@article {Berger2017,
	title = {{Second-Order Recursive Filtering on the Rigid-Motion Lie Group SE(3) Based on Nonlinear Observations},
	journal = {J. Math. Imag. Vision},
	volume = {58},
	number = {1},
	year = {2017},
	pages = {102{\textendash}129},
	author = {Johannes Berger and Lenzen, F. and Florian Becker and Neufeld, A. and Schn{\"o}rr, C.}
}
@conference {Neufeld-et-al-2015a,
	title = {Estimating Vehicle Ego-Motion and Piecewise Planar Scene Structure from Optical Flow in a Continuous Framework},
	booktitle = {37th German Conference on Pattern Recognition},
	year = {2015},
	note = {in press},
	author = {Neufeld, Andreas and Johannes Berger and Florian Becker and Lenzen, Frank and Christoph Schn{\"o}rr}
}
@conference {Berger-et-al-2015a,
	title = {Second Order Minimum Energy Filtering on SE(3) with Nonlinear Measurement Equations},
	booktitle = {Scale Space and Variational Methods in Computer Vision (SSVM 2015)},
	year = {2015},
	publisher = {Springer International Publishing},
	organization = {Springer International Publishing},
	abstract = {Accurate camera motion estimation is a fundamental build- ing block for many Computer Vision algorithms. For improved robustness, temporal consistency of translational and rotational camera velocity is often assumed by propagating motion information forward using stochastic filters. Classical stochastic filters, however, use linear approximations for the non-linear observer model and for the non-linear structure of the underlying Lie Group SE(3) and have to approximate the unknown posteriori distribution. In this paper we employ a non-linear measurement model for the camera motion estimation problem that incorporates multiple observation equations. We solve the underlying filtering problem using a novel Minimum Energy Filter on SE(3) and give explicit expressions for the optimal state variables. Experiments on the challenging KITTI benchmark show that, although a simple motion model is only employed, our approach improves rotational velocity esti- mation and otherwise is on par with the state-of-the-art.},
	doi = {10.1007/978-3-319-18461-6_32},
	url = {http://dx.doi.org/10.1007/978-3-319-18461-6_32},
	author = {Johannes Berger and Andreas Neufeld and Florian Becker and Frank Lenzen and Christoph Schn{\"o}rr}
}
@conference {Berger-et-al-2015a,
	title = {Second Order Minimum Energy Filtering on SE(3) with Nonlinear Measurement Equations},
	booktitle = {Scale Space and Variational Methods in Computer Vision (SSVM 2015)},
	year = {2015},
	author = {Johannes Berger and Neufeld, Andreas and Florian Becker and Lenzen, Frank and Christoph Schn{\"o}rr}
}
@booklet {Berger-et-al-2015b,
	title = {Second-Order Recursive Filtering on the Rigid-Motion Lie Group SE(3) Based on Nonlinear Observations},
	year = {2015},
	abstract = {Camera motion estimation from observed scene features is an important task in image processing to increase the accuracy of many methods, e.g. optical flow and structure-from-motion. Due to the curved geometry of the state space SE(3) and the non-linear relation to the observed optical flow, many recent filtering approaches use a first-order approximation and assume a Gaussian a posteriori distribution or restrict the state to Euclidean geometry. The physical model is usually also limited to uniform motions. 
