@article {Szeliski2008,
	title = {A comparative study of energy minimization methods for Markov random fields with smoothness-based priors},
	journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
	volume = {30},
	number = {6},
	year = {2008},
	pages = {1068{\textendash}1080},
	publisher = {Springer-Verlag},
	abstract = {Among the most exciting advances in early vision has been the development of efficient energy minimization algorithms for pixel-labeling tasks such as depth or texture computation. It has been known for decades that such problems can be elegantly expressed as Markov random fields, yet the resulting energy minimization problems have been widely viewed as intractable. Recently, algorithms such as graph cuts and loopy belief propagation (LBP) have proven to be very powerful: for example, such methods form the basis for almost all the top-performing stereo methods. However, the tradeoffs among different energy minimization algorithms are still not well understood. In this paper we describe a set of energy minimization benchmarks and use them to compare the solution quality and running time of several common energy minimization algorithms. We investigate three promising recent methods graph cuts, LBP, and tree-reweighted message passing in addition to the well-known older iterated conditional modes (ICM) algorithm. Our benchmark problems are drawn from published energy functions used for stereo, image stitching, interactive segmentation, and denoising. We also provide a general-purpose software interface that allows vision researchers to easily switch between optimization methods. Benchmarks, code, images, and results are available at http://vision.middlebury.edu/ MRF/. {\textcopyright} 2008 IEEE.},
	keywords = {Belief propagation, Global optimization, Graph Cuts, Markov random fields, Performance evaluation},
	issn = {01628828},
	doi = {10.1109/TPAMI.2007.70844},
	url = {http://vision.middlebury.edu/MRF.},
	author = {Szeliski, Richard and Zabih, Ramin and Scharstein, Daniel and Veksler, Olga and Kolmogorov, Vladimir and Agarwala, Aseem and Tappen, Marshall and Carsten Rother}
}
@article {Szeliski2008a,
	title = {A comparative study of energy minimization methods for Markov random fields with smoothness-based priors},
	journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
	volume = {30},
	number = {6},
	year = {2008},
	month = {jun},
	pages = {1068{\textendash}1080},
	abstract = {Among the most exciting advances in early vision has been the development of efficient energy minimization algorithms for pixel-labeling tasks such as depth or texture computation. It has been known for decades that such problems can be elegantly expressed as Markov random fields, yet the resulting energy minimization problems have been widely viewed as intractable. Recently, algorithms such as graph cuts and loopy belief propagation (LBP) have proven to be very powerful: for example, such methods form the basis for almost all the top-performing stereo methods. However, the tradeoffs among different energy minimization algorithms are still not well understood. In this paper we describe a set of energy minimization benchmarks and use them to compare the solution quality and running time of several common energy minimization algorithms. We investigate three promising recent methods graph cuts, LBP, and tree-reweighted message passing in addition to the well-known older iterated conditional modes (ICM) algorithm. Our benchmark problems are drawn from published energy functions used for stereo, image stitching, interactive segmentation, and denoising. We also provide a general-purpose software interface that allows vision researchers to easily switch between optimization methods. Benchmarks, code, images, and results are available at http://vision.middlebury.edu/ MRF/. {\textcopyright} 2008 IEEE.},
	keywords = {Belief propagation, Global optimization, Graph Cuts, Markov random fields, Performance evaluation},
	issn = {01628828},
	doi = {10.1109/TPAMI.2007.70844},
	author = {Szeliski, Richard and Zabih, Ramin and Scharstein, Daniel and Veksler, Olga and Kolmogorov, Vladimir and Agarwala, Aseem and Tappen, Marshall and Carsten Rother}
}
@conference {Rother2004,
	title = {"GrabCut" - Interactive foreground extraction using iterated graph cuts},
	booktitle = {ACM Transactions on Graphics},
	volume = {23},
	number = {3},
	year = {2004},
	pages = {309{\textendash}314},
	abstract = {The problem of efficient, interactive foreground/background segmentation in still images is of great practical importance in image editing. Classical image segmentation tools use either texture (colour) information, e.g. Magic Wand, or edge (contrast) information, e.g. Intelligent Scissors. Recently, an approach based on optimization by graph-cut has been developed which successfully combines both types of information. In this paper we extend the graph-cut approach in three respects. First, we have developed a more powerful, iterative version of the optimisation. Secondly, the power of the iterative algorithm is used to simplify substantially the user interaction needed for a given quality of result. Thirdly, a robust algorithm for "border matting" has been developed to estimate simultaneously the alpha-matte around an object boundary and the colours of foreground pixels. We show that for moderately difficult examples the proposed method outperforms competitive tools.},
	keywords = {Alpha Matting, Foreground extraction, Graph Cuts, Image Editing, Interactive Image Segmentation},
	issn = {07300301},
	doi = {10.1145/1015706.1015720},
	author = {Carsten Rother and Kolmogorov, Vladimir and Blake, Andrew}
}
