Differential Geometric Aspects of Image Processing
Dr. Marcelo Cárdenas
Office hour: Tuesday, 13:00 - 14:00.
Winter Term 2019
Lectures (3h) with exercises (1h), winter term 2019
Lectures: Tuesdays, 16-18,
Building E1.3, Room HS 003,
Building E1.3, Room HS 003
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 –
Undergraduate knowledge of mathematics. Students should be familiar with basic
concepts of multivariate calculus and linear algebra as covered in introductory
maths course. 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 of the following Thursday.
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.
- Tuesday, February 25, 2020, Building E1.3, Lecture Hall 016, 14:00-16:00
- Monday, March 16, 2020, Building E1.1, Lecture Hall 106, 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.
Participants of the course can download the lecture materials here
Slides of the lecture
||Deadline for Submission
|| Solution to H1
|| Oct 31, lecture break
|| Solution to H2
|| Nov 14, lecture break
|| Solution to H3
|| Dec 12, lecture break
|| Solution to H4
|| Feb 11, lecture break
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.
References for topological and differential geometric foundations:
M. do Carmo,
Differential geometry of curves and surfaces.
Prentice Hall 1976.
M. do Carmo,
H. W. Guggenheimer,
de Gruyter 1982.
Further references will be given during the lecture.