Publications of Martin Welk

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To appear – Under review – 2024 – 2023 – 2022 – 2021 – 2020 – 2019 – 2018 – 2017 – 2016 – 2015 – 2014 – 2013 – 2012 – 2011 – 2010 – 2009 – 2008 – 2007 – 2006 – 2005 – 2004 – 2003 – 2000 – 1999 – 1998 – 1997 – 1996

    To appear

  1. M. Welk:
    Extended order-p means and modes of continuous densities.
    Accepted for Austrian Journal of Statistics.
    Download preprint from this site.

  2. W. Ainhauser, M. Welk:
    Parameter identification for pattern-generating reaction-diffusion systems – Towards generative texture descriptors.
    Presented at AIRoV – The First Austrian Symposium on AI, Robotics, and Vision, 26–27 March 2024, Innsbruck, Austria.
    To appear in the proceedings volume with Innsbruck University Press.
    Download paper (self-archived) and supplemental material from this site.

  3. C. Gapp, E. Tappeiner, M. Welk, R. Schubert:
    Multimodal medical disease classification with LLaMA II.
    Presented at AIRoV – The First Austrian Symposium on AI, Robotics, and Vision, 26–27 March 2024, Innsbruck, Austria.
    To appear in the proceedings volume with Innsbruck University Press.
    Technical report arXiv:cs.AI:2412.01306, December 2024. DOI 10.48550/arXiv.2412.01306​.
    Download technical report from arXiv preprint server.

  4. M. Welk:
    Multivariate medians for image and shape analysis.
    Accepted for publication in a volume of Mathematics and Visualization, Springer, Cham.
    Technical report arXiv:eess.IV:1911.00143, October 2019 (last updated June 2021). DOI 10.48550/arXiv.1911.00143​.
    Technical report cn2by (Open Science Framework), November 2019 (last updated June 2021). DOI 10.31219/osf.io/cn2by​.
    Download technical report from arXiv preprint server, technical report from Open Science Framework preprint server.

    5. Top of page

    Under review

  5. M. Kahra, M. Breuß, A. Kleefeld, M. Welk:
    Matrix-Valued LogSumExp Approximation for Colour Morphology.
    Technical Report, arXiv:cs.CV:2411.10141, November 2024. DOI 10.48550/arXiv.2411.10141​.
    Download technical report from arXiv preprint server.

    6. Top of page

    2024

  6. M. Kahra, M. Breuß, A. Kleefeld, M. Welk:
    An approach to colour morphological supremum formation using the LogSumExp approximation.
    In S. Brunetti, A. Frosini, S. Rinaldi, eds., Discrete Geometry and Mathematical Morphology (DGMM 2024), Lecture Notes in Computer Science, Vol. 14605, pp. 325–337, Springer, Cham, 2024. DOI 10.1007/978-3-031-57793-2_25​.
    Technical report arXiv:cs.CV:2312.13792, December 2023. DOI 10.48550/arXiv.2312.13792​.
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    7. Top of page

    2023

  7. C. Gapp, M. Welk:
    Curvature-based denoising of vector-valued images.
    In R. P. Barneva, V. E. Brimkov, G. Nordo, eds., Combinatorial Image Analysis (IWCIA 2022), Lecture Notes in Computer Science, Vol. 13348, pp. 270–287, Springer, Cham, 2023. DOI 10.1007/978-3-031-23612-9_17​.
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    8. Top of page

    2022

  8. G. Laribi, M. Welk:
    Towards quality assessment of blind deconvolution with shift compensation.
    Proc. 26th International Conference on Pattern Recognition (ICPR 2022), 21–25 August 2022, Montréal (Québec, Canada), pp. 421–427, IEEE, 2022. DOI 10.1109/ICPR56361.2022.9956217​.
    Download paper (self-archived) from this site. – Publisher's version.

  9. M. Welk:
    Equivariance-based analysis of PDE evolutions related to multivariate medians.
    In É. Baudrier, B. Naegel, A. Krähenbühl, M. Tajine, eds., Discrete Geometry and Mathematical Morphology (DGMM 2022), Lecture Notes in Computer Science, Vol. 13493, pp. 193–205, Springer, Cham, 2022. DOI 10.1007/978-3-031-19897-7_16​.
    Download paper (self-archived) from this site. – Publisher's version.

  10. E. Tappeiner, M. Welk, R. Schubert:
    Tackling the class imbalance problem of deep learning based head and neck organ segmentation.
    International Journal of Computer Assisted Radiology and Surgery, Vol. 17, 2103–2111, 2022. DOI 10.1007/s11548-022-02649-5​.
    Technical report arXiv:cs.CV:2201.01636, January 2022 (last updated April 2022). DOI 10.48550/arXiv.2201.01636​.
    Download publisher's version (open access); technical report from arXiv preprint server.

