Karl Schrader

Position: Research Assistant E-mail: schrader -at- mia.uni-saarland.de (please replace anti-spam -at- by @) Address: Mathematical Image Analysis Group Faculty of Mathematics and Computer Science, Saarland University Campus E1.7 66041 Saarbrücken, Germany Office: Room 4.07 Building E1.7, Saarbrücken Campus see also Contact

• Mathematical Foundations of Deep Learning
• Integrating Partial Differential Equations into Neural Networks
• Designing Neural Architectures Inspired by Numerical Algorithms

Journal Papers

1. 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.
   Invited Paper.
   Also available as arXiv:2107.14742 [math.NA], 2023.
2. 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.
   Also available as arXiv:2108.13993 [cs.LG], revised March 2022.
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.
   Invited Paper.
   Also available as arXiv:2208.14371 [eess.IV], November 2023.

Conference Papers

4. 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, Springer, Cham, 2021.
   Also available as arXiv:2103.15419 [math.NA], March 2021.
5. K. Schrader, T. Alt, J. Weickert, M. Ertel:
   CNN-based Euler’s Elastica Inpainting with Deep Energy and Deep Image Prior.
   Proc. 10th European Workshop on Visual Information Processing (EUVIP 2022, Lisbon, Portugal, Sept. 2022), IEEE, 2022
   Also available as arXiv:2207.07921 [cs.CV], July 2022.
6. 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, Springer, Cham, 2023.
   Also available as arXiv:2303.10096 [eess.IV], March 2023.
7. K. Schrader, J. Weickert, M. Krause:
   Anisotropic Diffusion Stencils: From Simple Derivations over Stability Estimates to ResNet Implementations.
   To appear.
   Also available as arXiv:2309.05575 [math.NA], September 2023.

Theses

8. K. Schrader:
   Translating Anisotropic Diffusion into Residual Networks.
   M.Sc. Thesis in Computer Science,
   Saarland University, Saarbrücken, Germany, October 2020.
   


Teaching

Courses

• Winter term 2020:
  Seminar Deep Learning and Optimisation for Visual Computing
• Summer term 2021:
  Seminar Connections of Deep Learning and PDEs for Visual Computing
  Proseminar Naturinspirierte Optimierung
• Winter term 2021:
  Seminar Milestones and Advances in Image Analysis
  Proseminar Simulation der Welt
• Summer term 2022:
  Lecture Model-driven Deep Learning Lab for Image Analysis
• Winter term 2022:
  Teaching Assistant and Tutor for Differential Equations in Image Processing and Computer Vision
• Summer term 2023:
  Tutor for Image Compression
  Seminar Probabilistic Diffusion: Theory and Applications
• Winter term 2024:
  Teaching Assistant for Mathematics for Computer Scientists I
• Summer term 2025:
  Teaching Assistant and Tutor for Image Processing and Computer Vision

Supervised Students

Ongoing
• Simon Sabri Schönhofen: Binary Mask Optimization: Iterative Neural Networks for Enhanced Image Inpainting
• Harishanth Sivakumaran: Exploring PINNs for PDE-based Image Processing
• Justus Störk

Finished

• Michael Sonntag: Solving Horn-Schunck Optic Flow Model Using Deep Energies
• Siddhartha: Analysis of CNN filters in Deep Neural Networks



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