We propose a second-order minimum energy filter with a generalized kinematic model that copes with the full geometry of SE(3) as well as with the nonlinear dependencies between the state space and observations. The derived filter enables reconstructing motions correctly for synthetic and real scenes, e.g. from the KITTI benchmark. Our experiments confirm that the derived minimum energy filter with higher-order state differential equation copes with higher-order kinematics and is also able to minimize model noise. We also show that the proposed filter is superior to state-of-the-art extended Kalman filters on Lie groups in the case of linear observations and that our method reaches the accuracy of modern visual odometry methods.},
	keywords = {Constant Acceleration Model, Lie Group, Minimum Energy Filter, Optimal Control, Recursive Filtering, Visual Odometry},
	url = {http://arxiv.org/abs/1507.06810},
	author = {Johannes Berger and Frank Lenzen and Florian Becker and Andreas Neufeld and Christoph Schn{\"o}rr}
}
@booklet {Berger-et-al-2015b,
	title = {Second-Order Recursive Filtering on the Rigid-Motion Lie Group SE(3) Based on Nonlinear Observations},
	year = {2015},
	note = {ArXiv, preprint},
	url = {http://arxiv.org/abs/1507.06810},
	author = {Johannes Berger and Lenzen, Frank and Florian Becker and Neufeld, Andreas and Christoph Schn{\"o}rr}
}
@incollection {Becker2014,
	title = {Optical Flow},
	year = {2014},
	note = {in press},
	publisher = {Springer},
	edition = {2nd},
	author = {Florian Becker and Petra, Stefania and Christoph Schn{\"o}rr},
	editor = {Scherzer, O.}
}
@article {Lenzen-et-al-14,
	title = {Solving Quasi-Variational Inequalities for Image Restoration with Adaptive Constraint Sets},
	journal = {SIAM J. Imag. Sci.},
	volume = {7},
	number = {4},
	year = {2014},
	pages = {2139{\textendash}2174},
	author = {Lenzen, F. and Lellmann, J. and Florian Becker and Schn{\"o}rr, C.}
}
@article {Lenzen-et-al-14,
	title = {Solving Quasi-Variational Inequalities for Image Restoration with Adaptive Constraint Sets},
	journal = {SIAM J.~Imag.~Sci.},
	volume = {7},
	number = {4},
	year = {2014},
	pages = {2139--2174},
	author = {Frank Lenzen and Lellmann, J. and Florian Becker and Christoph Schn{\"o}rr}
}
@article {lenzen_14_solving,
	title = {Solving QVIs for Image Restoration with Adaptive Constraint Sets},
	journal = {SIAM Journal on Imaging Sciences (SIIMS), in press},
	year = {2014},
	note = {1},
	author = {Frank Lenzen and Lellmann, J. and Florian Becker and Christoph Schn{\"o}rr}
}
@conference {Lenzen-2013-ssvm,
	title = {Adaptive Second-Order Total Variation: An Approach Aware of Slope Discontinuities},
	booktitle = {Proceedings of the 4th International Conference on Scale Space and Variational Methods in Computer Vision (SSVM) 2013},
	volume = {54},
	year = {2013},
	pages = {371--398},
	publisher = {Springer},
	organization = {Springer},
	author = {Frank Lenzen and Florian Becker and Lellmann, Jan}
}
@conference {lenzen_13_adaptive,
	title = {Adaptive Second-Order Total Variation: An Approach Aware of Slope
Discontinuities},
	booktitle = {Proceedings of the 4th International Conference on Scale Space and
Variational Methods in Computer Vision SSVM},
	volume = {7893},
	year = {2013},
	note = {1},
	pages = {61-73},
	publisher = {Springer},
	organization = {Springer},
	doi = {10.1007/978-3-642-38267-3_6},
	author = {Frank Lenzen and Florian Becker and Lellmann, J.}
}
@conference {petra_13_bsmart,
	title = {B-SMART: Bregman-Based First-Order Algorithms for Non-Negative
Compressed Sensing Problems},
	booktitle = {Proceedings of the 4th International Conference on Scale Space and
