Research

Symbolbild Forschung: Der UdS-Campus halb als unvollständige Pixeldarstellung, halb wiederhergestellt durch Inpainting
© Pascal Peter und Karl Schrader, 2025

Research Interests

  • Image Inpainting: Reconstruction of missing image data.
  • Sparse Data Optimisation: Selecting image pixels or other sparse representations for high quality reconstructions.
  • Image Compression: Storing images at high fidelity at low coding cost.
  • Mathematical Foundations of Deep Learning: Finding mathematical interpretations for existing deep learning approaches or inspiring deep learning models from mathematics.
  • Scale-Space Theory: Embedding images into hiearchical families of gradual simplifications.
 

Publications

Journal Papers (13)

  1. D. Gaa, V. Chizhov, P. Peter, J. Weickert, R. D. Adam:
    Connecting image inpainting with denoising in the homogeneous diffusion setting.
    Advances in Continuous and Discrete Models, Vol. 2025, Article No. 74, 2025

  2. P. Peter:
    Generalised diffusion probabilistic scale-spaces.
    Journal of Mathematical Imaging and Vision, Vol. 66, 639-656, June 2024.
    Invited Paper.

  3. P. Peter, K. Schrader, T. Alt, J. Weickert:
    Deep spatial and tonal optimisation for homogeneous diffusion inpainting.
    Pattern Analysis and Applications, Vol. 26, No. 4, 1585-1600, November 2023.
    Invited Paper.

  4. T. Alt, K. Schrader, M. Augustin, P. Peter, J. Weickert:
    Connections between numerical algorithms for PDEs and neural networks.
    Journal of Mathematical Imaging and Vision, June 2022.
    Invited Paper.
    Also available as arXiv:2107.14742 [math.NA], revised March 2022.

  5. T. Alt, K. Schrader, J. Weickert, P. Peter, M. Augustin:
    Designing rotationally invariant neural networks from PDEs and variational methods.
    Research in the Mathematical Sciences, Vol. 9, No. 3, Article 52, Sept. 2022.
    Also available as arXiv:2108.13993 [cs.LG], revised March 2022.

  6. R. M. K. Mohideen, P. Peter, J. Weickert:
    A systematic evaluation of coding strategies for sparse binary images.
    Signal Processing: Image Communication, Vol. 99, Article 116424, November 2021.
    Also available as arXiv:2010.13634 [eess.IV], revised July 2021.

  7. M. Breuß, J. Buhl, A. M. Yarahmadi, M. Bambach, P. Peter:
    A simple approach to stiffness enhancement of a printable shape by Hamilton-Jacobi skeletonization.
    Procedia Manufacturing, Vol. 47, 1190-1196, 2020.

  8. L. Hoeltgen, P. Peter, M. Breuß:
    Clustering-Based Quantisation for PDE-Based Image Compression.
    Signal, Image and Video Processing, Vol. 12, No. 3, 411-419, Vol. 12, No. 3, 411-419 March 2018.
    Revised version of arXiv:1706.06347 [cs.CV], June 2017

  9. N. Amrani, J. Serra-Sagrista, P. Peter, J. Weickert:
    Diffusion-based inpainting for coding remote-sensing data.
    IEEE Geoscience and Remote Sensing Letters, Vol. 14, No. 8, 1203-1207, August 2017.
    Also available as Technical Report, Universitat Autonoma de Barcelona, Spain, March 2017, ddd.uab.cat/record/174184.

  10. P. Peter, L. Kaufhold, J. Weickert: 
    Turning diffusion-based image colorization into efficient color compression.
    IEEE Transactions on Image Processing, Vol. 26, No. 2, 860-869, February 2017.
    Revised version of Technical Report No. 370, Department of Mathematics, Saarland University, Saarbrücken, Germany, December 2015.

  11. P. Peter, S. Hoffmann, F. Nedwed, L. Hoeltgen, J. Weickert:
    Evaluating the true potential of diffusion-based inpainting in a compression context.
    Signal Processing: Image Communication, Vol. 46, 40-53, August 2016.
    Revised version of Technical Report No. 373, Department of Mathematics, Saarland University, Saarbrücken, Germany, January 2016.

  12. P. Peter, C. Schmaltz, N. Mach, M. Mainberger, J. Weickert:
    Beyond Pure Quality: Progressive Modes, Region of Interest Coding, and Real Time Video Decoding for PDE-based Image Compression. 
    Journal of Visual Communication and Image Representation, Vol. 31, 253-265, August 2015.
    Revised version of Technical Report No. 354, Department of Mathematics, Saarland University, Saarbrücken, Germany, January 2015.

  13. C. Schmaltz, P. Peter, M. Mainberger, F. Ebel, J. Weickert, A. Bruhn: 
    Understanding, optimising, and extending data compression with anisotropic diffusion. 
    International Journal of Computer Vision, Vol. 108, No. 3, 222-240, July 2014.
    Revised version of Technical Report No. 329, Department of Mathematics, Saarland University, Saarbrücken, Germany, March 2013.

