Mathematical Image Analysis Group, Saarland University

Porfessor

Bernhard Burgeth

(Former Group Member)

E-mail: burgeth(AT)mia.uni-saarland.de

Address: see: New homepage

Bernhard Burgeth received his diploma and doctoral degree in mathematics from the University of Erlangen-Nürnberg (Germany) in 1991 and 1996, respectively. He worked as research assistant at the University of Erlangen-Nürnberg, as researcher (DFG research grant) at McGill University, Montreal (Canada), and the Technical University Eindhoven (The Netherlands).
At the Karlsruhe Research Center he was involved for four years with the numerical simulation of combustion processes.
He joint the Mathematical Image Analysis Group of Professor Weickert in 2002 where he is currently an assistant professor at Saarland University (Saarbrücken, Germany). His research interests comprises mathematical modelling, probabilistic concepts, and methods based on differential equations in image processing. More recent research is focused on image processing tools for tensor/matrix fields and their applications.
His habilitation thesis is entitled "Scale Space Analysis and Matrix Field Processing".

Research interests

Mathematical methods in image processing, in particular

partial differential equations
processing of tensor fields
scale space analysis
mathematical morphology
analytic and stochastic tools for image processing
applications to medical image analysis

Selected Scientific Activities

Organiser (together with David H. Laidlaw)

Dagstuhl Seminar:
New Developments in the Visualization and Processing of Tensor Fields

Program Committee

Invited Talks

BMT, Technical University Eindhoven, 09.07.2003.
Level-Set Methods for Tensor-Valued Data.
Faculty of Mathematics and Computer Science, University of Passau, 14.06.2005.
Analysis of Matrix-valued Data in Image Processing.
CWI, Amsterdam, 10.05.2006,
Mathematical Morphology for Matrix-Fields
Institute for Embedded Systems, Technical University Eindhoven, 11.05.2006.
Mathematical Morphology for Matrix-Fields
Conference: Mathematics and Image Analysis, MIA'06
University Paris Dauphine, Paris, 18.-21. September, 2006
Morphology for Matrix-Fields: Ordering vs PDE-Based Approach
GSF, Munich Neuherberg, 25.10.2006.
Approaches to Morphology for Matrix-Fields
Workshop: Image Analysis and Inverse Problems
TU/e, Eindhoven, 10.-13. December, 2006
Nonlinear PDEs for the Processing of Matrix-Fields
Workshop: Journées de Metz 2007
Mathematics Laboratory LMAM - University of Metz, 3.-4. May, 2007
PDE-based Image Compression
Faculty of Mathematics, Lübeck University, 27. 06. 2007
PDE-Based Image Processing for Matrix Fields
Workshop: Workshop on Bioimaging II / PDEs
ohann Radon Institute for Computational and Applied Mathematics (RICAM), Linz, 19.-23. November, 2007
PDEs for the Processing of Tensor Fields

Teaching, current term

Lecture in winter term 2008/2009:
Probabilistic Methods in Image Analysis
(in English)

Teaching, previuos terms

Seminar in the winter term 2002/2003 (with Prof. Weickert):
Level Set Methods
(in English)

Lecture in summer term 2003:
Konvexe Analysis: Einführung und Anwendungen
(in German)

Lecture in winter term 2003/04:
Mathematical Morphology in Image Processing
(in English)

Lecture in winter term 2004/05:
Probabilistic Methods in Image Processing
(in English)

Seminar in the winter term 2004/05:
Geometrische Algebra im Computer-Vision-Bereich

Lecture in summer term 2005:
Differential Equations in Image Processing and Computer Vision
(in English)

Lecture in winter term 2005/06:
Introduction to Pattern Recognition
(in English)

Seminar in winter term 2005/06:
Visualisation and Processing of Tensor Fields
(in English)

Lecture in winter term 2006/07:
Image Processing and Computer Visison
(in English)

Lecture in summer term 2007:
Mathematical Morphology in Image Processing
(in English)

Lecture in winterterm 2007/08:
Mathematik für Informatiker III

Lecture in summer term 2008:
Integral Equations in Visual Computing
(in English)

Publications:

2008 >> 2007 >> 2006 >> 2005 >> 2004 >> 2003 >> 2002 >> 2001

B. Burgeth, M. Breuß, S. Didas, J. Weickert:
PDE-based Morphology for Matrix Fields: Numerical Solution Schemes.
Technical Report No. 220, Faculty of Mathematics and Computer Science, Saarland University, Saarbrücken, Germany, September 2008.

S. Didas, J. Weickert, B. Burgeth:
Properties of Higher Order Nonlinear Diffusion Filtering.
Technical Report No. 215, Department of Mathematics, Saarland University, Saarbrücken, Germany, August 2008.

L. Pizarro, B. Burgeth, S. Didas, J. Weickert:
A generic neighbourhood filtering framework for matrix fields
European Conference on Computer Vision – ECCV 2008
Lecture Notes in Computer Science, Springer, Berlin, 2008, accepted for publication.

