Publications of Martin Welk

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2011 – 2010 – 2009 – 2008 – 2007 – 2006 – 2005 – 2004 – 2003 – 2000 – 1999 – 1998 – 1997 – 1996

    2011

  1. S. Hanaoka, K. Fritscher, M. Welk, M. Nemoto, Y. Masutani, N. Hayashi, K. Ohtomo, R. Schubert:
    3-D graph cut segmentation with Riemannian metrics to avoid the shrinking problem.
    Accepted for 14th International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI2011), Toronto, Canada, September 18–22, 2011. To appear in Lecture Notes in Computer Science, Springer, Berlin.

  2. A. Elhayek, M. Welk, J. Weickert:
    Simultaneous interpolation and deconvolution model for the 3-D reconstruction of cell images. Accepted for 33rd Annual Symposium of the German Association for Pattern Recognition (DAGM2011), Frankfurt/Main, Germany, August 30–September 2, 2011. To appear in Lecture Notes in Computer Science, Springer, Berlin.

  3. M. Welk:
    Amoeba active contours.
    3rd International Conference on Scale Space and Variational Methods in Computer Vision (SSVM2011), Ein Gedi, Israel, May 29–June 2, 2011. To appear in Lecture Notes in Computer Science, Springer, Berlin.
    Download from IBIA group, Hall/Tyrol. – Publisher's homepage: www.springerlink.com

  4. M. Welk, M. Breuß, O. Vogel:
    Morphological amoebas are self-snakes.
    Journal of Mathematical Imaging and Vision, 2010, Vol. 39, 87–99, 2011.
    Revised version of Technical Report No. 259, Department of Mathematics, Saarland University, Saarbrücken, Germany, February 2010.
    Download paper from IBIA group, Hall/Tyrol, technical report from MIA group, Saarbrücken. – Journal homepage: Journal of Mathematical Imaging and Vision

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    2010

  5. M. Welk:
    Robust Variational Approaches to Positivity-Constrained Image Deconvolution.
    Technical Report No. 261, Department of Mathematics, Saarland University, Saarbrücken, Germany, March 2010.
    Download from MIA group, Saarbrücken

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    2009

  6. K. Hagenburg, M. Breuß, O. Vogel, J. Weickert, M. Welk:
    A lattice Boltzmann model for rotationally invariant dithering.
    In G. Bebis, R. Boyle, B. Parvin, D. Koracin, Y. Kuno, J. Wang, R. Pajarola, P. Lindstrom, A. Hinkenjann, M. L. Encarnação, C. T. Silva, D. Coming (Eds.): Advances in Visual Computing. Lecture Notes in Computer Science, Vol. 5876, pp. 949–959, Springer, Berlin, 2009.

  7. M. Welk, M. Breuß, O. Vogel:
    Differential equations for morphological amoebas.
    Updated with an erratum. – In M.H.F. Wilkinson and J.B.T.M. Roerdink (Eds.): Proceedings of Ninth International Symposium on Mathematical Morphology, Lecture Notes in Computer Science, vol. 5720, pp. 104–114, Springer, Berlin, 2009.
    Download from MIA group, Saarbrücken

  8. M. Welk, G. Gilboa, J. Weickert:
    Theoretical foundations for discrete forward-and-backward diffusion filtering.
    In: X.-C. Tai, K. Mørken, M. Lysaker, K.-A. Lie (Eds.): Scale-Space and Variational Methods in Computer Vision, Lecture Notes in Computer Science, vol. 5567, pp. 527–538. Springer, Berlin, 2009.
    Download from MIA group, Saarbrücken

  9. M. Backes, T. Chen, M. Dürmuth, H. Lensch, M. Welk:
    Tempest in a teapot: compromising reflections revisited.
    Proc. 30th IEEE Symposium on Security and Privacy, Oakland, USA, pp. 315–327. IEEE Computer Society, 2009.

