Advanced numerical techniques with applications in image processing

Place and time:

Room: The course will be at KTH Stockholm, Sweden
Lectures : 9.00 a.m. - 12.30 a.m.
Tutorials: 2.00 p.m. - 5:30 p.m.

News:

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Overview:

The course will cover three interlinked topics. In the first part, we will give an introduction to the techniques of a hardware-aware program optimization that can accelerate the execution of numerical algorithms on modern single- and multi-core architectures significantly. In the second part of the course, students will learn to apply these methods in the context of efficient multilevel and multigrid methods for the solution of partial differential equations. In the final part of the course, we will show how these algorithms can be used to solve image processing problems, such as image denoising or motion detection. As integral part of the course, the students will get hands-on-experience through daily computer lab sessions. Participants should have an understanding of basic iterative methods for solving linear systems and a solid programming background as prerequisites.

Lecture Topics (preliminary):

1. Discretization and Solution Methods for PDEs
2. Iterative solvers for linear systems of equations
3. Elementary concepts of modern computer architectures
4. Code restructuring techniques, Vectorization
5. Parallel programming techniques
6. Geometric Multigrid: Idea and Basics
7. Multigrid Convergence Analysis and Local Fourier Analysis
8. Efficient Multigrid Implementation
9. Algebraic Multigrid
10. Why using Multigrid Methods in Computer Vision and Medical Image Processing?
11. Image Processing Basics
12. An Overview of Modelling Techniques in Imaging
13. Applications: Image Denoising, Image Inpainting, Image Segmentation, Optical Flow, Image Registration

Tutorials (using C++) / Demonstrations

1. Red-Black Gauss-Seidel (RBGS) Solver
2. Performance Optimization of the RBGS Solver
3. Multigrid Poisson Solver, Multigrid Smoothing Rates
4. Efficient Multigrid Implementation
5. Image Processing Basics
6. Example Application in Image Processing

Teaching Material

Slides

Assignment Sheets

Literature

• S. Goedecker und Adolfy Hoisie.
  Performance Optimization of Numerically Intensive Codes, SIAM, 2001.
• Briggs, Henson, McCormick
  A Multigrid Tutorial. SIAM, ISBN 0-89871-462-1
• Koestler
  Multigrid HowTo: A simple Multigrid solver in C++ in less than 200 lines of code.
  Tech. Report 08-3, Lehrstuhl für Informatik 10, Friedrich-Alexander-Universität Erlangen-Nürnberg, 2008.