Publications of Martin Welk

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    2018

  1. L. Bergerhoff, M. Cardenas, J. Weickert, M. Welk:
    Modelling stable backward diffusion and repulsive swarms with convex energies and range constraints.
    Proc. 11th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR 2017, Oct. 2017, Venice, Italy), Lecture Notes in Computer Science, Springer, Cham, in press.
    Download from MIA group, Saarbrücken.
  2. Top of page

    2017

  3. M. Welk, J. Weickert, G. Gilboa:
    A discrete theory and efficient algorithms for Forward-and-Backward diffusion filtering.
    Technical Report, Isaac Newton Institute for Mathematical Sciences, Cambridge, September 2017.
    Download technical report from Isaac Newton Institute for Mathematical Sciences, Cambridge.
  4. M. Welk, J. Weickert:
    An efficient and stable two-pixel scheme for 2D Forward-and-Backward diffusion.
    In F. Lauze, Y. Dong, A.B. Dahl, eds., Scale Space and Variational Methods in Computer Vision, Lecture Notes in Computer Science, Vol. 10302, pp. 94–106, Springer, Cham, 2017, DOI 10.1007/978-3-319-58771-4_8.
    Download from this site Publisher's version.
  5. M. Welk:
    Robust blind deconvolution with convolution-spectrum-based kernel regulariser and Poisson-noise data term.
    In F. Lauze, Y. Dong, A.B. Dahl, eds., Scale Space and Variational Methods in Computer Vision, Lecture Notes in Computer Science, Vol. 10302, pp. 159–171, Springer, Cham, 2017, DOI 10.1007/978-3-319-58771-4_13.
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  6. M. Welk:
    PDE for bivariate amoeba median filtering.
    In J. Angulo, S. Velasco-Forero, F. Meyer, eds., Mathematical Morphology and Its Applications in Signal and Image Processing, Lecture Notes in Computer Science, Vol. 10225, pp. 271–283, Springer, Cham, 2017, DOI 10.1007/978-3-319-57240-6_22.
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  7. M. Welk:
    Superresolution alignment with innocence assumption: Towards a fair quality measurement for blind deconvolution.
    In P. M. Roth, M. Vincze, W. Kubinger, A. Müller, B. Blaschitz, S. Stolc, eds., Proceedings of the OAGM-ARW Joint Workshop: Vision, Automation and Robotics, May 10–12, 2017, Vienna, Austria, 145–150, Verlag der Technischen Universität Graz, 2017. DOI 10.3217/978-3-85125-524-9-29.
    Also available as Technical Report hal-01592311 (HAL preprint server) and Technical Report qf45c (Open Science Framework, DOI 10.17605/OSF.IO/QF45C).
    Download Publisher's version (open access) from Verlag der Technischen Universität Graz, Graz, technical report from HAL preprint server, technical report from Open Science Framework preprint server.
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    2016

  9. M. Welk:
    Amoeba techniques for shape and texture analysis.
    In M. Breuß, A. Bruckstein, P. Maragos, S. Wuhrer, eds., Perspectives in Shape Analysis, Springer, Cham, 2016, DOI 10.1007/978-3-319-24726-7_4.
    Revised version of Technical Report arXiv:cs.CV:1411.3285, November 2014; last revision (v2) June 2015.
    Download technical report from arXiv preprint server.Publisher's version.
  10. M. Welk:
    Multivariate median filters and partial differential equations.
    Journal of Mathematical Imaging and Vision, Vol. 56, No. 2, 320–351, 2016, DOI 10.1007/s10851-016-0645-9.
    Revised version of Technical Report arXiv:cs.CV:1509.08082, September 2015; last revision (v2) March 2016.
    Download technical report from arXiv preprint server.Publisher's version.
  11. M. Welk:
    Graph entropies in texture segmentation of images.
    In M. Dehmer, F. Emmert-Streib, Z. Chen, X. Li, Y. Shi, eds., Mathematical Foundations and Applications of Graph Entropy, Chapter 7, pages 203–231, Wiley, 2016, DOI 10.1002/9783527693245.ch7.
    Revised version of Technical Report arXiv:cs.CV:1512.08424, December 2015.
    Download technical report from arXiv preprint server.
  12. P. Moser, M. Welk:
    Robust blind deconvolution using convolution spectra of images.
    In K. Niel, P. M. Roth, M. Vincze, eds., 1st OAGM-ARW Joint Workshop: Vision Meets Robotics, May 11–13, 2016, Wels, Austria, 69–78, OCG, 2016.
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  13. M. Welk, A. Kleefeld, M. Breuß:
    Quantile filtering of colour images via symmetric matrices.
    Mathematical Morphology: Theory and Applications, Vol. 1, No. 1, 136–174, 2016, DOI 10.1515/mathm-2016-0008.
    Download paper from journal home page (Open Access).
  14. M. Welk:
    A robust variational model for positive image deconvolution.
    Signal, Image and Video Processing, Vol. 10, No. 2, 369–378, 2016, DOI 10.1007/s11760-015-0750-z.
    Revised version of Technical Report arXiv:cs.CV:1310.2085, October 2013, and of Technical Report No. 261, Department of Mathematics, Saarland University, Saarbrücken, Germany, March 2010.
    Download technical report (2013) from arXiv preprint server.Publisher's version.
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    2015

