Special Functions and Transformations in Image Processing: FNSPE-CTU & MFF-CUNI


Advanced course on selected topics of image analysis

Major attention is paid to image moments, moment-based features, wavelet transform, and to their applications in image processing, namely in object recognition, edge detection, noise removal, image registration, and image compression. Numerous practical applications and experimental results are presented in the lectures.

This course is taught in the same form at the MFF CUNI and FJFI CTU.



Summer semester 2022/23:

Lectures will be on WEDNESDAY 10:00 - 11:30 in UTIA (meeting at 9:50 in the lobby)

First lecture 21. 2. 2024

The lecture will take place in the UTIA building. The course is not centrally scheduled at the MFF. Arrangement for lecture - students who have the course registered in SIS will receive info via email.

Classes take place only in the summer semester.


  • Geometric moments, definitions, and basic properties

  • complex moments

  • moment invariants to rotation and scaling

  • moment invariants to affine transform

  • moment invariants to convolution/blurring and combined invariants

  • orthogonal polynomials and orthogonal moments (Legendre moments, Fourier-Mellin moments, Zernike moments)

  • discrete moments and their effective calculation

  • introduction to wavelet transform (WT)

  • edge and corner detection by means of the WT

  • image denoising by means of the WT

  • image registration by means of the WT

  • wavelet-based image compression (block quantizing)

  • other applications of the WT in image processing


The files contain most of the slides used. This is not the complete lecture content; the knowledge recorded in the files is insufficient to pass the exam!


[1] Jan Flusser, Tomáš Suk and Barbara Zitová, 2D and 3D Image Analysis by Moments, Wiley & Sons Ltd., 2016

[2] Jan Flusser, Tomáš Suk and Barbara Zitová, Moments and Moment Invariants in Pattern Recognition, Wiley & Sons Ltd., 2009 (317 pp., ISBN 978-0-470-69987-4)


Recordings of lectures

Below you can find the recorded lectures from LS 2020/21. The first two are unfortunately not recorded, the third one is missing the last 20 minutes.

Lecture 3 - 3D rotation, affine invariants 1
Lecture 5 - invariants to convolution 1
Lecture 7 - invariants to convolution 3
Lecture 9 - wavelets introduction 1
Lecture 11 - wavelets applications 3
Lecture 4 - affine invariants 2, moment matching
Lecture 6 - invariants to convolution 2
Lecture 8 - Numerical calculations of the moment
Lecture 10 - wavelet applications 2