    11. Top of page

    2021

  11. M. Welk:
    Diffusion, pre-smoothing and gradient descent.
    In A. Elmoataz, J. Fadili, Y. Quéau, J. Rabin, L. Simon, eds., Scale Space and Variational Methods in Computer Vision (SSVM) 2021, Lecture Notes in Computer Science, Vol. 12679, pp. 78–90, Springer, Cham, 2021. DOI 10.1007/978-3-030-75549-2_7​.
    Download paper (self-archived) from this site. – Publisher's version.

  12. M. Welk, J. Weickert:
    PDE evolutions for M-smoothers in one, two, and three dimensions.
    Journal of Mathematical Imaging and Vision, Vol. 63, No. 2, 157–185, 2021. DOI 10.1007/s10851-020-00986-1​.
    Technical report arXiv:eess.IV:2007.13191, July 2020. DOI 10.48550/arXiv.2007.13191​.
    Download technical report from arXiv preprint server. – Publisher's version – publisher's screen-reader version (freely accessible).

  13. A. Felgenhauer, H.-D. Gronau, R. Labahn, W. Ludwicki, W. Moldenhauer, J. Prestin, M. Rüsing, E. Wegert, M. Welk:
    Die schönsten Aufgaben der Mathematik-Olympiade in Deutschland. 300 ausgewählte Aufgaben und Lösungen der Olympiadeklassen 11 bis 13.
    (The most beautiful problems from the Mathematical Olympiad in Germany. 300 selected problems with solutions from class levels 11 to 13.)
    Springer, Heidelberg 2021. ISBN 978-3-662-63182-9 (E-Book 978-3-662-63183-6). DOI 10.1007/978-3-662-63183-6​.

    14. Top of page

    2020

  14. M. Welk:
    Asymptotic analysis of bivariate half-space median filtering.
    In P. M. Roth, G. Steinbauer, F. Fraundorfer, M. Brandstötter, R. Perko, eds., Proceedings of the Joint Austrian Computer Vision and Robotics Workshop 2020, pp. 151–156, Verlag der Technischen Universität Graz, Graz, 2020. DOI 10.3217/978-3-85125-752-6-34​.
    Download publisher's version (open access) from TUGraz DIGITAL Library.

  15. F. Recla, M. Welk:
    Powder bed analysis in additive manufacturing using image processing.
    In P. M. Roth, G. Steinbauer, F. Fraundorfer, M. Brandstötter, R. Perko, eds., Proceedings of the Joint Austrian Computer Vision and Robotics Workshop 2020, pp. 122–123, Verlag der Technischen Universität Graz, Graz, 2020. DOI 10.3217/978-3-85125-752-6-28​.
    Download publisher's version (open access) from TUGraz DIGITAL Library.

  16. L. Bergerhoff, M. Cárdenas, J. Weickert, M. Welk:
    Stable backward diffusion models that minimise convex energies.
    Journal of Mathematical Imaging and Vision, Vol. 62, No. 6–7, 941–960, 2020. DOI 10.1007/s10851-020-00976-3​.
    Technical report arXiv:math.NA:1903.03491, March 2019. DOI 10.48550/arXiv.1903.03491​.
    Download paper (open access) from publisher, technical report from arXiv preprint server.

  17. E. Tappeiner, S. Pröll, K. Fritscher, M. Welk, R. Schubert:
    Training of head and neck segmentation networks with shape prior on small datasets.
    International Journal of Computer Assisted Radiology and Surgery, Vol. 15, 1417–1425, 2020. DOI 10.1007/s11548-020-02175-2​.
    Download publisher's version.

    18. Top of page

    2019

  18. M. Welk, M. Breuß, V. Sridhar:
    Matrix morphology with extremum principle.
    In B. Burgeth, A. Kleefeld, B. Naegel, N. Passat, B. Perret, eds., Mathematical Morphology and its Applications to Signal and Image Processing, Lecture Notes in Computer Science, Vol. 11564, pp. 177–188, Springer, Cham, 2019. DOI 10.1007/978-3-030-20867-7_14​.
    Download paper (self-archived) from this site. – Publisher's version.

  19. M. Welk, M. Breuß:
    The convex-hull-stripping median approximates affine curvature motion.
    In M. Burger, J. Lellmann, J. Modersitzki, eds., Scale Space and Variational Methods in Computer Vision (SSVM) 2019, Lecture Notes in Computer Science, Vol. 11603, pp. 199–210, Springer, Cham, 2019. DOI 10.1007/978-3-030-22368-7_16​.
    Download paper (self-archived) from this site. – Publisher's version.

