- Digital image (format, color spaces, sampling, quantization, basic task of image processing),
- Basic Cluster and segmentation algorithms ( Mittel, K-means-Algorithms),
- Intensity transformations (Gamma correction, histogram specification),
- Filter (linear filter, bilateral filter, M-regularisator, in particular: median filter),
- Fourier series and discrete Fourier Transform (Series convergence, DFT, FFT),
- Multidimensional Fourier series (DFT, applications in image processing),
- Continuous Fourier Transform,
- Windowed Fourier Transform (Heisenberg's Uncertainty Principle, Gabor Transform).
Foundations in Mathematical Image Processing (M, 9.0 LP, AUSL)
|Module Number||Module Name||CP (Effort)|
|MAT-65-10-M-4||Foundations in Mathematical Image Processing||9.0 CP (270 h)|
|CP, Effort||9.0 CP = 270 h|
|Position of the semester||1 Sem. irreg.|
|Level|| Bachelor (Specialization)|
+ further Lecturers of the department Mathematics
|Area of study||[MAT-SPAS] Analysis and Stochastics|
|Reference course of study||[MAT-88.105-SG] M.Sc. Mathematics|
|Livecycle-State||[AUSL] Phase-out period|
Without a proof of successful participation in the exercise classes, only 6 credit points will be awarded for the module.
|Type/SWS||Course Number||Title||Choice in |
|SL||SL is |
required for exa.
Foundations in Mathematical Image Processing
|P||84 h||186 h||
Examination achievement PL1
- Form of examination: oral examination (20-30 Min.)
- Examination Frequency: irregular (by arrangement)
- Examination number: 84225 ("Foundations in Mathematical Image Processing")
Evaluation of grades
The grade of the module examination is also the module grade.
Competencies / intended learning achievements
In addition, the students have learnt the basic problems and concepts of classical Fourier analysis with numerous practical applications. They have mastered the most important methods and will be able to apply them to selected tasks from image processing. They have understood the proofs presented in the lecture and are able to comprehend and explain them.
By completing the given exercises, the students have developed a skilled, precise and independent handling of the terms, propositions and techniques taught in the lecture. In addition, they have learnt how to apply these techniques to new problems, analyze them and develop solution strategies.
- K. Bredies, D. Lorenz: Mathematische Bildverarbeitung. Einführung in Grundlagen und moderne Theorie,
- T. Chan, J. Shen: Image processing and analysis. Variational, PDE, Wavelet, and Stochastic Methods,
- O. Scherzer, M. Grasmair, H. Grossauer, M. Haltmeier, F. Lenzen: Variational Methods in Imaging.
Literature on computer science aspects:
- R. C. Gonzalez, R. E. Woods: Digital Image Processing,
- B. Jähne: Digital Image Processing,
- C. Solomon, T. Breckon: Fundamentals of Digital Image Processing. A Practical Approach with Examples in Matlab.
Literature on Fourier Analysis:
- G. Folland: Fourier Analysis and its Applications,
- G. Folland: Real Analysis,
- T. Körner: Fourier Analysis,
- H. Nussbaumer: Fast Fourier Transforms and Convolution Algorithms,
- J. Ramanathan: Methods of Applied Fourier Analysis.
Requirements for attendance of the module (informal)
- [MAT-10-1-M-2] Fundamentals of Mathematics (M, 28.0 LP)
- [MAT-14-11-M-3] Introduction to Numerical Methods (M, 9.0 LP)
- [MAT-14-14-M-3] Stochastic Methods (M, 9.0 LP)
Requirements for attendance of the module (formal)None
References to Module / Module Number [MAT-65-10-M-4]
|Course of Study||Section||Choice/Obligation|
|[MAT-88.105-SG] M.Sc. Mathematics||[Core Modules (non specialised)] Applied Mathematics||[WP] Compulsory Elective|
|[MAT-88.118-SG] M.Sc. Industrial Mathematics||[Core Modules (non specialised)] General Mathematics||[WP] Compulsory Elective|
|[MAT-88.706-SG] M.Sc. Mathematics International||[Core Modules (non specialised)] Applied Mathematics||[WP] Compulsory Elective|