@conference {Hornacek2014,
	title = {Highly overparameterized optical flow using PatchMatch belief propagation},
	booktitle = {Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)},
	volume = {8691 LNCS},
	number = {PART 3},
	year = {2014},
	pages = {220{\textendash}234},
	abstract = {Motion in the image plane is ultimately a function of 3D motion in space. We propose to compute optical flow using what is ostensibly an extreme overparameterization: depth, surface normal, and frame-to-frame 3D rigid body motion at every pixel, giving a total of 9 DoF. The advantages of such an overparameterization are twofold: first, geometrically meaningful reasoning can be called upon in the optimization, reflecting possible 3D motion in the underlying scene; second, the {\textquoteright}fronto-parallel{\textquoteright} assumption implicit in the use of traditional matching pixel windows is ameliorated because the parameterization determines a plane-induced homography at every pixel. We show that optimization over this high-dimensional, continuous state space can be carried out using an adaptation of the recently introduced PatchMatch Belief Propagation (PMBP) energy minimization algorithm, and that the resulting flow fields compare favorably to the state of the art on a number of small- and large-displacement datasets. {\textcopyright} 2014 Springer International Publishing.},
	keywords = {9 DoF, large displacement, optical flow, PatchMatch, PMBP},
	isbn = {9783319105772},
	issn = {16113349},
	doi = {10.1007/978-3-319-10578-9_15},
	author = {Horn{\'a}{\v c}ek, Michael and Besse, Frederic and Kautz, Jan and Fitzgibbon, Andrew and Carsten Rother}
}
@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}
}