  20. M. Welk, J. Weickert:
    PDE evolutions for M-smoothers: From common myths to robust numerics.
    In M. Burger, J. Lellmann, J. Modersitzki, eds., Scale Space and Variational Methods in Computer Vision (SSVM) 2019, Lecture Notes in Computer Science, Vol. 11603, pp. 236–248, Springer, Cham, 2019. DOI 10.1007/978-3-030-22368-7_19​.
    Download paper (self-archived) from this site. – Publisher's version.

  21. M. Welk:
    Quantile filters for multivariate images.
    In A. Pichler, P. M. Roth, R. Sablatnig, G. Stübl, M. Vincze, eds., Proceedings of the ARW & OAGM Workshop 2019, May 9–10, 2019, Steyr, Austria, pp. 159–164, Verlag der Technischen Universität Graz, Graz, 2019. DOI 10.3217/978-3-85125-663-5-32​.
    Download publisher's version (open access) from TUGraz DIGITAL Library.

    22. Top of page

    2018

  22. M. Welk, J. Weickert, G. Gilboa:
    A discrete theory and efficient algorithms for Forward-and-Backward diffusion filtering.
    Journal of Mathematical Imaging and Vision, Vol. 60, No. 9, 1399–1426, 2018. DOI 10.1007/s10851-018-0847-4​.
    Technical report NI17005, Isaac Newton Institute for Mathematical Sciences, Cambridge, September 2017 (updated September 2018).
    Download technical report from Isaac Newton Institute for Mathematical Sciences, Cambridge. – Publisher's version.

  23. M. Welk, M. Urschler, P. M. Roth, eds.:
    Proceedings of the OAGM Workshop 2018: Medical Image Analysis, May 15–16, 2018, Hall/Tyrol, Austria.
    Verlag der Technischen Universität Graz, Graz, 2018. DOI 10.3217/978-3-85125-603-1​.
    Download publisher's version (open access) from TUGraz DIGITAL Library.

  24. F. Schwanninger, M. Welk:
    Image texture classification with morphological amoeba descriptors.
    In M. Welk, M. Urschler, P. M. Roth, eds., Proceedings of the OAGM Workshop 2018: Medical Image Analysis, May 15–16, 2018, Hall/Tyrol, Austria, pp. 80–86, Verlag der Technischen Universität Graz, Graz, 2018. DOI 10.3217/978-3-85125-603-1-16​.
    Download publisher's version (open access) from TUGraz DIGITAL Library.

  25. L. Bergerhoff, M. Cárdenas, J. Weickert, M. Welk:
    Modelling stable backward diffusion and repulsive swarms with convex energies and range constraints.
    In M. Pelillo, E. Hancock, editors, Energy Minimization Methods in Computer Vision and Pattern Recognition, Lecture Notes in Computer Science, Vol. 10746, pp. 409–423, Springer, Cham, 2018. DOI 10.1007/978-3-319-78199-0_27​.
    Download paper (self-archived) from MIA group, Saarbrücken. – Publisher's version.

    26. Top of page

    2017

  26. 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 paper (self-archived) from this site. – Publisher's version.

  27. 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​.
    Download paper (self-archived) from this site. – Publisher's version.

  28. 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​.
    Download paper (self-archived) from this site. – Publisher's version.

  29. 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​.
    Technical report hal-01592311 (HAL preprint server), September 2017.
    Technical Report qf45c (Open Science Framework), September 2017. 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.

    30. Top of page

    2016

  30. 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​.
    Technical report arXiv:cs.CV:1411.3285, November 2014 (last updated June 2015). DOI 10.48550/arXiv.1411.3285​.
    Download technical report from arXiv preprint server. – Publisher's version.

  31. 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​.
    Technical report arXiv:cs.CV:1509.08082, September 2015 (last updated March 2016). DOI 10.48550/arXiv.1509.08082​.
    Download technical report from arXiv preprint server. – Publisher's version.

  32. 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​.
    Technical report arXiv:cs.CV:1512.08424, December 2015. DOI 10.48550/arXiv.1512.08424​.
    Download technical report from arXiv preprint server. – Publisher's version.

  33. 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. DOI 10.3217/978-3-85125-528-7-09​.
    Download paper (self-archived) from this site.

  34. 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 publisher's version (open access) from journal home page.