  10. S. Barbieri, M. Welk, J. Weickert:
    A variational approach to the registration of tensor-valued images.
    In S. Aja-Fernandez, R. de Luis-Garcia, D. Tao, X. Li (Eds.): Tensors in Image Processing and Computer Vision, pages 59–77, Springer, London, 2009.
    Revised version of Technical Report No. 221, Department of Mathematics, Saarland University, Saarbrücken, Germany, September 2008.
    Download (technical report) from MIA group, Saarbrücken

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    2008

  11. S. Barbieri, M. Welk, J. Weickert:
    Variational registration of tensor-valued images.
    Proc. CVPR Workshop »Tensors in Image Processing and Computer Vision«, Anchorage, Alaska, USA, 23 June 2008, pages 1–6.

  12. I. Galić, J. Weickert, M. Welk, A. Bruhn, A. Belyaev, H.-P. Seidel:
    Image compression with anisotropic diffusion.
    Journal of Mathematical Imaging and Vision, Vol. 31, 255–269, 2008.
    Download from publisher (open access). – Journal homepage: Journal of Mathematical Imaging and Vision

  13. M. Welk, G. Steidl, J. Weickert:
    Locally analytic schemes: a link between diffusion filtering and wavelet shrinkage.
    Applied and Computational Harmonic Analysis, Vol. 24, 195–224, 2008.
    Download from MIA group, Saarbrücken. – Journal homepage: Applied and Computational Harmonic Analysis

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    2007

  14. M. Welk:
    Dynamic and Geometric Contributions to Digital Image Processing.
    Habilitation thesis, submitted to Saarland University, 2007.

  15. M. Welk, P. Kim, P. Olver:
    Numerical invariantization for morphological PDE schemes.
    In F. Sgallari, A. Murli, N. Paragios (Eds.), Scale Space and Variational Methods in Computer Vision. Lecture Notes in Computer Science, Vol. 4485, 508–519, Springer, Berlin, 2007.
    Download from MIA group, Saarbrücken.

  16. M. Welk, J. G. Nagy:
    Variational deconvolution of multi-channel images with inequality constraints.
    In J. Martí et al. (Eds.), Pattern Recognition and Image Analysis. Lecture Notes in Computer Science, Vol. 4477, 386–393, Springer, Berlin, 2007.
    Download from MIA group, Saarbrücken.

  17. O. Demetz, J. Weickert, A. Bruhn, M. Welk:
    Beauty with variational methods: an optic flow approach to hairstyle simulation.
    In F. Sgallari, A. Murli, N. Paragios (Eds.), Scale Space and Variational Methods in Computer Vision. Lecture Notes in Computer Science, Vol. 4485, 825-836, Springer, Berlin, 2007.
    Download from MIA group, Saarbrücken.

  18. M. Welk, J. Weickert, F. Becker, C. Schnörr, C. Feddern, B. Burgeth:
    Median and related local filters for tensor-valued images.
    Signal Processing, Vol. 87, 291–308, 2007.
    Revised version of Technical Report No. 135, Department of Mathematics, Saarland University, Saarbrücken, Germany, April 2005.
    Download paper or technical report from MIA group, Saarbrücken. – Journal homepage: Signal Processing

  19. M. Welk, J. Weickert, I. Galić:
    Theoretical foundations for spatially discrete 1-D shock filtering.
    Image and Vision Computing, Vol. 25, No. 4, 455–463, 2007.
    Revised version of Technical Report No. 150, Department of Mathematics, Saarland University, Saarbrücken, Germany, 2005.
    Download paper or technical report from MIA group, Saarbrücken. – Journal homepage: Image and Vision Computing

  20. M. Breuß, M. Welk:
    Staircasing in semidiscrete stabilised inverse diffusion algorithms.
    Journal of Computational and Applied Mathematics, Vol. 206, No. 1, 520–533, 2007.
    Revised version of Technical Report No. 165, Department of Mathematics, Saarland University, Saarbrücken, Germany, January 2006.
    Download (technical report) from MIA group, Saarbrücken.

  21. 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, 2007.

  22. B. Burgeth, A. Bruhn, S. Didas, J. Weickert, M. Welk:
    Morphology for tensor data: ordering versus PDE-based approach.
    Image and Vision Computing, 2007.

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    2006

  23. M. Welk, J. Weickert, G. Steidl:
    From tensor-driven diffusion to anisotropic wavelet shrinkage.
    In H. Bischof, A. Leonardis, A. Pinz (Eds.): Computer Vision – ECCV 2006. Lecture Notes in Computer Science, Vol. 3951, 391–403. Springer, Berlin, 2006.
    Download from MIA group, Saarbrücken.

