Differential Geometric Aspects of Image Processing
Prof. Dr. Joachim Weickert
Summer Term 2015
Lectures (2h) with exercises (1h), summer term 2015
Lectures: Monday 12.15-13-.5,
Building E1.7, Room 4.12,
First Lecture: Tuesday, April 21, 2015
Tutorials: Friday 10-12, every other week,
Building E1.3, Lecture Hall 003,
Next Tutorial: Friday, June 26, 2015
Specialised course in mathematical image analysis,
suitable for students in mathematics and computer science programs.
Participants learn how concepts of differential geometry can be applied
in image processing.
Entrance requirements –
Assessments / Exams –
We moved the lectures to Monday, 12-14, E.17, 4.12
Please register for this course in HISPOS until May 27.
There is NO lecture on June 2.
Start of the lectures:
We decided to start the lectures at 8.25 am
and include a 5min break.
Registration for the course:
The registration period is over.
Please remember that you have to register online for the exam in the
system of the Saarland University.
Undergraduate knowledge of mathematics. For computer science students,
this requirement is met by having completed the
Mathematics for Computer Scientists lecture cycle.
Mathematical prerequisites which exceed the basic mathematics courses
are provided within the lecture.
Previous knowledge in either digital image processing
or differential geometry is therefore helpful but not required.
The course is concerned with modern methods of digital image processing which
rely on the differential geometry of curves and surfaces. This includes methods
of image enhancement (like smoothing procedures) as well as feature extraction
and segmentation (like locating contours using active contour models).
The lecture aims at combining theoretical foundation directly with a variety of
applications from the above-mentioned fields; the range of topics extends up to
recent research problems.
An introduction to the relevant concepts and results from differential geometry
will be included in the course.
curves and surfaces in Euclidean space
curve and surface evolutions
variational formulations and gradient descents
diffusion on manifolds
active contours and active regions.
The homework assignments are intended to be solved at home and have to be
submitted in the lecture break, or earlier. In order to qualify for the exam
you must obtain 50% of the possible points on average.
If you have qualified for the exam, you may participate in both exams.
The better grade counts.
- Thursday, August 6, 2015, Building E1.1, Lecture Hall 002, 14:00-16:00
- Tuesday, October 13, 2015, Building E1.1, Lecture Hall 002, 14:00-16:00
Please do not forget to bring your student ID card with you.
These are the rules during the exams:
- For the exams, you can use the course material (including lecture
notes and example solutions from this web page) and hand-written
notes, but neither books nor any other printed material.
- Pocket calculators are not allowed.
- Mobile phones, PDAs, laptops and other electronic devices have to
be turned off.
- Please keep the student ID card ready for an attendance check during
- You are not allowed to take the exam sheets with you.
- Solutions that are written with pencil will not be graded.
Geometric Curve Evolution and Image Processing.
Lecture Notes in Mathematics, vol. 1805, Springer, Berlin 2003.
Numerical Geometry of Images.
Springer, Berlin 2004.
S. Osher, N. Paragios, eds.,
Geometric Level Set Methods in Imaging, Vision and Graphics.
Springer, Berlin 2003.
Geometric Partial Differential Equations and Image Analysis.
Cambridge University Press 2001.
Articles from journals and conferences.
Further references will be given during the lecture.
Participants of the course can download the lecture materials here
Slides of the lecture
||Deadline for Submission
||Date of Discussion
|| Solution to H1
|| May 5, lecture break
|| May 8
| H2 ||
Solution to H2
|| May 19, lecture break
|| May 22
||May 29. Update 1:
added in H2.1
|| Solution to H3
|| June 9, lecture break
|| June 12
| H4 ||
Solution to H4
|| June 22, lecture break
|| June 26
| H5 ||
Solution to H5
|| July 6, lecture break
|| July 10
Martin Schmidt /
July 24, 2015