Course detail

Numerical Methods of Image Analysis

FSI-TNM Acad. year: 2025/2026 Winter semester

Supervisor

prof. RNDr. Miloslav Druckmüller, CSc.

Department

Institute of Mathematics

Learning outcomes of the course unit

Prerequisites

Planned learning activities and teaching methods

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.

Language of instruction

Czech

Aims

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

Specification of controlled education, way of implementation and compensation for absences

The study programmes with the given course

Programme N-FIN-P: Physical Engineering and Nanotechnology, Master's
branch ---: no specialisation, 5 credits, compulsory

Programme N-PMO-P: Precise Mechanics and Optics, Master's
branch ---: no specialisation, 5 credits, compulsory-optional

Programme N-MAI-P: Mathematical Engineering, Master's
branch ---: no specialisation, 5 credits, compulsory

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, 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