Numerical Methods of Image Analysis (FSI-TNM)

Academic year 2025/2026
Supervisor: prof. RNDr. Miloslav Druckmüller, CSc.  
Supervising institute: ÚM all courses guaranted by this institute
Teaching language: Czech
Aims of the course unit:

The aim of the course is to provide students with information about modern mathematical methods of image processing, including implementation of basic methods.
Learning outcomes and competences:
 
Prerequisites:
 
Course contents:
 
Teaching methods and criteria:
 
Assesment methods and criteria linked to learning outcomes:

Course-unit credit based on a semestral project.
Exam has a written and an oral part.

 

Missed lessons can be compensated via aditional exercises.
Controlled participation in lessons:
 
Type of course unit:
    Lecture  13 × 2 hrs. optionally                  
    Computer-assisted exercise  13 × 2 hrs. compulsory                  
Course curriculum:
    Lecture

1. Principles of classic and digital photography
2. Numeric image representation, graphics formats, image data compression
3. Images reconstruction, statistical image characteristics
4. Pixel values transforms
5. Convolution, space domain filtration
6. Fourier transform, frequency domain filtration
7. Low-pass and high-pass filters, nonlinear filters
8. Adaptive filters
9. Additive noise - analysis and filtration
10. Impulse noise - analysis and filtration
11. Image segmentation
12. Object analysis
13. Pattern recognition and object classification
    Computer-assisted exercise

1. Color spaces, histogram, pixel-value transformation
2. Fourier transform of functions of two real variables
3. Discrete Fourier transform
4. Visualization of Fourier spectrum, its basic modifications
5. Searching for disctinct directions in images
6. Image filtration - high-pass, low-pass
7. Cosine transform, JPG, notch-filter
8. Image registration, phase correlation
9. Additive noise
10. Impulse noise
11. Image segmentation - thresholding, edge detection
12. Object analysis, moment method
13. Reserve of the lecturer, semestral project
Literature - fundamental:
1. Pratt, W. K.: Digital Image Processing (Second Edition), New York: Wiley 1991
2. Petrou, M., and Bosdogianni, P., Image Processing: The Fundamentals, John Wiley& Sons, 1999.
3.

FOLLAND, Gerald B, 1992. Fourier analysis and its applications. Providence: American Mathematical Society, 433 s. Pure and applied undergraduate texts. ISBN 978-0-8218-4790-9.
4.

BEZVODA, Václav, Josef JEŽEK, Stanislav SAIC a Karel SEGETH, 1988. Dvojrozměrná diskrétní Fourierova transformace a její použití: I. Teorie a obecné užití. 1. Praha: Státní pedagogické nakladatelství, n. p., 181 s. ISBN 17-135-88.
Literature - recommended:
1. Klíma, M.; Bernas, M.; Hozman J.; Dvořák, P. : Zpracování obrazové informace, , 0
2. Druckmüller, M.; Heriban, P.: Digital Image Processing System 5.0, , 0
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
N-FIN-P full-time study --- no specialisation -- Cr,Ex 5 Compulsory 2 2 W
N-MAI-P full-time study --- no specialisation -- Cr,Ex 5 Compulsory 2 2 W
N-PMO-P full-time study --- no specialisation -- Cr,Ex 5 Compulsory-optional 2 2 W