Variational Methods in Computer Vision SSVM},
	year = {2013},
	note = {1},
	pages = {110-124},
	doi = {10.1007/978-3-642-38267-3_10},
	author = {Stefania Petra and Christoph Schn{\"o}rr and Florian Becker and Frank Lenzen}
}
@conference {Petra-2013-bsmart,
	title = {B-SMART: Bregman-Based First-Order Algorithms for Non-Negative Compressed Sensing Problems},
	booktitle = {Proceedings of the 4th International Conference on Scale Space and Variational Methods in Computer Vision (SSVM) 2013},
	volume = {7893},
	year = {2013},
	pages = {110-124},
	publisher = {Springer},
	organization = {Springer},
	author = {Stefania Petra and Christoph Schn{\"o}rr and Florian Becker and Frank Lenzen}
}
@article {lenzen_13_class,
	title = {A Class of Quasi-Variational Inequalities for Adaptive Image Denoising
and Decomposition},
	journal = {Computational Optimization and Applications (COAP)},
	volume = {54 (2)},
	year = {2013},
	note = {1},
	pages = {371-398},
	doi = {10.1007/s10589-012-9456-0},
	author = {Frank Lenzen and Florian Becker and Lellmann, J. and Stefania Petra and Christoph Schn{\"o}rr}
}
@article {Lenzen-et-al-13,
	title = {A class of quasi-variational inequalities for adaptive image denoising and decomposition},
	journal = {Computational Optimization and Applications},
	volume = {54},
	number = {2},
	year = {2013},
	pages = {371-398},
	publisher = {Springer Netherlands},
	issn = {0926-6003},
	url = {http://dx.doi.org/10.1007/s10589-012-9456-0},
	author = {Frank Lenzen and Florian Becker and Lellmann, Jan and Stefania Petra and Christoph Schn{\"o}rr}
}
@conference {lenzen_13_denoising,
	title = {Denoising Strategies for Time-of-Flight Data},
	booktitle = {Time-of-Flight Imaging: Algorithms, Sensors and Applications},
	volume = {8200},
	year = {2013},
	note = {1},
	pages = {24-25},
	publisher = {Springer},
	organization = {Springer},
	doi = {10.1007/978-3-642-44964-2_2},
	author = {Frank Lenzen and Kim, K. I. and Sch{\"a}fer, H. and Nair, R. and Stephan Meister and Florian Becker and Christoph S. Garbe},
	editor = {Grzegorzek, M. and Theobalt, C. and Andreas Kolb and Theobalt, C. and Reinhard Koch}
}
@incollection {Lenzen2013stategies,
	title = {Denoising Strategies for Time-of-Flight Data},
	volume = {8200},
	year = {2013},
	pages = {25-45},
	publisher = {Springer},
	author = {Frank Lenzen and Kim, Kwang In and Sch{\"a}fer, Henrik and Nair, Rahul and Stephan Meister and Florian Becker and Christoph S. Garbe},
	editor = {Grzegorzek, Marcin and Theobalt, Christian and Andreas Kolb and Theobalt, Christian and Reinhard Koch}
}
@article {Becker-et-al-13a,
	title = {Variational Recursive Joint Estimation of Dense Scene Structure and Camera Motion from Monocular High Speed Traffic Sequences},
	journal = {International Journal of Computer Vision},
	volume = {105},
	year = {2013},
	pages = {269--297},
	publisher = {Springer US},
	issn = {0920-5691},
	doi = {10.1007/s11263-013-0639-7},
	url = {http://dx.doi.org/10.1007/s11263-013-0639-7},
	author = {Florian Becker and Frank Lenzen and J{\"o}rg H. Kappes and Christoph Schn{\"o}rr}
}
@article {Becker-et-al-13a,
	title = {Variational Recursive Joint Estimation of Dense Scene Structure and Camera Motion from Monocular High Speed Traffic Sequences},
	journal = {International Journal of Computer Vision},
	volume = {105},
	year = {2013},
	pages = {269{\textendash}297},
	publisher = {Springer US},
	keywords = {Dense depth map, Recursive formulation, Structure from motion, Variational approach},
	issn = {0920-5691},
	doi = {10.1007/s11263-013-0639-7},
	url = {http://dx.doi.org/10.1007/s11263-013-0639-7},
	author = {Florian Becker and Lenzen, Frank and Kappes, J{\"o}rg H. and Christoph Schn{\"o}rr}
