- Projective Geometry
- Projective Geometry describes the relationship between the real, 3D, world and it's projection onto film or, these days, a CCD-chip. I've dabbled some with projective invariants4,6, that is measurements which remain unchanged under all possible projective transformations (and allow you to recognise an object from any image, no matter what it looks like in the image), but mainly I'm interested in the behaviour of (measurement) errors under projection6,7.
- 3D Reconstructions
- Of course much of the motivation to study projective geometry stems from the desire to reconstruct the 3D-world from (one or more) 2D images. In the distant past I've mostly been concerned with tomographic methods for 3D-reconstruction1,2,3, but these days I am really more interested in methods which can work with a single image4,9,10.
- Archaeometry
- Archaeometry is concerned with measurements on archaeological finds. I more or less happened on this by chance, since I had done some work on the reconstruction of rotationally symmetric objects from single images4, and since most archaeological finds are pottery, which is rotationally symmetric. However, here I'm not so much interested in the 3D reconstruction (although this is an interesting subject too, in particular when dealing with individual shards), but in the classification of objects based on their 2D-contour9.

Falls Sie ein Student sind und nach einer Studien oder Diplomarbeit ausschau halten, finden Sie hier genauere Informationen. Insbesondere kann ich Arbeiten auf den Gebieten 3D-Rekonstruktion und Archäometry anbieten. Falls das Ihren Interessen nicht so entgegen kommt, sollten Sie auch mal einen Blick auf die anderen bei KOGS angebotenen Themen werfen.

If you are a student looking for a Diploma-thesis (Diplomarbeit), please note that I can offer several interesting subjects in particular in connection with 3D-reconstruction and archaeometry - some are described here, but you can always contact me for related topics. You might also want to have a look at other subjects currently on offer at KOGS.

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In late 1992 and early 1993 I was fulfilling my internship at Philips GmbH, Forschungsabteilung Technische Systeme Hamburg. Due to my previous experiences with the simulator for the flame-tomography I was assigned the task to write a simulator for an MRI-scanner. The objects in question were very simple head-phantoms like the one to the left, essentially simple, 2D, geometric objects (this was 1992, mind). As its input the program would take a description of the phantom, and as it's output the simulator would generate data which could then directly be fed back into the tomography-software used at Philips; the reconstruction could then be compared with reconstructions of an actual phantom in an actual MRI-scanner.

In late 1991, early 1992 I was working on this project as my "Studienarbeit" (3rd year project, BS-thesis). The goal was to get a tomographic reconstruction of the temperature distribution inside a burning flame (assumed rotationally symmetric) from 4 images taken with narrow-band spectral filters. The trick here is to model the flame both as emitting but also as absorbing light. At that time no hardware was available for the task (albeit ordered), and it was my task to write software which would simulate the burning flame, and also to write software which would do the tomographic reconstruction.

One thing which we learnt from doing the simulations (not that one
couldn't have found out applying some little error-propagation and
common sense) was that we would need a camera with either a
12 Bit linear or 8 Bit logarithmic resolution - both
something not readily available in 1991, which ultimately doomed
this project.

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- 1/99-8/99, 2/00-9/06
- Hamburg University's Cognitive Systems Group, Prof. Bernd Neuman
- 3/98-12/98
- The University of Freiburg's Institute of Pattern Recognition and Image Processing, Prof. Hans Burkhard
- 5/94-2/98
- The TU Hamburg-Harburg's now somewhat obsolete Computer Vision group (TI-1), Prof. Hans Burkhard
- 7/93-1/94, 4/94-5/94, 7/95-10/95
- The University of Oxford's Robotics Research Group, the Visual Geometry Group, Dr. Andrew Zisserman (my old homepage)
- 10/92-1/93, 4/93-5/93
- Philips GmbH, Forschungsabteilung Technische Systeme Hamburg, Dr. Karsten Ottenberg

*Error propagation in geometry-based grouping*, Albert-Ludwigs-Universität Freiburg, Institut für Informatik, Fakultät für Angewandte Wissenschaften, Doktorarbeit, 2006

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[Abstract] [Pdf, 11MB] :

Fachbereich Informatik, Universität Hamburg (Hrsg.): *Ancient Ceramics: Computer aided Classification*, Mitteilung. FBI-HH-M-338/06, 2006

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[Abstract] [pdf, 401KB] [ps.gz, 455KB] ; ; ;

*Error-Bounds on Curvature Estimation*. In: Scale Space: Springer-Verlag, Berlin, 2003, S. 657--666

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[pdf, 200KB] [Abstract, 1.0KB] :

Fachbereich Informatik, Universität Hamburg (Hrsg.): *Comparison of Different Approaches for the Calculation of Projective Symmetry or the Axis of a SHGC*, Bericht. FBI-HH-253/03, 2003

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[Abstract] [pdf, 1.1MB] ;

Fachbereich Informatik, Universität Hamburg (Hrsg.): *Error-Bounds on Curvature Estimation*, Bericht. FBI-HH-252/03, 2003

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*Projective Reconstruction of Surfaces of Revolution*. In: **Michaelis**, **B.** (Hrsg.); **Krell**, **G.** (Hrsg.): 25. DAGM-Symposium Mustererkennung. Lecture Notes in Computer Science. Bd. 2781: Springer-Verlag, Berlin, 2003. - ISBN 3-540-40861-4, S. 265--272

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*Grouping based on Projective Geometry Constraints and Uncertainty*. In: Proceedings of the Sixth International Conference on Computer Vision: Narosa Publishing House, New Delhi, 1998. - ISBN 81-7319-221-9, S. 739--746

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[ps.gz, 1.3MB] [Abstract, 1.0KB] :

Albert-Ludwigs-Universität, Freiburg, Institut für Informatik (Hrsg.): *MOVIS: Über die Entwicklung eines ersten Prototypen einer Blindenbrille*, Interner Bericht. 3/98, 1998

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Technische Informatik I, TU-HH (Hrsg.): *Grouping based on Projective Geometry Constraints and Uncertainty*, Interner Bericht. 1/97, 1997

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*An Experimental Comparison of Appearance and Geometric Model Based Recognition*, 1996

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*An Experimental Comparison of Appearance and Geometric Model Based Recognition*. In: Proc. Object Representation in Computer Vision II. LNCS 1144: Springer-Verlag, 1996, S. 247--269

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*Class-Based Grouping in Perspective Images*. In: Proceedings of the Fifth International Conference on Computer Vision, 1995, S. 183--188

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*Advanced Quality Inspection through Physics-Based Vision*. In: Proc. of the the International Symposium Machine Vision in the Industrial Practice, 1995

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*Viewpoint-Invariant Representation of Generalized Cylinders Using the Symmetry Set*. In: British Machine Vision Conference, 1994

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*MORSE: A 3D Object Recognition System based on Geometric Invariants*. In: **Kaufmann**, **Morgan** (Hrsg.): Image Understanding Workshop, 1994, S. II:1393--1402

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*Transfer and Invariants of Surfaces of Revolution*, Technische Universität Hamburg-Harburg, Diplomarbeit, 1994

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