Richard Steffen and Jan-Michael Frahm and Wolfgang Förstner, "Relative Bundle Adjustment based on Trifocal Constraints", In ECCV Workshop on Reconstruction and Modeling of Large-Scale 3D Virtual Environments. 2010.

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In this paper we propose a novel approach to bundle adjustment for large-scale camera configurations. The method does not need to include the 3D points in the optimization as parameters. Additionally, we model the parameters of a camera only relative to a nearby camera to achieve a stable estimation of all cameras. This guarantees to yield a normal equation system with a numerical condition, which practically is independent of the number of images. Secondly, instead of using the classical perspective relation between object point, camera and image point, we use epipolar and trifocal constraints to implicitly establish the relations between the cameras via the object structure. This avoids the explicit reference to 3D points thereby handling points far from the camera in a numerically stable fashion. We demonstrate the resulting stability and high convergence rates using synthetic and real data.

@inproceedings{Steffen2010Relative,
  author = {Steffen, Richard and Frahm, Jan-Michael and F\"orstner, Wolfgang},
  title = {Relative Bundle Adjustment based on Trifocal Constraints},
  booktitle = {ECCV Workshop on Reconstruction and Modeling of Large-Scale 3D Virtual Environments},
  year = {2010},
  doi = {10.1007/978-3-642-35740-4_22}
}

Richard Steffen, "Visual SLAM from image sequences acquired by unmanned aerial vehicles". Thesis at: Institute of Photogrammetry, University of Bonn. 2009.

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Die Verwendung der Triangulation zur Lösung des Problems der gleichzeitigen Lokalisierung und Kartierung findet seit Jahren ihren Eingang in die Entwicklung autonomer Systeme. Aufgrund von Echtzeitanforderungen dieser Systeme erreichen rekursive Schätzverfahren, insbesondere Kalmanfilter basierte Ansätze, große Beliebtheit. Bedauerlicherweise, treten dabei durch die Nichtlinearität der Triangulation einige Effekte auf, welche die Konsistenz und Genauigkeit der Lösung hinsichtlich der geschätzten Parameter maßgeblich beeinflussen. In der Literatur existieren dazu einige interessante Lösungsansätze, um diese genauigkeitsrelevanten Effekte zu minimieren. Die Motivation dieser Arbeit ist die These, dass die KaImanfilter basierte Lösung der Triangulation zur Lokalisierung und Kartierung aus Bildfolgen von unbemannten Drohnen realisierbar ist. Im Gegensatz zur klassischen Aero-Triangulation treten dadurch zusätzliche Aspekte in den Vordergrund, die in dieser Arbeit beleuchtet werden. Der erste Beitrag dieser Arbeit besteht in der Herleitung eines generellen Verfahrens zum rekursiven Verbessern im KaImanfilter mit impliziten Beobachtungsgleichungen. Wir zeigen, dass die klassischen Verfahren im Kalmanfilter eine Spezialisierung unseres Ansatzes darstellen. Im zweite Beitrag erweitern wir die klassische Modellierung für ein Einkameramodell im Kalmanfilter und formulieren linear berechenbare Bewegungsmodelle. Neben verschiedenen Verfahren zur Initialisierung von Neupunkten im Kalmanfilter aus der Literatur stellen wir in einem dritten Hauptbeitrag ein neues Verfahren vor. Am Beispiel von Bildfolgen eines unbemannten Flugobjektes zeigen wir in dieser Arbeit als vierten Beitrag, welche Genauigkeit zur Lokalisierung und Kartierung durch Triangulation möglich ist. Schließlich wird anhand von empirischen Untersuchungen unter Verwendung simulierter und realer Daten einer Bildfolge eines photogrammetrischen Streifens gezeigt und verglichen, welchen Einfluß die Initialisierungsmethoden für Neupunkte im Kalmanfilter haben und welche Genauigkeiten für diese Szenarien erreichbar sind.