  24. M. Breuß, M. Welk:
    A conservative shock filter model for the numerical approximation of conservation laws.
    Applied Mathematics Letters, 19:954–959, 2006.
    Revised version of Technical Report No. 157, Department of Mathematics, Saarland University, Saarbrücken, Germany, November 2005.
    Download (technical report) from MIA group, Saarbrücken.

  25. H. Löbler, T. Posselt, M. Welk:
    Optimal compensation rules for integrated services.
    OR Spectrum, 28:355–373, 2006.

  26. C. Feddern, J. Weickert, B. Burgeth, M. Welk:
    Curvature-driven PDE methods for matrix-valued images.
    International Journal of Computer Vision, 69(1):93–107, 2006.
    Revised version of Technical Report No. 104, Department of Mathematics, Saarland University, Saarbrücken, Germany, April 2004.
    Download (technical report) from MIA group, Saarbrücken.

  27. 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.

  28. B. Burgeth, M. Welk, C. Feddern, J. Weickert:
    Mathematical morphology on tensor data using the Loewner ordering.
    In J. Weickert, H. Hagen (Eds.): Visualization and Processing of Tensor Fields, 357–368, Springer, Berlin, 2006.

  29. J. Weickert, M. Welk:
    Tensor field interpolation with PDEs.
    In J. Weickert, H. Hagen (Eds.): Visualization and Processing of Tensor Fields, 315–325, Springer, Berlin, 2006.
    Revised version of Technical Report No. 142, Department of Mathematics, Saarland University, Saarbrücken, Germany, 2005.
    Download (technical report) from MIA group, Saarbrücken.

  30. 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.
    Download (technical report) from MIA group, Saarbrücken.

  31. J. Weickert, G. Steidl, P. Mrázek, M. Welk, T. Brox:
    Diffusion filters and wavelets: What can they learn from each other?
    In N. Paragios, Y. Chen, O. Faugeras (Eds.): Handbook of Mathematical Models in Computer Vision, 3–16. Springer, New York, 2006.
    Also available as Preprint No. 77, DFG Priority Programme 1114, University of Bremen, Germany, January 2005.
    Download (technical report) from MIA group, Saarbrücken.

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    2005

  32. I. Galić, J. Weickert, M. Welk, A. Bruhn, A. Belyaev, H.-P. Seidel:
    Towards PDE-based image compression.
    In N. Paragios, O. Faugeras, T. Chan, C. Schnörr (Eds.): Variational, Geometric, and Level Set Methods in Computer Vision. Lecture Notes in Computer Science, Vol. 3752, Springer, Berlin, 37–48, 2005.
    Download from MIA group, Saarbrücken.

  33. M. Welk, D. Theis, J. Weickert:
    Variational deblurring of images with uncertain and spatially variant blurs.
    In W. Kropatsch, R. Sablatnig, A. Hanbury (Eds.): Pattern Recognition. Lecture Notes in Computer Science, Vol. 3663, 485–492, Springer, Berlin, 2005.
    Download from MIA group, Saarbrücken.

  34. M. Welk, J. Weickert:
    Semidiscrete and discrete well-posedness of shock filtering.
    In C. Ronse, L. Najman, E. Decencière (Eds.): Mathematical Morphology: 40 Years On. Computational Imaging and Vision, Vol. 30, Springer, Dordrecht, 311–320, 2005.
    Download from MIA group, Saarbrücken.

  35. 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.

  36. M. Welk, F. Becker, C. Schnörr, J. Weickert:
    Matrix-valued filters as convex programs.
    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, 204–216, 2005.
    Download from MIA group, Saarbrücken.

  37. M. Welk, A. Bergmeister, J. Weickert:
    Denoising of audio data by nonlinear diffusion.
    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, 598–609, 2005.
    Download from MIA group, Saarbrücken.

  38. M. Welk, D. Theis, T. Brox, J. Weickert:
    PDE-based deconvolution with forward-backward diffusivities and diffusion tensors.
    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, 585–597, 2005.
    Download from MIA group, Saarbrücken.

