Lecture "Mathematical Image Processing" SS2016
Summary:
Mathematical image processing is a relatively new research field, which gained a lot of attention recently. Typically, one associates the term 'image processing' with software like Adobe Photoshop. However, there are many different contexts in which image processing is crucial. Applications include the detection of distant celestial bodies in astronomy, the automatic delineation of pathological tumour tissue in biomedical imaging, or the data restauration of damaged cultural heritage. Besides, most powerful techniques are based on mathematical foundations such as Fourier analysis, variational methods, or partial differential equations. In this lecture we aim to give a comprehensive introduction to the field of image processing based on a solid mathematical foundation. We focus hereby especially on optimization problems for variational models. The general idea is to define the optimal image as the solution of a minimization problem reflecting certain desired properties for the ideal image. We investigate various data and regularization terms that suit well in different image processing tasks. Applications discussed within this lecture cover denoising, deblurring, inpainting, and segmentation tasks. We will incorporate practical sessions with programming exercises (based on Mathworks Matlab) into this lecture in order to support the deeper understanding of concepts and algorithms. Please note that this lecture will be given in English.Important dates:
- April 25th to June 20th: Registration phase in QIS-POS for the lecture and the practice groups
Organization:
- Responsible readers: Dr. Camille Sutour, Dr. Daniel Tenbrinck
- Adequate for master studies in mathematics
- Weekly hours: Monday/Thursday, 10.15-12.00am (4 SWS) in lecture hall M4
- Admission to final oral exam by reaching at least 50% of points in practical assignments
Matlab:
To download Matlab please visit this ZIV website and use your university credentials: ZIVdavA german tutorial for using Matlab can be found here: Matlab Tutorial
Literature:
Image Processing script from 2007 (Martin Burger)[Chambolle 2004] A. Chambolle: An algorithm for total variation minimization and applications. Journal of Mathematical Imaging and Vision, 20(1-2):89-97,2004.
[Chambolle-Pock 2011] A. Chambolle, T. Pock: A first-order primal-dual algorithm for convex problems with applications to imaging. Journal of Mathematical Imaging and Vision, 40(1):120-145, 2011.
[Chan-Vese 2001] T. Chan, L. Vese: Active Contours without Edges. IEEE TIP 10(2):266-277, 2001
[Mumford-Shah 1989] D. Mumford, J. Shah: Optimal Approximations by Piecewise Smooth Functions and Associated Variational Problems. Comm. Pure Appl. Math. 42(5):577-685, 1989
Lecture slides:
Slides from lecture on April 11thSlides from lecture on April 14th (modified: May 20th)
Slides from lecture on April 18th (modified: May 20th)
Slides from lecture on April 21th
Slides from lecture on May 23rd
Slides from lecture on May 30th
Slides from lecture on June 09th
Slides from lecture on July 04th
Slides from lecture on July 07th
Practical exercises:
Exercise sheet #1Solutions for sheet #1Exercise sheet #2Solutions for sheet #2
Exercise sheet #3Solutions for sheet #3Data and auxiliary functions for sheet #3