  16. M. Breuß, D. W. Cunningham, M. Welk:
    Scale spaces for cognitive systems: a position paper.
    In D. W. Cunningham, P. Hofstedt, K. Meer, I. Schmitt, eds., Proc. 45. Jahrestagung der Gesellschaft für Informatik, INFORMATIK 2015. Informatik, Energie und Umwelt, Cottbus, Germany, Sept. 28–Oct. 2, 2015, Lecture Notes in Informatics, vol. P-246, pp. 1253–1255, Gesellschaft für Informatik, Bonn 2015.
  17. M. Welk, P. Raudaschl, T. Schwarzbauer, M. Erler, M. Läuter:
    Fast and robust linear motion deblurring.
    Signal, Image and Video Processing, Vol. 9, No. 5, 1221–1234, 2015, DOI 10.1007/s11760-013-0563-x.
    Revised version of Technical Report arXiv:cs.CV:1212.2245, December 2012.
    Download technical report from arXiv preprint server.Publisher's version
  18. M. Welk:
    Analysis of amoeba active contours.
    Journal of Mathematical Imaging and Vision, Vol. 52, 37–54, 2015, DOI 10.1007/s10851-014-0524-1.
    Revised version of Technical Report arXiv:cs.CV:1310.0097, September 2013.
    Download paper from this site, technical report from arXiv preprint server.Publisher's version.
  19. M. Welk, A. Kleefeld, M. Breuß:
    Non-adaptive and amoeba quantile filters for colour images.
    In J.A. Benediktsson, J. Chanussot, L. Najman, H. Talbot, eds., Mathematical Morphology and Its Applications to Signal and Image Processing, Lecture Notes in Computer Science, Vol. 9082, pp. 398–409, Springer, Cham, 2015, DOI 10.1007/978-3-319-18720-4_34.
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  20. M. Welk:
    Partial differential equations for bivariate median filters.
    In J.-F. Aujol, M. Nikolova, N. Papadakis, eds., Scale Space and Variational Methods in Computer Vision, Lecture Notes in Computer Science, Vol. 9087, pp. 53–65, Springer, Cham, 2015, DOI 10.1007/978-3-319-18461-6_5.
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  21. A. Kleefeld, M. Breuß, M. Welk, B. Burgeth:
    Adaptive filters for color images: median filtering and its extensions.
    In A. Trémeau, R. Schettini, S. Tominaga, eds., Computational Color Imaging, Lecture Notes in Computer Science, Vol. 9016, pp. 149–158, Springer, Cham, 2015, DOI 10.1007/978-3-319-15979-9_15.
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    2014

  23. M. Welk:
    Discrimination of image textures using graph indices.
    In M. Dehmer, F. Emmert-Streib, eds., Quantitative Graph Theory: Mathematical Foundations and Applications, Chapter 12, pages 355–386, CRC Press, 2014, DOI 10.1201/b17645-13.
    Publisher's version.
  24. M. Welk, M. Breuß:
    Morphological amoebas and partial differential equations.
    In P.W. Hawkes, ed., Advances in Imaging and Electron Physics, Vol. 185, pp. 139–212. Elsevier, 2014.
    DOI 10.1016/B978-0-12-800144-8.00003-3.
    Publisher's version.
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    2013