}
@article {becker_13_variational,
	title = {Variational Recursive Joint Estimation of Dense Scene Structure and
Camera Motion from Monocular High Speed Traffic Sequences},
	journal = {International Journal of Computer Vision},
	volume = {105 (3)},
	year = {2013},
	note = {1},
	pages = {269-297},
	doi = {10.1007/s11263-013-0639-7},
	author = {Florian Becker and Frank Lenzen and J{\"o}rg H. Kappes and Christoph Schn{\"o}rr}
}
@article {Becker-et-al-11b,
	title = {Variational Adaptive Correlation Method for Flow Estimation},
	journal = {IEEE Transactions on Image Processing},
	volume = {21},
	number = {6},
	year = {2012},
	pages = {3053 -- 3065},
	doi = {10.1109/TIP.2011.2181524},
	author = {Florian Becker and Wieneke, Bernhard and Stefania Petra and Schr{\"o}der, Andreas and Christoph Schn{\"o}rr}
}
@article {Becker-et-al-11b,
	title = {Variational Adaptive Correlation Method for Flow Estimation},
	journal = {IEEE Transactions on Image Processing},
	volume = {21},
	number = {6},
	year = {2012},
	month = {June},
	pages = {3053 {\textendash} 3065},
	doi = {10.1109/TIP.2011.2181524},
	author = {Florian Becker and Wieneke, Bernhard and Petra, Stefania and Schr{\"o}der, Andreas and Christoph Schn{\"o}rr}
}
@conference {Lenzen-et-al-11,
	title = {Variational Image Denoising with Adaptive Constraint Sets},
	booktitle = {Proceedings of the 3rd International Conference on Scale Space and Variational Methods in Computer Vision 2011},
	year = {2012},
	pages = {206-217},
	publisher = {Springer},
	organization = {Springer},
	author = {Lenzen, Frank and Florian Becker and Lellmann, Jan and Petra, Stefania and Christoph Schn{\"o}rr}
}
@conference {Lenzen-et-al-11,
	title = {Variational Image Denoising with Adaptive Constraint Sets},
	booktitle = {LNCS},
	year = {2012},
	pages = {206-217},
	publisher = {Springer},
	organization = {Springer},
	author = {Frank Lenzen and Florian Becker and Lellmann, Jan and Stefania Petra and Christoph Schn{\"o}rr}
}
@article {becker_11_variational2,
	title = {Variational Adaptive Correlation Method for Flow Estimation},
	journal = {IEEE Transactions on Image Processing},
	volume = {21, 6},
	year = {2011},
	note = {1},
	pages = {3053 - 3065},
	doi = {10.1109/TIP.2011.2181524},
	author = {Florian Becker and Wieneke, B. and Stefania Petra and Schr{\"o}der, A. and Christoph Schn{\"o}rr}
}
@conference {lenzen_11_variational,
	title = {Variational Image Denoising with Adaptive Constraint Sets},
	booktitle = {Proceedings of the 3nd International Conference on Scale Space and
Variational Methods in Computer Vision 2011, in press},
	volume = {6667},
	year = {2011},
	note = {1},
	pages = {206-217},
	publisher = {Springer},
	organization = {Springer},
	doi = {10.1007/978-3-642-24785-9_18},
	author = {Frank Lenzen and Florian Becker and Lellmann, J. and Stefania Petra and Christoph Schn{\"o}rr}
}
@conference {becker_11_variational,
	title = {Variational Recursive Joint Estimation of Dense Scene Structure and
Camera Motion from Monocular High Speed Traffic Sequences},
	booktitle = {2011 IEEE International Conference on Computer Vision ICCV},
	year = {2011},
	note = {1},
	pages = {1692-1699},
	doi = {10.1109/ICCV.2011.6126432},
	author = {Florian Becker and Frank Lenzen and J{\"o}rg H. Kappes and Christoph Schn{\"o}rr},
	editor = {Metaxas, D. N. and Quan, L. and Van Gool, L. J. and Sanfeliu, A.}
}
@conference {Becker-et-al-11a,
	title = {Variational Recursive Joint Estimation of Dense Scene Structure and Camera Motion from Monocular High Speed Traffic Sequences},
	booktitle = {2011 IEEE International Conference on Computer Vision (ICCV)},