M. Krause, R. M. Alles, B. Burgeth, J. Weickert
Retinal vessel detection via second derivative of local Radon transform
Technical Report No. 212, Department of Mathematics, Saarland University, Saarbrücken, Germany, June 2008.

S. Tari, B. Burgeth, I. Tari
How to Use a Modified Laplacian for Shape Analysis
submitted to IEEE Transactions PAMI.

Z. Belhachmi, D. Bucur, B. Burgeth, J. Weickert:
How to choose Interpolation Data in Images.
Technical Report No. 205, Department of Mathematics, Saarland University, Saarbrücken, Germany, 2008.

2008 >> 2007 >> 2006 >> 2005 >> 2004 >> 2003 >> 2002 >> 2001

B. Burgeth, S. Didas, and J. Weickert.
A General Structure Tensor Concept and Coherence-Enhancing Diffusion Filtering for Matrix Fields
Technical Report No. 197, Department of Mathematics, Saarland University, Saarbrücken, Germany, July 2007.

S. Setzer, G. Steidl, B. Popilka and B. Burgeth.
Variational methods for denoising matrix fields,
In: D. H. Laidlaw and J. Weickert (Eds): Visualization and Processing of Tensor Fields: Advances and Perspectives. Springer, Berlin, in print.

B. Burgeth, S. Didas, L. Florack, and J. Weickert.
A generic approach to diffusion filtering of matrix-fields.
Computing, vol. 81, 179–197, Springer, Berlin, 2007.

G. Steidl, S. Setzer, B. Popilka, and B. Burgeth.
Restoration of matrix fields by SOCP.
Computing, vol. 81, 161–178, Springer, Berlin, 2007.

M. Breuß, B. Burgeth, J. Weickert:
Anisotropic continuous-scale morphology.
In Proceedings of the 3rd Iberian Conference on Pattern Recognition and Image Analysis, IbPRIA, June 6–8, 2007, Girona, Spain, Lecture Notes in Computer Science, Springer, Berlin, 2007.

B. Burgeth, S. Didas, L. Florack, and J. Weickert.
Singular PDEs for the processing of matrix-valued data.
In F. Sgallari, A. Murli, and N. Paragios, editors, Scale-Space and Variational Methods in Image Processing, Lecture Notes in Computer Science, vol. 4485, 556-567, Springer, Berlin, 2007.

R. Duits, B. Burgeth:
Scale spaces on Lie groups.
In F. Sgallari, A. Murli, and N. Paragios, editors, Scale-Space and Variational Methods in Image Processing, Lecture Notes in Computer Science, vol. 4485, 300-312, Springer, Berlin, 2007.

2008 >> 2007 >> 2006 >> 2005 >> 2004 >> 2003 >> 2002 >> 2001

T. Schultz, B. Burgeth, J. Weickert:
Flexible Segmentation and Smoothing of DT-MRI Fields Through a Customisable Structure Tensor.
Second International Symposium, ISVC 2006 Lake Tahoe. Lecture Notes in Computer Science, Vol. 4291, 455-464, Springer, Berlin, 2006.
Awarded the ISVC 2006 Best Paper Award.

B. Burgeth, A. Bruhn, S. Didas, J. Weickert, M. Welk:
Morphology for Tensor Data: Ordering versus PDE-Based Approach.
Image and Vision Computing, special issue "ISMM 05", 2006, accepted.
Revised version of Technical Report No. 162, Department of Mathematics, Saarland University, Saarbrücken, Germany, December 2005.

B. Burgeth, J. Weickert, S. Tari:
Minimally stochastic schemes for singular diffusion equations.
In X.-C. Tai, K.-A. Lie, T. F. Chan, S. Osher (Eds.): Image Processing Based on Partial Differential Equations, 325-339, Springer, Berlin, 2007.

B. Burgeth, N. Papenberg, A. Bruhn, M. Welk, J. Weickert:
Mathematical Morphology for Tensor Data Induced by the Loewner Ordering in Higher Dimensions.
Signal Processing, special issue "Tensor Signal Processing", 2006.
Revised version of Technical Report No. 161, Department of Mathematics, Saarland University, Saarbrücken, Germany, December 2005.

M. Welk, J. Weickert, F. Becker, C. Schnörr, C. Feddern, B. Burgeth:
Median and related local filters for tensor-valued images.
Signal Processing, special issue Tensor Signal Processing, 2006.
Revised version of Technical Report No. 135, Department of Mathematics, Saarland University, Saarbrücken, Germany, April 2005.

C. Feddern, J. Weickert, B. Burgeth, M. Welk:
Curvature-driven PDE methods for matrix-valued images.
International Journal of Computer Vision, 2006.
Revised version of Technical Report No. 104, Department of Mathematics, Saarland University, Saarbrücken, Germany, April 2004.

