@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}
}
@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}
}
@conference {LenzenBerger2015,
	title = {Solution-Driven Adaptive Total Variation Regularization},
	booktitle = {LNCS},
	year = {2015},
	publisher = {Springer International Publishing},
	organization = {Springer International Publishing},
	abstract = {We consider solution-driven adaptive variants of Total Variation, in which the adaptivity is introduced as a fixed point problem. We provide existence theory for such fixed points in the continuous domain. For the applications of image denoising, deblurring and inpainting, we provide experiments which demonstrate that our approach in most cases outperforms state-of-the-art regularization approaches.},
	doi = {10.1007/978-3-319-18461-6_17},
	url = {http://dx.doi.org/10.1007/978-3-319-18461-6_17},
	author = {Frank Lenzen and Johannes Berger}
}
@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}
}
@conference {Schaefer2013depth,
	title = {Depth and Intensity Based Edge Detection in Time-of-Flight Images},
	booktitle = {3DV-Conference, 2013 International Conference on},
	year = {2013},
	pages = {111-118},
	doi = {10.1109/3DV.2013.23},
	author = {Sch{\"a}fer, Henrik and Frank Lenzen and Christoph S. Garbe}
}
@conference {schaefer_13_depth,
	title = {Depth and Intensity Based Edge Detection in Time-of-Flight Images},
	booktitle = {3D Imaging, Modeling, Processing, Visualization and Transmission
(3DIMPVT), 2013 International Conference on},
	year = {2013},
	note = {1},
	pages = {111-118},
	publisher = {IEEE},
	organization = {IEEE},
	doi = {10.1109/3DV.2013.23},
	author = {Sch{\"a}fer, H. and Frank Lenzen and Christoph S. Garbe}
}
@article {lellmann_13_optimality,
	title = {Optimality Bounds for a Variational Relaxation of the Image Partitioning
Problem},
	journal = {Journal of Mathematical Imaging and Vision},
	volume = {47 (3)},
	year = {2013},
	note = {1},
	pages = {239-257},
	doi = {10.1007/s10851-012-0390-7},
	author = {Lellmann, Jan and Frank Lenzen and Christoph Schn{\"o}rr}
}
@incollection {Nair2013survey,
	title = {A Survey on Time-of-Flight Stereo Fusion},
	volume = {8200},
	year = {2013},
	pages = {105-127},
	publisher = {Springer},
	author = {Nair, Rahul and Ruhl, Kai and Frank Lenzen and Stephan Meister and Sch{\"a}fer, Henrik and Christoph S. Garbe and Eisemann, Martin and Magnor, Marcus and Daniel Kondermann},
	editor = {Grzegorzek, Marcin and Theobalt, Christian and Andreas Kolb and Reinhard Koch}
}
@conference {nair_13_survey,
	title = {A Survey on Time-of-Flight Stereo Fusion},
	booktitle = {Time-of-Flight Imaging: Algorithms, Sensors and Applications},
	volume = {8022},
	year = {2013},
	pages = {105-127},
	publisher = {Springer},
	organization = {Springer},
	doi = {10.1007/978-3-642-44964-2_6},
	author = {Nair, R. and Ruhl, K. and Frank Lenzen and Stephan Meister and Sch{\"a}fer, H. and Christoph S. Garbe and Eisemann, M. and Daniel Kondermann},
	editor = {Grzegorzek, M. and Theobalt, C. and Andreas Kolb and Reinhard Koch}
}
@incollection {Lefloch2013foundations,
	title = {Technical Foundation and Calibration Methods for Time-of-Flight Cameras},
	volume = {8200},
	year = {2013},
	pages = {3-24},
	publisher = {Springer},
	author = {Damien Lefloch and Rahul Nair and Frank Lenzen and Henrik Sch{\"a}fer and Lee Streeter and Michael J. Cree and Reinhard Koch and Andreas Kolb},
	editor = {Grzegorzek, Marcin and Theobalt, Christian and Koch, Reinhard and Kolb, Andreas}
}
@conference {lefloch_13_technical,
	title = {Technical Foundation and Calibration Methods for Time-of-Flight Cameras},