Book Chapters (1)
  1. P. Peter and M. Breuß
    Refined Homotopic Thinning Algorithms and Quality Measures for Skeletonisation Methods.
    M. Breuß, A. Bruckstein, P. Maragos (Eds.): Innovations for Shape Analysis: Models and Algorithms. Mathematics and Visualization, 77-92, Springer, Berlin, 2013.
    Revised version of Technical Report No. 312, Department of Mathematics, Saarland University, Saarbrücken, Germany, July 2012. 
     
Conference Papers (25)

  1. J. Gierke, P. Peter:
    Skeletonisation scale-spaces.
    To appear in Scale Space and Variational Methods in Computer Vision. Lecture Notes in Computer Science, Springer, Cham, 2025.
    Also available as arXiv:2503.03450 [eess.IV], March 2025.

  2. T. Fischer, P. Peter, J. Weickert, E. Ilg:
    Neuroexplicit diffusion models for inpainting of optical flow fields.
    Proc. 41st International Conference on Machine Learning (ICML 2024, Vienna, Austria, July 2024), Proceedings of Machine Learning Research, Vol. 235, 13691-13705, 2024

  3. P. Bungert, P. Peter, J. Weickert:
    Image blending with osmosis.
    In L. Calatroni, M. Donatelli, S. Morigi, M. Prato, M. Santavesaria (Eds.): Scale Space and Variational Methods in Computer Vision. Lecture Notes in Computer Science, Vol. 14009, Springer, Cham, 652-664, 2023.
    Also available as arXiv:2303.07762 [eess.IV], March 2023.

  4. P. Peter:
    Generalised scale-space properties for probabilistic diffusion.
    In L. Calatroni, M. Donatelli, S. Morigi, M. Prato, M. Santavesaria (Eds.): Scale Space and Variational Methods in Computer Vision. Lecture Notes in Computer Science, Vol. 14009, Springer, Cham, 601-613, 2023.
    Also available as arXiv:2303.07900 [eess.IV], March 2023.

  5. K. Schrader, P. Peter, N. Kämper, J. Weickert:
    Efficient neural generation of 4K masks for homogeneous diffusion inpainting.
    In L. Calatroni, M. Donatelli, S. Morigi, M. Prato, M. Santavesaria (Eds.): Scale Space and Variational Methods in Computer Vision. Lecture Notes in Computer Science, Vol. 14009, Springer, Cham, 16-28, 2023.
    Also available as arXiv:2303.10096 [eess.IV], March 2023.

  6. P. Peter:
    A Wasserstein GAN for joint learning of inpainting and its spatial optimisation.
    In H. Wang, W. Lin, P. Manoranjan, G. Xiao, K.L. Chan, X. Wang, G. Ping, H. Jiang: Image and Video Technology. Lecture Notes in Computer Science, Vol. 13763, Springer, Cham, 132-145, 2023.
    Also available as arXiv:2202.05623 [eess.IV], revised December 2022.

  7. T. Alt, P. Peter, J. Weickert:
    Learning sparse masks for diffusion-based image inpainting.
    In A. J. Pinho, P. Georgieva, L. F. Teixeira, J. A. Sánchez (Eds.): Pattern Recognition and Image Analysis. Lecture Notes in Computer Science, Vol. 13256, Springer, Cham, 528-539, 2022.
    Also available as arXiv:2110.02636 [eess.IV], revised March 2022.

  8. S. Andris, J. Weickert, T. Alt, P. Peter:
    JPEG meets PDE-based image compression.
    In Proc. 35th Picture Coding Symposium (PCS 2021, Bristol, UK, June 2021), IEEE Press, 2021.
    Also available as arXiv:2011.11289 [eess.IV], revised May 2021.

  9. P. Peter:
    Quantisation scale-spaces.
    In A. Elmoataz, J. Fadili, Y. Quéau, J. Rabin, L. Simon (Eds.): Scale Space and Variational Methods in Computer Vision. Lecture Notes in Computer Science, Vol. 12679, Springer, Cham, 15-26, 2021.
    Also available as arXiv:2103.10491 [eess.IV], March 2021.

  10. T. Alt, P. Peter, J. Weickert, K. Schrader:
    Translating numerical concepts for PDEs into neural architectures.
    In A. Elmoataz, J. Fadili, Y. Quéau, J. Rabin, L. Simon (Eds.): Scale Space and Variational Methods in Computer Vision. Lecture Notes in Computer Science, Vol. 12679, Springer, Cham, 294-306, 2021.
    Also available as arXiv:2103.15419 [math.NA], March 2021.

  11. S. Andris, P. Peter, R. M. K. Mohideen, J. Weickert, S. Hoffmann:
    Inpainting-based video compression in FullHD.
    In A. Elmoataz, J. Fadili, Y. Quéau, J. Rabin, L. Simon (Eds.): Scale Space and Variational Methods in Computer Vision. Lecture Notes in Computer Science, Vol. 12679, Springer, Cham, 425-436, 2021.
    Also available as arXiv:2008.10273 [eess.IV], revised May 2021.

