Differential Equations in Image Processing and Computer Vision
Check out our welcome flyer for a quick overview.
Synopsis: 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.
Hybrid lectures take place weekly in the following time slots:
Tuesday 8:30-10 s.t.
Friday 14-16 c.t.
You can either participate in person in E1.3, Lecture Hall 001 or online in Teams (see Timetable). Recordings will be made available on Teams.
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.
Weekly theoretical and programming assignments will be complemented by classroom work designed for group work. You are encouraged to connect with your fellow students and solve the problems together. The teaching staff will be available to assist you and check your solutions. For all assignments, a written solution will also offered online. More details on the tutorials and admission requirements will be published here later.
If you have questions concerning the tutorials, please do not hesitate to contact Michael Ertel.
There will be two exams, one takes place at the end of the lecture period and a second one just before the start of the next semester. The exams are planned as written closed book exams and dates will be announced closer to the beginning of the lecture period.
You can find the detailed rules for our exams in the self test assignment in the Teams file repository.
You can participate in both exams, and the better grades counts. Please remember that you have to register online for the exam in the HISPOS system of the Saarland University.
If you cannot attend the exam, contact Michael Ertel as early as possible. In case you have proof that you cannot take part for medical reasons or you have another exam on the same day, we can offer you an oral exam as a replacement. Note that we need written proof (e.g. a certificate from a physician/Krankenschein) for the exact date of the exam.
Lecture content in form slides and assignments are available for download online. Access will be granted after registration. In addition, we will provide pre-recoreded lecture videos. Note that the initial registration requires manual confirmation and can thus be delayed a bit.
The assignments and the source code needed for the programming assignments will be provided here during the semester.
There is no specific text book for this class, but many of our image processing topics are covered in one of the following books:
- J. Bigun: Vision with Direction. Springer, Berlin, 2010.
- R. C. Gonzalez, R. E. Woods: Digital Image Processing. Addison-Wesley, International Edition, 2017.
- K. D. Tönnies: Grundlagen der Bildverarbeitung. Pearson Studium, München, 2005.
Computer vision books include
- R. Klette: Concise Computer Vision. Springer, London, 2014.
- R. Szeliski: Computer Vision: Algorithms and Applications. Springer, New York, Second Edition, 2022.
- E. Trucco, A. Verri: Introductory Techniques for 3-D Computer Vision. Prentice Hill, Upper Saddle River, 1998.
These and further books can be found in the mathematics and computer science library.
Furthermore, there is an interesting online compendium, where many researchers have written survey articles.
If you are looking for a specific reference, check out the Annotated Computer Vision Bibliography.
Many highly cited articles can be found via the Google Scholar webpage.