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Differential Equations in Image Processing and Computer Vision
Winter Term 2019 / 2020
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Differential Equations in Image Processing and Computer Vision
Three Computer Science Teaching Awards
(Summer Terms 2003 and 2006, Winter Term 2015/2016)
One Mathematics Teaching Award (Summer Term 2009)
Lecturer:
Dr. Joachim Weickert
Coordinator of tutorials:
Aaron Wewior
Winter Term 2019 / 2020
Lectures (4h) with theoretical exercises (2h)
(9 ETCS points)
Lectures:
Wednesday, 10-12 a.m., Building E 1.3, Lecture Hall 001
Friday, 10-12 a.m., Building E 1.3, Lecture Hall 001
First lecture: Wednesday, October 16
Tutorials: 2 hours each week; see below.
News – Synopsis – Prerequisites – Tutorials – Registration – Written Exams – Contents – Self Test – Material for the Programming Assignments – Example Solutions for the Assignments – References
26.08.20: The results of the second exam are online.
06.07.20: The second exam is rescheduled for August 24th. For further information click here. If you have any questions, contact Aaron Wewior.
17.03.20: The second exam is postponed until further notice.
16.02.20: The results of the first exam are online.
06.02.20: The list of admitted students is online.
18.10.19: Registration is closed.
16.10.19: Registration is open.
24.09.19: The lecture on Friday, November 1, has been moved to Thursday, October 31, 6 p.m. due to a public holiday.
Many modern techniques in image processing and computer vision make
use of methods based on partial differential equations (PDEs) and
variational calculus. Moreover, many classical methods may be
reinterpreted as approximations of PDE-based techniques. In this
course we will get an in-depth insight into these methods.
For each of these techniques, we will discuss the basic ideas
as well as theoretical and algorithmic aspects. Examples from
the fields of medical imaging and computer aided quality control
illustrate the various application possibilities.
Since this class guides its participants to many
research topics in our group, its attendance is required for
everyone who wishes to pursue a master thesis in our group.
Equally suited for students of visual computing, mathematics and computer science. Requires undergraduate knowledge in mathematics (e.g. ''Mathematik für Informatiker I-III''). Knowledge in image processing or differential equations is useful, but not required. The lectures will be given in English.
The tutorials include homework assignments (theory and programming) as well as classroom assignments. The programming assignments give an intuition about the way how image processing and computer vision algorithms work, while the theoretical assigments provide additional mathematical insights. Classroom assignments are supposed to be easier and should guide you gently to the main themes.
For the homework assignments you can obtain up to 24 points per week.
Actively participating in the classroom assignments gives you 12 more
points per week, regardless of the correctness of your solutions.
To qualify for both exams you need 2/3 of all possible points.
For 13 weeks, this comes down to 13 x 24 = 312 points.
Working in groups of up to 3 people is permitted, but all persons must be
in the same tutorial group.
If you miss a tutorial because you are sick, you can still get the points
for participation, if you bring a doctor's certificate.
If you have questions concerning the tutorials, please do not hesitate
to contact
Aaron Wewior.
Two groups are scheduled:
- Group 1 (in English):
Monday, 4:15-6:00 pm, Building E1.3, Seminar Room 016
Tutor: Sarah Andris
Office Hour: Thursday: 16:00 - 17:00
Building E1.7, Room 4.07 - Group 2 (English only):
Tuesday, 8:30-10:00 am, Building E1.3, Seminar Room 016
Tutor: Jón Arnar Tómasson
Office Hour: Wednesday, 14:15 - 15:15
Building E1.7, Room 4.16
The tutorial group can be reached via the mail address
dic-x@mia.uni-saarland.de
where x has to be replaced by the group name
(m1 or t1).
Registration is now closed. You can still check in which group you are via web form.
There will be two written exams. The first one will be at the beginning and the second one at the end of the semester break.
The first written exam will take place on
Friday, February 14, 2020 from 2:00 p.m. to 5:00 p.m.
in Building E 2.2, Günter Hotz Lecture Theatre.
The second written exam will take place on
Monday, August 24, 2020 from 2:00 p.m. to 5:00 p.m.
in Building E 1.3, Lecture Hall 002.
