Course detail
Numerical Methods of Image Analysis
FSI-TNM Acad. year: 2025/2026 Winter semester
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
Supervisor
Department
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 written test.
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 programming techniques.
Basic knowledge of classic and digital photography, modern mathematical methods of image processing,
image analysis and pattern recognition.
The study programmes with the given course
Programme N-MAI-P: Mathematical Engineering, Master's, compulsory
Programme N-FIN-P: Physical Engineering and Nanotechnology, Master's, compulsory
Programme N-PMO-P: Precise Mechanics and Optics, Master's, compulsory-optional
Type of course unit
Lecture
26 hours, optionally
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 hours, compulsory
Syllabus
1. Color spaces, histogram
2. Image visualization – pixel value transformation
3. Fourier transform of functions of two real variables and its properties
4. One-dimensional and two-dimensional discrete Fourier transform
5. Visualization of spectrum, its basic modifications
6. Convolution, image filtration, additive noise
7. Impulse noise
8. Analysis of directions in image
9. Image registration, phase correlation
10. Image compression, cosine transform, JPG
11. Image segmentation – thresholding, edge detection
12. Object analysis, moment method
13. Reserve of the lecturer, semestral project