Course detail

Numerical Methods of Image Analysis

FSI-TNMAcad. year: 2025/2026

The course familiarises students with the digital image processing theory and selected topics of image analysis. It focuses on digital image representation and reconstruction, filtration in frequency and spatial domain, noise analysis and filtration, image enhancement, image segmentation, objects analysis and recognition, analysis of multi-spectral images.

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

prof. RNDr. Miloslav Druckmüller, CSc.

Department

Institute of Mathematics (ÚM)

Entry knowledge

Real and complex analysis, functional analysis, basic knowledge of programming

Rules for evaluation and completion of the course

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

 

Missed lessons can be compensated via aditional exercises.

Aims

The aim of the course is to provide students with information about modern mathematical methods of image processing, including implementation of basic methods.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

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. (CS)
Petrou, M., and Bosdogianni, P., Image Processing: The Fundamentals, John Wiley& Sons, 1999. (EN)
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. (EN)
Pratt, W. K.: Digital Image Processing (Second Edition), New York: Wiley 1991 (EN)

Recommended reading

Druckmüller, M.; Heriban, P.: Digital Image Processing System 5.0, , 0 (CS)
Klíma, M.; Bernas, M.; Hozman J.; Dvořák, P. : Zpracování obrazové informace, , 0 (CS)

Classification of course in study plans

  • Programme N-FIN-P Master's 2 year of study, winter semester, compulsory
  • Programme N-MAI-P Master's 2 year of study, winter semester, compulsory
  • Programme N-PMO-P Master's 2 year of study, winter semester, compulsory-optional

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

prof. RNDr. Miloslav Druckmüller, CSc.

Syllabus

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

26 hod., compulsory

Teacher / Lecturer

prof. RNDr. Miloslav Druckmüller, CSc.

Syllabus

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