	booktitle = {Time-of-Flight Imaging: Algorithms, Sensors and Applications},
	volume = {8200},
	number = {3-24},
	year = {2013},
	publisher = {Springer},
	organization = {Springer},
	doi = {10.1007/978-3-642-44964-2_1},
	author = {Lefloch, D. and Nair, R. and Frank Lenzen and Sch{\"a}fer, H. and Streeter, L. and Michael J. Cree},
	editor = {Reinhard Koch and Grzegorzek, M. and Theobalt, C. and Andreas Kolb and Andreas Kolb 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_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}
}
@conference {schaefer_12_edge,
	title = {Edge Detection in Time-of-Flight Images},
	booktitle = {submitted to ECCV, 2nd Workshop on Consumer Depth Cameras for Computer
Vision},
	year = {2012},
	note = {1},
	author = {Sch{\"a}fer, H. and Frank Lenzen and Stephan Meister and Christoph S. Garbe}
}
@conference {nair_12_high,
	title = {High Accuracy TOF and Stereo Sensor Fusion at Interactive Rates},
	booktitle = {submitted to ECCV 2012},
	volume = {7584},
	year = {2012},
	note = {1},
	pages = {1-11},
	publisher = {Springer},
	organization = {Springer},
	doi = {10.1007/978-3-642-33868-7_1},
	author = {Nair, R. and Frank Lenzen and Sch{\"a}fer, H. and Stephan Meister and Christoph S. Garbe and Daniel Kondermann}
}
@conference {Nair2012highaccuracy,
	title = {High accuracy TOF and stereo sensor fusion at interactive rates},
	booktitle = {Computer Vision--ECCV 2012. Workshops and Demonstrations},
	year = {2012},
	pages = {1--11},
	publisher = {Springer Berlin Heidelberg},
	organization = {Springer Berlin Heidelberg},
	author = {Nair, Rahul and Frank Lenzen and Stephan Meister and Sch{\"a}fer, Henrik and Christoph S. Garbe and Daniel Kondermann}
}
@article {Lellmann-et-al-12,
	title = {Optimality Bounds for a Variational Relaxation of the Image Partitioning Problem},
	journal = {Journal of Mathematical Imaging and Vision},
	volume = {47},
	number = {3},
	year = {2012},
	pages = {239-257},
	publisher = {Springer},
	issn = {0924-9907},
	doi = {10.1007/s10851-012-0390-7},
	author = {Lellmann, Jan and Frank Lenzen 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}
}
@conference {lenzen_11_denoising,
	title = {Denoising Time-Of-Flight Data with Adaptive Total Variation},
	booktitle = {Proceedings ISVC},
	year = {2011},
	note = {1},
	pages = {337-346},
	publisher = {Springer},
	organization = {Springer},
	doi = {10.1007/978-3-642-24028-7_31},
	author = {Frank Lenzen and Sch{\"a}fer, H. and Christoph S. Garbe}
}
@conference {Lellmann2011,
	title = {Optimality Bounds for a Variational Relaxation of the Image Partitioning Problem},
	booktitle = {Energy Min. Meth. Comp. Vis. Patt. Recogn.},
	volume = {6819},
	year = {2011},
	pages = {132--146},
	publisher = {Springer},
	organization = {Springer},
	author = {Lellmann, Jan and Frank Lenzen and Christoph Schn{\"o}rr},
	editor = {Boykov, Y. and Kahl, F. and Schmidt, F. R. and Lempitsky, V. F.}
}
@conference {lellmann_11_optimality,
	title = {Optimality Bounds for a Variational Relaxation of the Image Partitioning
Problem},
	booktitle = {Energy Min. Meth. Comp. Vis. Patt. Recogn.},
	year = {2011},
	note = {1},
	pages = {132-146},
	publisher = {Springer},
	organization = {Springer},
	doi = {10.1234/12345678},
	author = {Lellmann, J. and Frank Lenzen 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-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_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.}
}
@article {lellmann_10_optimality,
	title = {Optimality Bounds for Variational Relaxations of Optimal Partition
Problems},
	year = {2010},
	note = {1},
	author = {Lellmann, J. and Frank Lenzen and Christoph Schn{\"o}rr}
}