@phdthesis{Steffen2009Visual,
  author = {Steffen, Richard},
  title = {Visual SLAM from image sequences acquired by unmanned aerial vehicles},
  school = {Institute of Photogrammetry, University of Bonn},
  year = {2009}
}

Christian Beder and Richard Steffen, "Incremental estimation without specifying a-priori covariance matrices for the novel parameters", In VLMP Workshop on CVPR. Anchorage, USA 2008.

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We will present a novel incremental algorithm for the task of online least-squares estimation. Our approach aims at combining the accuracy of least-squares estimation and the fast computation of recursive estimation techniques like the Kalman filter. Analyzing the structure of least-squares estimation we devise a novel incremental algorithm, which is able to introduce new unknown parameters and observations into an estimation simultaneously and is equivalent to the optimal overall estimation in case of linear models. It constitutes a direct generalization of the well-known Kalman filter allowing to augment the state vector inside the update step. In contrast to classical recursive estimation techniques no artificial initial covariance for the new unknown parameters is required here. We will show, how this new algorithm allows more flexible parameter estimation schemes especially in the case of scene and motion reconstruction from image sequences. Since optimality is not guaranteed in the non-linear case we will also compare our incremental estimation scheme to the optimal bundle adjustment on a real image sequence. It will be shown that competitive results are achievable using the proposed technique.

@inproceedings{Beder2008Incremental,
  author = {Beder, Christian and Steffen, Richard},
  title = {Incremental estimation without specifying a-priori covariance matrices for the novel parameters},
  booktitle = {VLMP Workshop on CVPR},
  year = {2008},
  doi = {10.1109/CVPRW.2008.4563139}
}

Richard Steffen and Wolfgang Förstner, "On Visual Real Time Mapping for Unmanned Aerial Vehicles", In 21st Congress of the International Society for Photogrammetry and Remote Sensing (ISPRS). Beijing, China, pp. 57-62 Part B3a. 2008.

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This paper addresses the challenge of a real-time capable vision system in the task of trajectory and surface reconstruction by aerial image sequences. The goal is to present the design, methods and strategies of a real-time capable vision system solving the mapping task for secure navigation of small UAVs with a single camera. This includes the estimation process, map representation, initialization processes, loop closing detection and exploration strategies. The estimation process is based on the Kalman-Filter and a landmark based map representation. We introduce a new initialization method for new observed landmarks. We will show that the initialization process and the exploration strategy has a significant effect on the accuracy of the estimated camera trajectory and of the map.

@inproceedings{Steffen2008Visual,
  author = {Steffen, Richard and F\"orstner, Wolfgang},
  title = {On Visual Real Time Mapping for Unmanned Aerial Vehicles},
  booktitle = {21st Congress of the International Society for Photogrammetry and Remote Sensing (ISPRS)},
  year = {2008},
  pages = {57-62 Part B3a}
}

Richard Steffen, "A Robust Iterative Kalman Filter Based On Implicit Measurement Equations", August, 2008.(TR-IGG-P-2008-08) 2008.

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In the field of robotics and computer vision recursive estimation of time dependent processes is one of the key tasks. Usually Kalman filter based techniques are used, which rely on explicit model functions, that directly and explicitly describe the effect of the parameters on the observations. However, some problems naturally result in implicit constraints between the observations and the parameters, for instance all those resulting in homogeneous equation systems. By implicit we mean, that the constraints are given by equations, that are not easily solvable for the observation vector. We derive an iterative extended Kalman filter framework based on implicit measurement equations. In a wide field of applications the possibility to use implicit constraints simplifies the process of specifying suitable measurement equations. As an extension we introduce a robustification technique similar to [Ting et.al 2007] and [Huber 1981], which allows the presented estimation scheme to cope with outliers. Furthermore we will present results for the application of the proposed framework to the structure-from-motion task in the case of an image sequence acquired by an airborne vehicle.