  26. N. Persch, A. Elhayek, M. Welk, A. Bruhn, S. Grewenig, K. Böse, A. Kraegeloh, J. Weickert:
    Enhancing 3-D Cell Structures in Confocal and STED Microscopy: A Joint Model for Interpolation, Deblurring and Anisotropic Smoothing.
    Measurement Science and Technology, Vol. 24, No. 12, 125703, 2013, DOI 10.1088/0957-0233/24/12/125703.
    Revised version of Technical Report No. 321, Department of Mathematics, Saarland University, Saarbrücken, Germany, January 2013.
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  27. M. Welk, M. Erler:
    Algorithmic optimisations for iterative deconvolution methods.
    In J. Piater, A. Rodríguez-Sánchez, eds., Proceedings of the 37th Annual Workshop of the Austrian Association for Pattern Recognition (ÖAGM/AAPR), 2013.
    Published on arxiv.org (Proceedings volume: 1304.1876, Paper: 1304.7211)
    Download from arXiv preprint server.
  28. M. Welk:
    Relations between amoeba median algorithms and curvature-based PDEs.
    In A. Kuijper, T. Pock, K. Bredies, H. Bischof, eds., Scale Space and Variational Methods in Computer Vision, Lecture Notes in Computer Science, Vol. 7893, pp. 392–403, Springer, Berlin, 2013, DOI 10.1007/978-3-642-38267-3_33.
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  29. J. Weickert, M. Welk, M. Wickert:
    L2-stable nonstandard finite differences for anisotropic diffusion.
    In A. Kuijper, T. Pock, K. Bredies, H. Bischof, eds., Scale Space and Variational Methods in Computer Vision, Lecture Notes in Computer Science, Vol. 7893, pp. 380–391, Springer, Berlin, 2013, DOI 10.1007/978-3-642-38267-3_32.
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  30. T. Schwarzbauer, M. Welk, C. Mayrhofer, R. Schubert:
    Automated quality inspection of microfluidic chips using morphologic techniques.
    In C. L. Luengo Hendriks, G. Borgefors, R. Strand, eds., Mathematical Morphology and its Applications to Signal and Image Processing, Lecture Notes in Computer Science, Vol. 7883, pp. 508–519, Springer, Berlin, 2013, DOI 10.1007/978-3-642-38294-9_43.
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  31. Top of page

    2012

  32. M. Welk:
    Amoeba active contours.
    In A. Bruckstein, B.M. ter Haar Romeny, A.M. Bronstein, M.M. Bronstein, eds., Scale Space and Variational Methods in Computer Vision. Third International Conference, SSVM 2011, Ein Gedi, Israel, May/June 2011. Lecture Notes in Computer Science, Vol. 6667, pp. 374–385, Springer, Berlin, 2012, DOI 10.1007/978-3-642-24785-9_32.
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  33. Top of page

    2011

  34. 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.
    In G. Fichtinger, A. Martel, T. Peters, eds., Medical Image Computing and Computer Assisted Intervention – MICCAI 2011, Lecture Notes in Computer Science, Vol. 6893, pp. 554–561, Springer, Berlin, 2011, DOI 10.1007/978-3-642-23626-6_68.
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  35. A. Elhayek, M. Welk, J. Weickert:
    Simultaneous interpolation and deconvolution model for the 3-D reconstruction of cell images. In R. Mester, M. Felsberg, eds., Pattern Recognition, Lecture Notes in Computer Science, Vol. 6835, pp. 316–325, Springer, Berlin, 2011, DOI 10.1007/978-3-642-23123-0_32.
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  36. M. Welk, M. Breuß, O. Vogel:
    Morphological amoebas are self-snakes.
    Journal of Mathematical Imaging and Vision, Vol. 39, 87–99, 2011, DOI 10.1007/s10851-010-0228-0.
    Revised version of Technical Report No. 259, Department of Mathematics, Saarland University, Saarbrücken, Germany, February 2010.
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  37. Top of page

    2010

  38. M. Welk:
    Robust Variational Approaches to Positivity-Constrained Image Deconvolution.
    Technical Report No. 261, Department of Mathematics, Saarland University, Saarbrücken, Germany, March 2010.
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  39. Top of page