  35. 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​.
    Technical report arXiv:cs.CV:1310.2085, October 2013. DOI 10.48550/arXiv.1310.2085​.
    Technical report No. 261, Department of Mathematics, Saarland University, Saarbrücken, Germany, March 2010.
    Download technical report (2013) from arXiv preprint server. – Publisher's version.

    36. Top of page

    2015

  36. 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., Informatik 2015, Tagung vom 28. September–2. Oktober 2015 in Cottbus. Lecture Notes in Informatics, vol. P-246, pp. 1253–1255, Gesellschaft für Informatik, Bonn 2015.
    Download paper (self-archived) from this site.

  37. 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​.
    Technical report arXiv:cs.CV:1212.2245, December 2012. DOI 10.48550/arXiv.1212.2245​.
    Download technical report from arXiv preprint server. – Publisher's version.

  38. 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​.
    Technical report arXiv:cs.CV:1310.0097, September 2013. DOI 10.48550/arXiv.1310.0097​.
    Download paper (self-archived) from this site – technical report from arXiv preprint server. – Publisher's version.

  39. 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​.
    Download paper (self-archived) from this site. – Publisher's version.

  40. 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​.
    Download paper (self-archived) from this site. – Publisher's version.

  41. 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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    42. Top of page

    2014

  42. 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/b17645-17​.
    Publisher's version.

  43. 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.

    44. Top of page

    2013

  44. 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​.
    Technical report No. 321, Department of Mathematics, Saarland University, Saarbrücken, Germany, January 2013.
    Download technical report from MIA group, Saarbrücken. – Publisher's version.

  45. 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). DOI 10.48550/arXiv.1304.7211​.
    Download paper (open access) from arXiv preprint server.

  46. 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​.
    Download paper (self-archived) from this site. – Publisher's version.

  47. 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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  48. 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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    49. Top of page

    2012

  49. 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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    50. Top of page

    2011

  50. 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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  51. 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​.
    Download paper (self-archived) from this site. – Publisher's version.

  52. 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​.
    Technical report No. 259, Department of Mathematics, Saarland University, Saarbrücken, Germany, February 2010.
    Download paper (self-archived) from this site, technical report from MIA group, Saarbrücken. – Publisher's version.

    53. Top of page

    2010

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

    54. Top of page

    2009

  54. 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​.
    Download paper (self-archived) from MIA group, Saarbrücken. – Publisher's version.

  55. 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 (self-archived) with erratum from MIA group, Saarbrücken. – Publisher's version.

  56. 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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  57. 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.

  58. 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​.
    Technical report No. 221, Department of Mathematics, Saarland University, Saarbrücken, Germany, September 2008.
    Download technical report from MIA group, Saarbrücken. – Publisher's version.

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    2008

  59. 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.

  60. 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​.
    Technical report No. 203, Department of Mathematics, Saarland University, Saarbrücken, Germany, 2008.
    Download paper (open access) from publisher, technical report from MIA group, Saarbrücken.

  61. 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​.
    Technical report No. 2100, Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, USA, February 2006.
    Download paper (self-archived) from MIA group, Saarbrücken, technical report from MIA group, Saarbrücken. – Publisher's version.

    62. Top of page

    2007

  62. M. Welk:
    Dynamic and Geometric Contributions to Digital Image Processing.
    Habilitation thesis, submitted to Saarland University, 2007.
    Online version last revised February 2016.
    Download online version from this site.

  63. 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​.
    Download paper (self-archived) from MIA group, Saarbrücken. – Publisher's version.

  64. 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​.
    Download paper (self-archived) from MIA group, Saarbrücken. – Publisher's version.

  65. 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​.
    Download paper (self-archived) from MIA group, Saarbrücken. – Publisher's version.

  66. 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​.
    Technical report No. 135, Department of Mathematics, Saarland University, Saarbrücken, Germany, April 2005.
    Download paper (self-archived) from MIA group, Saarbrücken, technical report from MIA group, Saarbrücken. – Publisher's version.

  67. 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​.
    Technical report No. 150, Department of Mathematics, Saarland University, Saarbrücken, Germany, 2005.
    Download paper (self-archived) from MIA group, Saarbrücken, technical report from MIA group, Saarbrücken. – Publisher's version.

  68. 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​.
    Technical report No. 165, Department of Mathematics, Saarland University, Saarbrücken, Germany, January 2006.
    Download technical report from MIA group, Saarbrücken. – Publisher's version.

  69. 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​.
    Technical report No. 161, Department of Mathematics, Saarland University, Saarbrücken, Germany, 2005.
    Download technical report from MIA group, Saarbrücken. – Publisher's version.