	year = {2011},
	pages = {1692 -- 1699},
	doi = {10.1109/ICCV.2011.6126432},
	author = {Florian Becker and Frank Lenzen and J{\"o}rg H. Kappes and Christoph Schn{\"o}rr}
}
@conference {Becker-et-al-11a,
	title = {Variational Recursive Joint Estimation of Dense Scene Structure and Camera Motion from Monocular High Speed Traffic Sequences},
	booktitle = {2011 IEEE International Conference on Computer Vision (ICCV)},
	year = {2011},
	pages = {1692 {\textendash} 1699},
	doi = {10.1109/ICCV.2011.6126432},
	author = {Florian Becker and Lenzen, Frank and Kappes, J{\"o}rg H. and Christoph Schn{\"o}rr}
}
@conference {Lellmann-et-al-09a,
	title = {Convex Multi-Class Image Labeling by Simplex-Constrained Total Variation},
	booktitle = {Scale Space and Variational Methods in Computer Vision (SSVM 2009)},
	volume = {5567},
	year = {2009},
	pages = {150-162},
	publisher = {Springer},
	organization = {Springer},
	author = {Lellmann, J. and J{\"o}rg H. Kappes and Yuan, J. and Florian Becker and Christoph Schn{\"o}rr},
	editor = {Tai, X.-C. and M{\'o}rken, K. and Lie, K.-A. and Lysaker, M.}
}
@conference {lellmann_09_convex2,
	title = {Convex Multi-Class Image Labeling by Simplex-Constrained Total Variation},
	booktitle = {Scale Space and Variational Methods in Computer Vision (SSVM 2009)},
	volume = {5567},
	year = {2009},
	note = {1},
	pages = {150-162},
	publisher = {Springer},
	organization = {Springer},
	doi = {10.1007/978-3-642-02256-2_13},
	author = {Lellmann, J. and J{\"o}rg H. Kappes and Yuan, J. and Florian Becker and Christoph Schn{\"o}rr and M{\'o}rken, K. and Lysaker, M.},
	editor = {Tai, X.-C. and Lie, K.-A.}
}
@conference {Lellmann2009a,
	title = {Convex Optimization for Multi-Class Image Labeling with a Novel Family of Total Variation Based Regularizers},
	booktitle = {IEEE International Conference on Computer Vision (ICCV)},
	year = {2009},
	pages = {646 -- 653},
	author = {Lellmann, J. and Florian Becker and Christoph Schn{\"o}rr}
}
@conference {lellmann_09_convex,
	title = {Convex Optimization for Multi-Class Image Labeling with a Novel Family
of Total Variation Based Regularizers},
	booktitle = {Proceedings of the IEEE Conference on Computer Vision (ICCV 09) Kyoto, Japan},
	year = {2009},
	note = {1},
	pages = {646-653},
	doi = {10.1109/ICCV.2009.5459176},
	author = {Lellmann, J. and Florian Becker and Christoph Schn{\"o}rr}
}
@phdthesis {Becker-diss-2009,
	title = {Variational Correlation and Decomposition Methods for Particle Image Velocimetry},
	year = {2009},
	publisher = {Heidelberg University, Faculty of Mathematics and Computer Sciences},
	type = {phddoctoral thesis},
	address = {Heidelberg, Germany},
	url = {http://www.ub.uni-heidelberg.de/archiv/9766/},
	author = {Florian Becker}
}
@techreport {Lellmann2008,
	title = {Convex Multi-Class Image Labeling by Simplex-Constrained Total Variation},
	year = {2008},
	institution = {IWR, University of Heidelberg},
	url = {http://www.ub.uni-heidelberg.de/archiv/8759/},
	author = {Lellmann, J. and J{\"o}rg H. Kappes and Yuan, J. and Florian Becker and Christoph Schn{\"o}rr}
}
@conference {Becker-et-al-08a,
	title = {Decomposition of Quadratric Variational Problems},
	booktitle = {Pattern Recognition -- 30th DAGM Symposium},
	volume = {5096},
	year = {2008},
	pages = {325--334},
	publisher = {Springer Verlag},
	organization = {Springer Verlag},
	author = {Florian Becker and Christoph Schn{\"o}rr}
}
@conference {becker_08_decomposition,
	title = {Decomposition of Quadratric Variational Problems},
	booktitle = {Pattern Recognition -- 30th DAGM Symposium},
	volume = {5096},
	year = {2008},
	note = {1},
	pages = {325--334},