  39. M. Welk, J. Weickert, G. Steidl:
    A four-pixel scheme for singular differential equations.
    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, 610–621, 2005.
    Download from MIA group, Saarbrücken.

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    2004

  40. G. Steidl, J. Weickert, T. Brox, P. Mrázek and M. Welk:
    On the equivalence of soft wavelet shrinkage, total variation diffusion, total variation regularization, and SIDEs.
    SIAM Journal on Numerical Analysis, Vol. 42, No. 2, 686–713, 2004.
    An extended version appeared as Technical Report No. 94, Department of Mathematics, Saarland University, Saarbrücken, Germany, August 2003.
    Download paper or technical report from MIA group, Saarbrücken. – Journal homepage: SIAM Journal on Numerical Analysis

  41. 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.
    Download from MIA group, Saarbrücken.

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    2003

  42. 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.
    Download from MIA group, Saarbrücken.

  43. M. Welk:
    Families of generalised morphological scale spaces.
    In L. D. Griffin, M. Lillholm (Eds.): Scale Space Methods in Computer Vision. Lecture Notes in Computer Science, Vol. 2695, Springer, Berlin, 770–784, 2003.
    Download from MIA group, Saarbrücken.

  44. T. Brox, M. Welk, G. Steidl, J. Weickert:
    Equivalence results for TV diffusion and TV regularisation.
    In L. D. Griffin, M. Lillholm (Eds.): Scale Space Methods in Computer Vision. Lecture Notes in Computer Science, Vol. 2695, Springer, Berlin, 86–100, 2003.
    Download from MIA group, Saarbrücken.

  45. P. Mrázek, J. Weickert, G. Steidl, M. Welk:
    On iterations and scales of nonlinear filters.
    In O. Drbohlav (Ed.): Computer Vision Winter Workshop 2003, Valtice, Czech Republic, pp. 61–66. Czech Pattern Recognition Society, 2003.
    Download from MIA group, Saarbrücken.

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    2000

  46. M. Welk:
    Covariant Differential Calculus on Quantum Euclidean Spheres.
    Czechoslovak Journal of Physics, 50(11):1379–1384, 2000.

  47. M. Welk:
    Covariant first order differential calculus on quantum Euclidean spheres.
    Preprint, arXiv.org:math.QA/0008183, 2000.
    Download from arXiv preprint server

  48. M. Welk:
    Covariant Differential Calculus on Quantum Projective Spaces.
    Czechoslovak Journal of Physics, 50(1):219–224, 2000.

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    1999

  49. M. Welk:
    Covariant first order differential calculus on quantum projective spaces.
    Preprint, arXiv.org:math.QA/9908069, 1999.
    Download from arXiv preprint server

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    1998

  50. M. Welk:
    Kovariante Differentialrechnung auf Quantensphären ungerader Dimension. Ein Beitrag zur nichtkommutativen Geometrie homogener Quantenräume.
    (Covariant differential calculus on quantum spheres of odd dimension. A contribution to the noncommutative geometry of quantum homogeneous spaces.)
    PhD thesis (in German), University of Leipzig, 1998.
    Download from Deutsche Nationalbibliothek (German National Library)

  51. M. Welk:
    Covariant Differential Calculus on Quantum Spheres of Odd Dimension.
    Czechoslovak Journal of Physics, 48(11):1507–1514, 1998.

  52. M. Welk:
    Differential Calculus on Quantum Spheres.
    Preprint, arXiv.org:math.QA/9802087, 1998.
    Download from arXiv preprint server

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    1997

  53. G. Balzuweit, R. Der, M. Herrmann, M. Welk:
    An Algorithm for Generalized Principal Curves with Adaptive Topology in Complex Data Sets.
    Technical Report No. 97-03, University of Leipzig, Institute for Informatics, 1997.
    Download from University of Leipzig Document Server.

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    1996

  54. G. Balzuweit, M. Welk, R. Der, G. Schüürmann:
    Nonlinear partial least-squares regression.
    In A. B. Bulsari, S. Kallio, D. Tsaptsinos (Eds.), Solving engineering problems with neural networks, Proceedings EANN'96, 495–498, Systems Engineering Association, Turku, 1996.

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Martin Welk 2011-07-28, © 2002–2011