SubjectsSubjects(version: 945)
Course, academic year 2023/2024
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Special Functions and Transformations in Image Processing - NPGR013
Title: Speciální funkce a transformace ve zpracování obrazu
Guaranteed by: Department of Software and Computer Science Education (32-KSVI)
Faculty: Faculty of Mathematics and Physics
Actual: from 2019
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Additional information:
Guarantor: prof. Ing. Jan Flusser, DrSc.
doc. RNDr. Barbara Zitová, Ph.D.
Class: DS, softwarové systémy
Informatika Mgr. - volitelný
M Mgr. MMIB > Povinně volitelné
Classification: Informatics > Computer Graphics and Geometry
Co-requisite : NPGR002
Annotation -
Last update: RNDr. Tomáš Holan, Ph.D. (30.04.2019)
The course broadens topics of the course NPGR002: Digital Image Processing. Main attention will be paid to several special functions and transformations (especially moment functions and wavelet transform) and their use in selected tasks of image processing - edge detection, noise removal, recognition of deformed objects, image registration, image compression, etc. Both the theory and practical applications will be discussed.
Course completion requirements - Czech
Last update: doc. RNDr. Barbara Zitová, Ph.D. (10.06.2018)

Předmět je zakončen ústní zkouškou s možností písemné přípravy. Zkouška spočívá ze zodpovězení jedné nebo více otázek se sylabu předmětu.

Na zkoušku je jeden řádný a dva opravné termíny.

Literature - Czech
Last update: T_KSVI (27.03.2008)

Syllabus -
Last update: T_KSVI (04.05.2005)

This is an 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.


  • 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

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