@conference {12450,
	title = {Entropy rate superpixel segmentation},
	booktitle = {2011 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)},
	year = {2011},
	month = {2011/06/20/25},
	pages = {2097 - 2104},
	publisher = {IEEE},
	organization = {IEEE},
	abstract = {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 {\textonehalf} 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.},
	keywords = {balancing function, Berkeley segmentation benchmark, Complexity theory, Entropy, entropy rate, graph construction, graph theory, graph topology, greedy algorithm, Greedy algorithms, homogeneous clusters, Image edge detection, Image segmentation, matrix algebra, matroid constraint, measurement, pattern clustering, Random variables, standard evaluation metrics, superpixel segmentation, vector spaces},
	isbn = {978-1-4577-0394-2},
	doi = {10.1109/CVPR.2011.5995323},
	author = {Ming-Yu Liu and Tuzel, O. and Ramalingam, S. and Chellapa, Rama}
}
