@article {Besse2014,
	title = {PMBP: PatchMatch Belief Propagation for correspondence field estimation},
	journal = {International Journal of Computer Vision},
	volume = {110},
	number = {1},
	year = {2014},
	month = {oct},
	pages = {2{\textendash}13},
	publisher = {Kluwer Academic Publishers},
	abstract = {PatchMatch (PM) is a simple, yet very powerful and successful method for optimizing continuous labelling problems. The algorithm has two main ingredients: the update of the solution space by sampling and the use of the spatial neighbourhood to propagate samples. We show how these ingredients are related to steps in a specific form of belief propagation (BP) in the continuous space, called max-product particle BP (MP-PBP). However, MP-PBP has thus far been too slow to allow complex state spaces. In the case where all nodes share a common state space and the smoothness prior favours equal values, we show that unifying the two approaches yields a new algorithm, PMBP, which is more accurate than PM and orders of magnitude faster than MP-PBP. To illustrate the benefits of our PMBP method we have built a new stereo matching algorithm with unary terms which are borrowed from the recent PM Stereo work and novel realistic pairwise terms that provide smoothness. We have experimentally verified that our method is an improvement over state-of-the-art techniques at sub-pixel accuracy level.},
	keywords = {Belief propagation, Correspondence fields, PatchMatch},
	issn = {15731405},
	doi = {10.1007/s11263-013-0653-9},
	author = {Besse, Frederic and Carsten Rother and Fitzgibbon, Andrew and Kautz, Jan}
}
@article {Besse2014b,
	title = {PMBP: PatchMatch Belief Propagation for correspondence field estimation},
	journal = {International Journal of Computer Vision},
	volume = {110},
	number = {1},
	year = {2014},
	pages = {2{\textendash}13},
	abstract = {PatchMatch (PM) is a simple, yet very powerful and successful method for optimizing continuous labelling problems. The algorithm has two main ingredients: the update of the solution space by sampling and the use of the spatial neighbourhood to propagate samples. We show how these ingredients are related to steps in a specific form of belief propagation (BP) in the continuous space, called max-product particle BP (MP-PBP). However, MP-PBP has thus far been too slow to allow complex state spaces. In the case where all nodes share a common state space and the smoothness prior favours equal values, we show that unifying the two approaches yields a new algorithm, PMBP, which is more accurate than PM and orders of magnitude faster than MP-PBP. To illustrate the benefits of our PMBP method we have built a new stereo matching algorithm with unary terms which are borrowed from the recent PM Stereo work and novel realistic pairwise terms that provide smoothness. We have experimentally verified that our method is an improvement over state-of-the-art techniques at sub-pixel accuracy level.},
	keywords = {Belief propagation, Correspondence fields, PatchMatch},
	issn = {15731405},
	doi = {10.1007/s11263-013-0653-9},
	author = {Besse, Frederic and Carsten Rother and Fitzgibbon, Andrew and Kautz, Jan}
}
@article {Besse2014a,
	title = {PMBP: PatchMatch Belief Propagation for correspondence field estimation},
	journal = {International Journal of Computer Vision},
	volume = {110},
	number = {1},
	year = {2014},
	pages = {2{\textendash}13},
	abstract = {PatchMatch (PM) is a simple, yet very powerful and successful method for optimizing continuous labelling problems. The algorithm has two main ingredients: the update of the solution space by sampling and the use of the spatial neighbourhood to propagate samples. We show how these ingredients are related to steps in a specific form of belief propagation (BP) in the continuous space, called max-product particle BP (MP-PBP). However, MP-PBP has thus far been too slow to allow complex state spaces. In the case where all nodes share a common state space and the smoothness prior favours equal values, we show that unifying the two approaches yields a new algorithm, PMBP, which is more accurate than PM and orders of magnitude faster than MP-PBP. To illustrate the benefits of our PMBP method we have built a new stereo matching algorithm with unary terms which are borrowed from the recent PM Stereo work and novel realistic pairwise terms that provide smoothness. We have experimentally verified that our method is an improvement over state-of-the-art techniques at sub-pixel accuracy level.},
	keywords = {Belief propagation, Correspondence fields, PatchMatch},
	issn = {15731405},
	doi = {10.1007/s11263-013-0653-9},
	author = {Besse, Frederic and Carsten Rother and Fitzgibbon, Andrew and Kautz, Jan}
}
@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}
}