@techreport{Steffen2008Robust,
  author = {Steffen, Richard},
  title = {A Robust Iterative Kalman Filter Based On Implicit Measurement Equations},
  year = {2008},
  number = {TR-IGG-P-2008-08}
}

Wolfgang Förstner and Richard Steffen, "Online geocoding and evaluation of large scale imagery without GPS", Photogrammetric Week, Heidelberg. D. Fritsch (Eds.) Vol. Wichmann Verlag 2007.

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Large scale imagery will be increasingly available due to the low cost of video cameras and unmanned aerial vehicles. Their use is broad: the documentation of traffic accidents, the effects of thunderstorms onto agricultural farms, the 3Dstructure of industrial plants or the monitoring of archeological excavation. The value of imagery depends on the availability of (1) information about the place and date during data capture, (2) of information about the 3D-structure of the object and (3) of information about the class or identity of the objects in the scene. Geocoding, problem (1), usually relies the availability of GPS-information, which however limits the use of imagery to outdoor applications. The paper discusses methods for geocoding and geometrical evaluation of such imagery and especially adresses the question in how far the methods can do without GPS.

@article{Forstner2007Online,
  author = {F\"orstner, Wolfgang and Steffen, Richard},
  editor = {D. Fritsch},
  title = {Online geocoding and evaluation of large scale imagery without GPS},
  journal = {Photogrammetric Week, Heidelberg},
  year = {2007},
  volume = {Wichmann Verlag}
}

Richard Steffen and Christian Beder, "Recursive Estimation with Implicit Constraints", In Proceedings of the DAGM 2007. F.A. Hamprecht and C. Schnörr and B. Jähne (Eds.) Heidelberg(4713), pp. 194-203. Springer. 2007.

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Recursive estimation or Kalman filtering usually relies on explicit model functions, that directly and explicitly describe the effect of the parameters on the observations. However, many problems in computer vision, including all those resulting in homogeneous equation systems, are easier described using implicit constraints between the observations and the parameters. By implicit we mean, that the constraints are given by equations, that are not easily solvable for the observation vector. We present a framework, that allows to incorporate such implicit constraints as measurement equations into a Kalman filter. The algorithm may be used as a black-box, simplifying the process of specifying suitable measurement equations for many problems. As a byproduct, the possibility of specifying model equations non-explicitly, some non-linearities may be avoided and better results can be achieved for certain problems.

@inproceedings{Steffen2007Recursive,
  author = {Steffen, Richard and Beder, Christian},
  editor = {F.A. Hamprecht and C. Schn\"orr and B. J\"ahne},
  title = {Recursive Estimation with Implicit Constraints},
  booktitle = {Proceedings of the DAGM 2007},
  publisher = {Springer},
  year = {2007},
  number = {4713},
  pages = {194--203},
  doi = {10.1007/978-3-540-74936-3_20}
}

Christian Beder and Richard Steffen, "Determining an initial image pair for fixing the scale of a 3d reconstruction from an image sequence", In Pattern Recognition. K. Franke and K.-R. Müller and B. Nickolay and R. Schäfer (Eds.) Berlin(4174), pp. 657-666. Springer. 2006.

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Algorithms for metric 3d reconstruction of scenes from calibrated image sequences always require an initialization phase for fixing the scale of the reconstruction. Usually this is done by selecting two frames from the sequence and fixing the length of their base-line. In this paper a quality measure, that is based on the uncertainty of the reconstructed scene points, for the selection of such a stable image pair is proposed. Based on this quality measure a fully automatic initialization phase for simultaneous localization and mapping algorithms is derived. The proposed algorithm runs in real-time and some results for synthetic as well as real image sequences are shown.

@inproceedings{Beder2006Determining,
  author = {Beder, Christian and Steffen, Richard},
  editor = {K. Franke and K.-R. M\"uller and B. Nickolay and R. Sch\"afer},
  title = {Determining an initial image pair for fixing the scale of a 3d reconstruction from an image sequence},
  booktitle = {Pattern Recognition},
  publisher = {Springer},
  year = {2006},
  number = {4174},
  pages = {657--666},
  doi = {10.1007/11861898_66}
}