    2009

  40. 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, DOI 10.1007/978-3-642-10520-3_91.
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  41. 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 Mathematical Morphology and its Applications to Signal and Image Processing, Lecture Notes in Computer Science, Vol. 5720, pp. 104–114, Springer, Berlin, 2009, DOI 10.1007/978-3-642-03613-2_10.
    Download paper with erratum from MIA group, Saarbrücken.Publisher's version.
  42. 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, DOI 10.1007/978-3-642-02256-2_44.
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  43. 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, DOI 10.1109/SP.2009.20.
    Publisher's version.
  44. 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, DOI 10.1007/978-1-84882-299-3_3.
    Revised version of Technical Report No. 221, Department of Mathematics, Saarland University, Saarbrücken, Germany, September 2008.
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    2008

  46. 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, DOI 10.1109/CVPRW.2008.4562964.
    Publisher's version.
  47. 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, DOI 10.1007/s10851-008-0087-0.
    Revised version of Technical Report No. 203, Department of Mathematics, Saarland University, Saarbrücken, Germany, 2008.
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  48. 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, DOI 10.1016/j.acha.2007.05.004.
    Revised version of Technical Report No. 2100, Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, USA, February 2006.
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    2007

  50. M. Welk:
    Dynamic and Geometric Contributions to Digital Image Processing.
    Habilitation thesis, submitted to Saarland University, 2007.
    Online version last revised February 2016.
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  51. 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, DOI 10.1007/978-3-540-72823-8_44.
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  52. M. Welk, J. G. Nagy:
    Variational deconvolution of multi-channel images with inequality constraints.
    In J. Martí, J.M. Benedí, A.M. Mendonça, J. Serrat, eds., Pattern Recognition and Image Analysis. Lecture Notes in Computer Science, Vol. 4477, 386–393, Springer, Berlin, 2007, DOI 10.1007/978-3-540-72847-4_50.
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  53. 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, DOI 10.1007/978-3-540-72823-8_71.
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  54. 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, DOI 10.1016/j.sigpro.2005.12.013.
    Revised version of Technical Report No. 135, Department of Mathematics, Saarland University, Saarbrücken, Germany, April 2005.
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  55. 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, DOI 10.1016/j.imavis.2006.06.001.
    Revised version of Technical Report No. 150, Department of Mathematics, Saarland University, Saarbrücken, Germany, 2005.
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  56. M. Breuß, M. Welk:
    Staircasing in semidiscrete stabilised inverse diffusion algorithms.
    Journal of Computational and Applied Mathematics, Vol. 206, No. 1, 520–533, 2007, DOI 10.1016/j.cam.2006.08.006.
    Revised version of Technical Report No. 165, Department of Mathematics, Saarland University, Saarbrücken, Germany, January 2006.
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  57. B. Burgeth, A. Bruhn, N. Papenberg, M. Welk, J. Weickert:
    Mathematical morphology for matrix fields induced by the Loewner ordering in higher dimensions.
    Signal Processing, Vol. 87, No. 2, pp. 277–290, 2007, DOI 10.1016/j.sigpro.2005.12.012.
    Revised version of Technical Report No. 161, Department of Mathematics, Saarland University, Saarbrücken, Germany, 2005.
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  58. B. Burgeth, A. Bruhn, S. Didas, J. Weickert, M. Welk:
    Morphology for matrix data: ordering versus PDE-based approach.
    Image and Vision Computing, Vol. 25, No. 4, pp. 496–511, 2007, DOI 10.1016/j.imavis.2006.06.002.
    Revised version of Technical Report No. 162, Department of Mathematics, Saarland University, Saarbrücken, Germany, December 2005.
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  59. Top of page