	author = {Florian Becker and Christoph Schn{\"o}rr}
}
@conference {Becker-et-al-08b,
	title = {A Variational Approach to Adaptive Correlation for Motion Estimation in Particle Image Velocimetry},
	booktitle = {Pattern Recognition {\textendash} 30th DAGM Symposium},
	series = {lncs},
	volume = {5096},
	year = {2008},
	pages = {335{\textendash}344},
	publisher = {Springer Verlag},
	organization = {Springer Verlag},
	author = {Florian Becker and Wieneke, Bernhard and Yuan, Jing and Christoph Schn{\"o}rr}
}
@conference {Becker-et-al-08b,
	title = {A Variational Approach to Adaptive Correlation for Motion Estimation in Particle Image Velocimetry},
	booktitle = {Pattern Recognition -- 30th DAGM Symposium},
	volume = {5096},
	year = {2008},
	pages = {335--344},
	publisher = {Springer Verlag},
	organization = {Springer Verlag},
	author = {Florian Becker and Wieneke, Bernhard and Yuan, Jing and Christoph Schn{\"o}rr}
}
@conference {becker_08_variational,
	title = {A Variational Approach to Adaptive Correlation for Motion Estimation
in Particle Image Velocimetry"},
	booktitle = {Pattern Recognition -- 30th DAGM Symposium},
	volume = {5096},
	year = {2008},
	note = {1},
	pages = {335-344},
	author = {Florian Becker and Wieneke, B. and Yuan, J. and Christoph Schn{\"o}rr}
}
@conference {Becker-et-al-08c,
	title = {Variational Correlation Approach to Flow Measurement with Window Adaption},
	booktitle = {14th International Symposium on Applications of Laser Techniques to Fluid Mechanics},
	year = {2008},
	pages = {1.1.3},
	author = {Florian Becker and Wieneke, Bernhard and Yuan, Jing and Christoph Schn{\"o}rr}
}
@conference {Becker-et-al-08c,
	title = {Variational Correlation Approach to Flow Measurement with Window Adaption},
	booktitle = {14th International Symposium on Applications of Laser Techniques to Fluid Mechanics},
	year = {2008},
	pages = {1.1.3},
	author = {Florian Becker and Wieneke, Bernhard and Yuan, Jing and Christoph Schn{\"o}rr}
}
@conference {becker_08_variational2,
	title = {Variational Correlation Approach to Flow Measurement with Window
Adaption},
	booktitle = {14th International Symposium on Applications of Laser Techniques
to Fluid Mechanics},
	year = {2008},
	note = {1},
	pages = {1.1.8},
	author = {Florian Becker and Wieneke, B. and Yuan, J. and Christoph Schn{\"o}rr}
}
@article {Welk-et-al-07,
	title = {Median and related local filters for tensor-valued images},
	journal = {Signal Processing},
	volume = {87},
	year = {2007},
	pages = {291-308},
	author = {Welk, M. and Weickert, J. and Florian Becker and Christoph Schn{\"o}rr and Feddern, C. and Burgeth, B.}
}
@article {Welk-et-al-07,
	title = {Median and related local filters for tensor-valued images},
	journal = {Signal Processing},
	volume = {87},
	year = {2007},
	pages = {291-308},
	author = {Welk, M. and Weickert, J. and Florian Becker and Schn{\"o}rr, C. and Feddern, C. and Burgeth, B.}
}
@conference {Welk-et-al-05a,
	title = {Matrix-Valued Filters as Convex Programs},
	booktitle = {Scale-Space 2005},
	series = {lncs},
	volume = {3459},
	year = {2005},
	pages = {204{\textendash}216},
	publisher = {Springer},
	organization = {Springer},
	author = {Welk, Martin and Florian Becker and Christoph Schn{\"o}rr and Weickert, Joachim}
}
@conference {Yuan-et-al-05b,
	title = {A Study of Non-Smooth Convex Flow Decomposition},
	booktitle = {Proc. Variational, Geometric and Level Set Methods in Computer Vision},
	series = {lncs},
	volume = {3752},
	year = {2005},
	pages = {1{\textendash}12},
	publisher = {Springer},
	organization = {Springer},
	author = {Yuan, Jing and Christoph Schn{\"o}rr and Steidl, Gabriele and Florian Becker}
}
