Efficient Multigrid Methods in Computer Vision and Medical Image Processing

Place and time:

Room: The course will be at KTH Stockholm, Sweden
Lectures :
Tutorials:

News:

Overview:

The course is intended to give an introduction to modern numerical methods for problems in computer vision and medical image processing. In these fields one approach to find mathematical models for e.g. image denoising, image segmentation, image registration, or motion detection in image sequences is to construct an energy functional that has to be minimized. This involves the numerical solution of a partial differential equation (PDE) by a multigrid method.
The course starts with an overview of different applications and discusses how one can derive mathematical models for them. After that the discretization and solution of the arising PDEs is treated. The main part of the course covers multigrid solvers, where a special focus will be on local Fourier analysis to estimate their convergence behavior and on their efficient implementation. During the course the students will implement some example applications like image denoising or motion detection.

Lecture Topics (preliminary):

1. Motivation and Applications: Why using Multigrid Methods in Computer Vision and Medical Image Processing?
2. Image Processing Basics
3. An Overview of Modelling Techniques in Imaging
4. Variational Approaches in Imaging
5. Discretization and Solution Methods for PDEs
6. Geometric Multigrid: Idea and Basics
7. Multigrid Convergence Analysis and Local Fourier Analysis
8. Efficient Multigrid Implementation
9. Linear Multigrid Techniques
10. Nonlinear Multigrid
11. Applications: Image Denoising, Image Inpainting, Image Segmentation, Optical Flow, Image Registration
12. Algebraic Multigrid

Tutorials/ Demonstrations

1. Image Processing Basics
2. Multigrid Poisson Solver, Multigrid Smoothing Rates (using MATLAB)
3. Efficient Multigrid Implementation (using C++)
4. Example Application

Literature