  12. F. Jost, P. Peter, J. Weickert:
    Compressing piecewise smooth images with the Mumford-Shah cartoon model.
    In Proc. 28th European Signal Processing Conference (EUSIPCO 2020, Amsterdam, Netherlands, January 2021), 511-515, 2021.
    Also available as arXiv:2003.05206 [eess.IV], March 2020.

  13. F. Jost, P. Peter, J. Weickert:
    Compressing flow fields with edge-aware homogeneous diffusion inpainting.
    Proc. 45th International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2020, Barcelona, Spain, May 2020), 2198-2202, 2020.
    Also available as arXiv:1906.12263 [eess.IV], October 2019.

  14. P. Peter:
    Fast inpainting-based compression: Combining Shepard interpolation with joint inpainting and prediction. 
    Proc. 2019 IEEE International Conference on Image Processing (ICIP 2019, Taipei, Taiwan, Sept. 2019), 3557-3561, 2019.

  15. M. Cárdenas, P. Peter, J. Weickert:
    Sparsification scale-spaces. 
    In J. Lellmann, M. Burger, J. Modersitzki (Eds.): Scale Space and Variational Methods. Lecture Notes in Computer Science, Vol. 11603, 303-314, Springer, Cham, 2019.

  16. P. Peter, J. Contelly, J. Weickert:
    Compressing audio signals with inpainting-based sparsification. 
    In J. Lellmann, M. Burger, J. Modersitzki (Eds.): Scale Space and Variational Methods. Lecture Notes in Computer Science, Vol. 11603, 92-103, Springer, Cham, 2019.

  17. L. Karos, P. Bheed, P. Peter, J. Weickert:
    Optimising data for exemplar-based inpainting.
    In J. Blanc-Talon, D. Helbert, W. Philips, D. Popescu, P. Scheunders (Eds.): Advanced Concepts for Intelligent Vision Systems. Lecture Notes in Computer Science, Vol. 11182, 547-558, Springer, Cham, 2018.

  18. R. D. Adam, P. Peter, J. Weickert:
    Denoising by inpainting.
    In F. Lauze, Y. Dong, A. B. Dahl (Eds.): Scale Space and Variational Methods in Computer Vision. Lecture Notes in Computer Science, Vol. 10302, 121-132, Springer, Cham, 2017.
     
  19. S. Andris, P. Peter, J. Weickert:
    A proof-of-concept framework for PDE-based video compression.
    Proc. 32nd Picture Coding Symposium (PCS 2016, Nuremberg, Germany, December. 2016), 1-5, 2016.
    PCS 2016 Best Poster Award.
     
  20. M. Schneider, P. Peter, S. Hoffmann, J. Weickert, Enric Meinhardt-Llopis:
    Gradients versus grey values for sparse image reconstruction and inpainting-based compression.
    In J. Blanc-Talon, C. Distante, W. Philips, D. Popescu, P. Scheunders (Eds.): Advanced Concepts for Intelligent Vision Systems. Lecture Notes in Computer Science, Vol. 10016, 1-13, Springer, Cham, 2016.
     
  21. P. Peter, S. Hoffmann, F. Nedwed, L. Hoeltgen, J. Weickert:
    From optimised inpainting with linear PDEs towards competitive image compression codecs.
    In T. Bräunl, B. McCane, M. Rivera, X. Yu (Eds.): Image and Video Technology. Lecture Notes in Computer Science, Vol. 9431, 63-74, Springer, Cham, 2016.
     
  22. P. Peter, J. Weickert:
    Compressing images with diffusion- and exemplar-based inpainting. 
    In J.-F. Aujol, M. Nikolova, N. Papadakis (Eds.): Scale Space and Variational Methods in Computer Vision. Lecture Notes in Computer Science, Vol. 9087, 154-165, Springer, Berlin, 2015.
     
  23. P. Peter, J. Weickert, A. Munk, T. Krivobokova, H. Li:
    Justifying tensor-driven diffusion from structure-adaptive statistics of natural images.
    In X.-C. Tai, E. Bae, T. F. Chan, M. Lysaker (Eds.): Energy Minimization Methods in Computer Vision and Pattern Recognition. Lecture Notes in Computer Science, Springer, Vol. 8932, 263-277, Berlin, 2015.
     
  24. P. Peter, J. Weickert:
    Colour image compression with anisotropic diffusion.
    Proc. 21st IEEE International Conference on Image Processing
    (ICIP 2014, Paris, France, October 2014), 4822-4826, 2014.
     
  25. P. Peter
    Three-dimensional data compression with anisotropic diffusion.
    J. Weickert, M. Hein, B. Schiele (Eds.): Pattern Recognition. Lecture Notes in Computer Science, Volume 8142, 231-236, Springer, Berlin, 2013.
     

Verantwortlich für die Inhalte dieses Webangebots

Dr. Pascal Peter
Akademischer Rat
Campus E2 4, 66123 Saarbrücken
Tel.: 0681 302-58096
peter(at)math.uni-saarland.de