  70. 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​.
    Technical report No. 162, Department of Mathematics, Saarland University, Saarbrücken, Germany, December 2005.
    Download technical report from MIA group, Saarbrücken. – Publisher's version.

    71. Top of page

    2006

  71. 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​.
    Download paper (self-archived) from MIA group, Saarbrücken. – Publisher's version.

  72. 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.
    Download technical report from MIA group, Saarbrücken. – Publisher's version.

  73. 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.

  74. 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​.
    Technical report No. 104, Department of Mathematics, Saarland University, Saarbrücken, Germany, April 2004.
    Download technical report from MIA group, Saarbrücken. – Publisher's version.

  75. 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.

  76. 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​.
    Technical report No. 160, Department of Mathematics, Saarland University, Saarbrücken, Germany, 2005.
    Download technical report from MIA group, Saarbrücken. – Publisher's version.

  77. 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​.
    Technical report No. 142, Department of Mathematics, Saarland University, Saarbrücken, Germany, 2005.
    Download technical report from MIA group, Saarbrücken. – Publisher's version.

  78. 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​.
    Technical report No. 143, Department of Mathematics, Saarland University, Saarbrücken, Germany, 2005.
    Download technical report from MIA group, Saarbrücken. – Publisher's version.

  79. 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​.
    Technical Report No. 77, DFG Priority Programme 1114, University of Bremen, Germany, January 2005.
    Download technical report from MIA group, Saarbrücken. – Publisher's version.

    80. Top of page

    2005

  80. 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​.
    Download paper (self-archived) from MIA group, Saarbrücken. – Publisher's version.

  81. 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​.
    Download paper (self-archived) from MIA group, Saarbrücken. – Publisher's version.

  82. 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​.
    Download paper (self-archived) from MIA group, Saarbrücken. – Publisher's version.

  83. B. Burgeth, N. Papenberg, A. Bruhn, M. Welk, C. Feddern, J. Weickert:
    Morphology for higher-dimensional tensor data via Loewner ordering.
    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​.
    Download paper (self-archived) from MIA group, Saarbrücken. – Publisher's version.

  84. 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​.
    Download paper (self-archived) from MIA group, Saarbrücken. – Publisher's version.

  85. 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​.
    Download paper (self-archived) from MIA group, Saarbrücken. – Publisher's version.

  86. 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 paper (self-archived) from MIA group, Saarbrücken. – Publisher's version.

  87. 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 paper (self-archived) from MIA group, Saarbrücken. – Publisher's version.

    88. Top of page

    2004

  88. 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​.
    Technical report (extended version) No. 94, Department of Mathematics, Saarland University, Saarbrücken, Germany, August 2003.
    Download paper (self-archived) from MIA group, Saarbrücken, technical report from MIA group, Saarbrücken. – Publisher's version.

  89. 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​.
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    90. Top of page

    2003

  90. 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 paper (self-archived) from MIA group, Saarbrücken. – Publisher's version.

  91. 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 paper (self-archived) from MIA group, Saarbrücken. – Publisher's version.

  92. 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 paper (self-archived) from MIA group, Saarbrücken. – Publisher's version.

  93. 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 paper (self-archived) from MIA group, Saarbrücken.

    94. Top of page

    2000

  94. 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.

  95. M. Welk:
    Covariant First Order Differential Calculus on Quantum Euclidean Spheres.
    Technical Report, arXiv.org:math.QA/0008183, 2000. DOI 10.48550/arXiv.math/0008183​.
    Download technical report from arXiv preprint server.

  96. M. Welk:
    Differential calculus on quantum projective spaces.
    Czechoslovak Journal of Physics, 50(1):219–224, 2000. DOI 10.1023/A:1022870308859​.
    Publisher's version.

    97. Top of page

    1999

  97. M. Welk:
    Covariant First Order Differential Calculus on Quantum Projective Spaces.
    Technical Report, arXiv.org:math.QA/9908069, 1999. DOI 10.48550/arXiv.math/9908069​.
    Download technical report from arXiv preprint server.

    98. Top of page

    1998

  98. 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 thesis from Deutsche Nationalbibliothek (German National Library).

  99. 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.

  100. M. Welk:
    Differential Calculus on Quantum Spheres.
    Technical Report, arXiv.org:math.QA/9802087, 1998. DOI 10.48550/arXiv.math/9802087​.
    Download technical report from arXiv preprint server.

    101. Top of page

    1997

  101. 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 technical report from University of Leipzig Document Server.

    102. Top of page

    1996

  102. 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.

    103. Top of page

Martin Welk 2025-01-13, © 2002–2025