    2006

  60. 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, DOI 10.1007/11744023_31.
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  61. M. Breuß, M. Welk:
    A conservative shock filter model for the numerical approximation of conservation laws.
    Applied Mathematics Letters, 19:954–959, 2006, DOI 10.1016/j.aml.2005.09.015.
    Revised version of Technical Report No. 157, Department of Mathematics, Saarland University, Saarbrücken, Germany, November 2005.
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  62. H. Löbler, T. Posselt, M. Welk:
    Optimal compensation rules for integrated services.
    OR Spectrum, 28:355–373, 2006, DOI 10.1007/s00291-005-0022-3.
    Publisher's version.
  63. 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, DOI 10.1007/s11263-006-6854-8.
    Revised version of Technical Report No. 104, Department of Mathematics, Saarland University, Saarbrücken, Germany, April 2004.
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  64. 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, DOI 10.1007/3-540-31272-2_21.
    Publisher's version.
  65. 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, DOI 10.1007/3-540-31272-2_22.
    Revised version of Technical Report No. 160, Department of Mathematics, Saarland University, Saarbrücken, Germany, 2005.
    Download technical report from MIA group, Saarbrücken.Publisher's version.
  66. 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, DOI 10.1007/3-540-31272-2_19.
    Revised version of Technical Report No. 142, Department of Mathematics, Saarland University, Saarbrücken, Germany, 2005.
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  67. 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, DOI 10.1007/3-540-31272-2_25.
    Revised version of Technical Report No. 143, Department of Mathematics, Saarland University, Saarbrücken, Germany, 2005.
    Download technical report from MIA group, Saarbrücken.Publisher's version.
  68. 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, DOI 10.1007/0-387-28831-7_1.
    Also available as Technical Report No. 77, DFG Priority Programme 1114, University of Bremen, Germany, January 2005.
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  69. Top of page

    2005

  70. 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, DOI 10.1007/11567646_4.
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  71. 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, DOI 10.1007/11550518_60.
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  72. 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, DOI 10.1007/1-4020-3443-1_28.
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  73. 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, DOI 10.1007/1-4020-3443-1_37.
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  74. 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, DOI 10.1007/11408031_18.
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  75. 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, DOI 10.1007/11408031_51.
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  76. 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, DOI 10.1007/11408031_50.
    Download from MIA group, Saarbrücken.Publisher's version.
  77. 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, DOI 10.1007/11408031_52.
    Download from MIA group, Saarbrücken.Publisher's version.
  78. Top of page

    2004

  79. 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, DOI 10.1137/S0036142903422429.
    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.Publisher's version.
  80. 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, DOI 10.1007/978-3-540-24673-2_13.
    Download from MIA group, Saarbrücken.Publisher's version.
  81. Top of page

    2003

  82. 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, DOI 10.1007/978-3-540-45243-0_3.
    Awarded a DAGM 2003 Paper Prize.
    Download from MIA group, Saarbrücken.Publisher's version.
  83. 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, DOI 10.1007/3-540-44935-3_54.
    Download from MIA group, Saarbrücken.Publisher's version.
  84. 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, DOI 10.1007/3-540-44935-3_7.
    Download from MIA group, Saarbrücken.Publisher's version.
  85. 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.
  86. Top of page

    2000

  87. M. Welk:
    Differential Calculus on Quantum Euclidean Spheres.
    Czechoslovak Journal of Physics, 50(11):1379–1384, 2000, DOI 10.1023/A:1022850116456.
    Publisher's version.
  88. M. Welk:
    Covariant first order differential calculus on quantum Euclidean spheres.
    Technical Report, arXiv.org:math.QA/0008183, 2000.
    Download from arXiv preprint server.
  89. M. Welk:
    Differential Calculus on Quantum Projective Spaces.
    Czechoslovak Journal of Physics, 50(1):219–224, 2000, DOI 10.1023/A:1022870308859.
    Publisher's v ersion.
  90. Top of page

    1999

  91. M. Welk:
    Covariant first order differential calculus on quantum projective spaces.
    Technical Report, arXiv.org:math.QA/9908069, 1999.
    Download from arXiv preprint server.
  92. Top of page

    1998

  93. 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).
  94. M. Welk:
    Covariant Differential Calculus on Quantum Spheres of Odd Dimension.
    Czechoslovak Journal of Physics, 48(11):1507–1514, 1998, DOI 10.1023/A:1021642214226.
    Publisher's version.
  95. M. Welk:
    Differential Calculus on Quantum Spheres.
    Technical Report, arXiv.org:math.QA/9802087, 1998.
    Download from arXiv preprint server.
  96. Top of page

    1997

  97. 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.
  98. Top of page

    1996

  99. 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.
  100. Top of page


Martin Welk 2018-03-29, © 2002–2018