Advanced topics in optimization: Mathematical image processing
- Summer term 2021
- Lecturer: Prof. Dr. Michael Hintermüller
- Course assistant: Dr. Guozhi Dong
News
- Due to the current Covid-19 outbreak, this course will take place online.
- The lectures and exercise sessions will take on the Zoom platform. Please ensure that you have a working setup for the connecting to a Zoom meeting. This page contains some information pertaining to Zoom and HU-Berlin
- Before every lecture of exercise session, enrolled students with HU email addresses will receive the relevant login information on their respective email addresses
Dates
- The lectures will take place on Thursday, 11:00 to 13:00.
- The exercise sessions will take place every second week, starting April 29th 2021
Syllabus
The special topic Mathematical Image Processing will be covered:- Mathematical Foundations
- Optimization Aspects in Mathematical Imaging
- Image Restoration
- Variational Approaches
- PDE-based Methods
- Numerical Solution Techniques
- Image Segmentation
- Geodesic Active Contours
- Mumford-Shah Model
Literature
To be updated as the course progresses.- Aubert, Gilles and Kornprobst, Pierre: Mathematical problems in image processing. Partial differential equations and the calculus of variations. Second edition, 2006
- Ekeland, Ivar and Temam, Roger. Convex analysis and variational problems, SIAM, 1999
- Chan, Tony F. and Shen, Jianhong: Image processing and analysis. Variational, PDE, wavelet, and stochastic methods, 2005
- Vogel, Curtis R.: Computational methods for inverse problems, 2002
- Chambolle, Antonin and Pock Thomas. An introduction to continuous optimization for imaging. Acta Numerica, Cambridge University Press, 2016, 25, pp.161-319.
Contact
- Prof. Dr. Michael Hintermüller, hint[at]math.hu-berlin.de
- Dr. Guozhi Dong, guozhi.dong[at]hu-berlin.de
Links
- Prof. Dr. Michael Hintermüller webpage
- Dr. Guozhi Dong webpage
- Department of Mathematics
- Mathematics students' council
Dates
The exercise session will take place from 13:00 to 15:00 on the following days:- 29th April 2021
13th20th May 2021- 3rd June 2021
17th24th June 2021- 15th July 2021
Exercise sheets
- Exercise sheet 1 Pepper image data of mat format and of jpg format
- Exercise sheet 2
- Exercise sheet 3
- Exercise sheet 4
- Exercise sheet 5 Image data with a pepper image and white noise seperated
Instructions
Exercise may consists of standard homework exercise and some problems for open discussion or for implementation. The former type usually has a definite answer, e.g. to prove or disprove some statement, while the latter perhaps has no determined or fixed answer, but allows you to develop or to implement with your own ideas.Homework exercises
- Homework exercises are to be solved ahead of time, in writing, and communicated via email to the course assistant.
- The deadline for submitting the homework is 36h before the start of the exercise session.
- The submission must be in one of the following formats:
- Legible scan or photograph of hand-written solutions. Those will have to be assembled in a single PDF document, and have the proper orientation. Improper submissions will not be graded. If it is not clear that the participant can achieve this result, the second format is recommended.
- Typeset solutions in the PDF form. The use of the TeX/LaTeX/ConteXt typesetting system is highly encouraged.
On the presentation
- During the week before the exercise session, course participants are expected to fill a poll with the exercises to present.
- The preparation consists of producing a pdf document (legible scan/photograph of hand-written notes or electronic notes)
- During the session, the presenter will be chosen from the poll list. The course participant will present his solution by sharing his screen and explaining orally the steps in the solution.
Module exam
- It will be a written exam. The participants are supposed to solving 5 sets of problems which are tightly relavant to the content of lectures and exercises communicated during the courses. The total time for writing the exam will be 3 hours.
- Due to the current situation, the exam will be done off site, i.e., it will be a "take home exam". However, the participants are not supposed to seek help from others or look for references for solving the problems. The answers must be prepared indepdently.
- The first exam will take place on Thursday 22nd of July 2021 from 10:00 to 13:00
- The second exam will take place on Thursday 23rd of September 2021 from 10:00 to 13:00