 - Ramalingam, S. A1 - Chellapa, Rama KW - balancing function KW - Berkeley segmentation benchmark KW - Complexity theory KW - Entropy KW - entropy rate KW - graph construction KW - graph theory KW - graph topology KW - greedy algorithm KW - Greedy algorithms KW - homogeneous clusters KW - Image edge detection KW - Image segmentation KW - matrix algebra KW - matroid constraint KW - measurement KW - pattern clustering KW - Random variables KW - standard evaluation metrics KW - superpixel segmentation KW - vector spaces AB - We propose a new objective function for superpixel segmentation. This objective function consists of two components: entropy rate of a random walk on a graph and a balancing term. The entropy rate favors formation of compact and homogeneous clusters, while the balancing function encourages clusters with similar sizes. We present a novel graph construction for images and show that this construction induces a matroid - a combinatorial structure that generalizes the concept of linear independence in vector spaces. The segmentation is then given by the graph topology that maximizes the objective function under the matroid constraint. By exploiting submodular and mono-tonic properties of the objective function, we develop an efficient greedy algorithm. Furthermore, we prove an approximation bound of ½ for the optimality of the solution. Extensive experiments on the Berkeley segmentation benchmark show that the proposed algorithm outperforms the state of the art in all the standard evaluation metrics. JA - 2011 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) PB - IEEE SN - 978-1-4577-0394-2 M3 - 10.1109/CVPR.2011.5995323 ER -