B. Burgeth, M. Welk, Ch. Feddern, J. Weickert:
Mathematical Morphology on Tensor Data Using the Loewner Ordering.
In J. Weickert, H. Hagen (Eds.): Visualization and Processing of Tensor Fields. Mathematics and Visualization, 357-367, Springer, Berlin, 2006.
Revised version of Technical Report No. 160, Department of Mathematics, Saarland University, Saarbrücken, Germany, December 2005.

J. Weickert, C. Feddern, M. Welk, B. Burgeth, T. Brox:
PDEs for tensor image processing.
In J. Weickert, H. Hagen (Eds.): Visualization and Processing of Tensor Fields, 399-414, Springer, Berlin, 2006.
Revised version of Technical Report No. 143, Department of Mathematics, Saarland University, Saarbrücken, Germany, 2005.

M. Welk, C. Feddern, B. Burgeth, J. Weickert:
Tensor median filtering and M-smoothing.
In J. Weickert, H. Hagen (Eds.): Visualization and Processing of Tensor Fields, 345-356, Springer, Berlin, 2006.

2008 >> 2007 >> 2006 >> 2005 >> 2004 >> 2003 >> 2002 >> 2001

B. Burgeth, S. Didas, J. Weickert:
The Bessel scale-space.
In O. F. Olsen, L. Florack, A. Kuijper (Eds.): Deep Structure, Singularities, and Computer Vision. Lecture Notes in Computer Science, Vol. 3753, 84 - 95, Springer, Berlin, 2005.

S. Didas, J. Weickert, B. Burgeth:
Stability and local feature enhancement of higher order nonlinear diffusion filtering.
In W. Kropatsch, R. Sablatnig, A. Hanbury (Eds.): Pattern Recognition. Lecture Notes in Computer Science, Vol. 3663, 451-458, Springer, Berlin, 2005.
B. Burgeth, J. Weickert:
An explanation for the logarithmic connection between linear and morphological system theory.
International Journal of Computer Vision, Vol. 64, No. 2/3, 157-169, Sept. 2005.
Revised version of Technical Report No. 95, Department of Mathematics, Saarland University, Saarbrücken, Germany, 2003.
B. Burgeth, N. Papenberg, A. Bruhn, M. Welk, C. Feddern, J. Weickert:
Mathematical morphology based on the Loewner ordering for tensor data.
In C. Ronse, L. Najman, E. Decencière (Eds.): Mathematical Morphology: 40 Years On. Computational Imaging and Vision, Vol. 30, Springer, Dordrecht, 407–418, 2005.
B. Burgeth, S. Didas, J. Weickert:
Relativistic scale-spaces.
In R. Kimmel, N. Sochen, J. Weickert (Eds.): Scale-Space and PDE Methods in Computer Vision. Lecture Notes in Computer Science, Vol. 3459, Springer, Berlin, 2005.
S. Didas, B. Burgeth, A. Imiya, J. Weickert:
Regularity and scale-space properties of fractional high order linear filtering.
In R. Kimmel, N. Sochen, J. Weickert (Eds.): Scale-Space and PDE Methods in Computer Vision. Lecture Notes in Computer Science, Vol. 3459, Springer, Berlin, 2005.

2008 >> 2007 >> 2006 >> 2005 >> 2004 >> 2003 >> 2002 >> 2001
T. Brox, J. Weickert, B. Burgeth, P. Mrázek:
Nonlinear structure tensors.
Image and Vision Computing.
Revised version of Technical Report No. 113, Department of Mathematics, Saarland University, Saarbrücken, Germany, 2004.

B. Burgeth, M. Welk, C. Feddern, J. Weickert:
Morphological operations on matrix-valued images.
In T. Pajdla, J. Matas (Eds.): Computer Vision - ECCV 2004. Lecture Notes in Computer Science, Vol. 3024, Springer, Berlin, 155-167, 2004.

2008 >> 2007 >> 2006 >> 2005 >> 2004 >> 2003 >> 2002 >> 2001

C. Feddern, J. Weickert, B. Burgeth:
Level-set methods for tensor-valued images.
In O. Faugeras, N. Paragios (Eds.): Proc. Second IEEE Workshop on Variational, Geometric and Level Set Methods in Computer Vision. Nice, France, 65-72. INRIA, Oct. 2003.

M. Welk, C. Feddern, B. Burgeth, J. Weickert:
Median filtering of tensor-valued images.
In B. Michaelis, G. Krell (Eds.): Pattern Recognition. Lecture Notes in Computer Science, Vol. 2781, Springer, Berlin, 17-24, 2003.
Awarded a DAGM 2003 Paper Prize.

B. Burgeth, J. Weickert:
An explanation for the logarithmic connection between linear and morphological system theory.
In L. D. Griffin, M. Lillholm (Eds.): Scale Space Methods in Computer Vision. Lecture Notes in Computer Science, Vol. 2695, Springer, Berlin, 325-339, 2003.

Other Publications

For publications in other fields (pure mathematics and numerical simulation of combustion processes) please contact burgeth -at- mia.uni-saarland.de

Updated by Bernhard Burgeth, September 17th, 2008