In order to qualify for the exams you need a total amount of 2/3 of all
possible points from the homework and classroom assignments.
In case of qualification, you are allowed to take part in both exams.
The better grade counts, but each exam will count as an attempt
individually.
Please check here whether you are admitted to the written exam. Additionally, you have to be registered for the exam in the HISPOS system. If you think that there is an error, please contact Aaron Wewior as soon as possible.
The exams will be closed book. These are the rules during the exams:
- You are allowed and obliged to bring three things to your desk only: Your student ID card (Studierendenausweis), a ball-pen that has no function other than writing, and a so-called cheat sheet. This cheat sheet is a A4 page with formulas or important equations from the lecture. Please note that the cheat sheet has to be handwritten by yourself. It will be collected at the end of the exam, and you can get it back at the exam inspection.
- In particular, electronic devices (including your cell phone), bags, jackets, briefcases, lecture notes, homework and classroom work solutions, additional handwritten notes, books, dictionaries, and paper are not allowed at your desk.
- Please keep your student ID card ready for an attendance check during the exam.
- Do not use pencils or pens that are erasable with a normal rubber.
- You are not allowed to take anything with you that contains information about the exam. A violation of this rule means failing the DIC course.
- You must stay until the exam is completely over.
The results of the first written exam can be found here, and the corresponding distribution of points and grades here.
Each student who has participated in the first written exam has the opportunity to inspect his/her graded solutions in room 4.10 in Bldg. E1.7 on Tuesday, February 18, 2020, from 2:15 p.m. to 3:15 p.m.
The results of the second written exam can be found here, and the corresponding distribution of points and grades here.
Each student who has participated in the second written exam has the opportunity to inspect his/her graded solutions in Lecture Hall 001 in Bldg. E1.3 on Friday, August 28, 2020, from 2:00 p.m. to 3:00 p.m.
Course material will be made available on this webpage in order to
support the classroom teaching and the tutorials, not to replace
them. Additional organisational information, examples and explanations
that may be relevant for your understanding and the exam are provided
in the lectures and tutorials. It is solely your responsibility
- not ours - to make sure that you receive this infomation.
The following table shows a preliminary list of topics that will be
covered during the semester.
Here you can download a self-test problem sheet, that contains 6 problems, which are intended to be similar in style and difficulty to a 180-minutes written exam.
| Date | Topic |
|---|---|
| 31/01 | Self Test Problem Sheet |
| 31/01 | Self Test Solution |
Here you can download the material for the programming assignments:
| Date | Topic |
|---|---|
| 18/10 | H1 - Linear Diffusion, Gaussian Convolution |
| 25/10 | H2 - Linear Diffusion |
| 30/10 | H3 - Nonlinear Isotropic Diffusion |
| 08/11 | H4 - Anisotropic Diffusion |
| 15/11 | H5 - FED, Decorrelation |
| 22/11 | H6 - Diffusion-Reaction Methods |
| 29/11 | H7 - Primal-Dual Methods for TV Regularisation |
| 06/12 | H8 - Iterated Bilateral Filtering |
| 13/12 | H9 - Osmosis |
| 20/12 | H11 - Optic Flow |
| 10/01 | H12 - Morphology |
| 17/01 | H13 - Curvature-Based Morphology |
Here you can download example solutions for the assignments:
| Date | Assignment |
|---|
- J. Weickert: Anisotropic Diffusion in Image Processing. Teubner, Stuttgart, 1998.
- G. Aubert and P. Kornprobst: Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations. Second Edition, Springer, New York, 2006.
- T. F. Chan and J. Shen: Image Processing and Analysis: Variational, PDE, Wavelet, and Stochastic Methods. SIAM, Philadelphia, 2005.
- F. Cao: Geometric Curve Evolutions and Image Processing. Lecture Notes in Mathematics, Vol. 1805, Springer, Berlin, 2003.
- R. Kimmel: The Numerical Geometry of Images. Springer, New York, 2004.
- G. Sapiro: Geometric Partial Differential Equations in Image Analysis. Cambridge University Press, 2001.
- Articles from journals and conferences.
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