Special Functions and Transformations in Image Analysis

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

The course broadens topics of the courses ROZ1 and ROZ2. 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.

Requirements:

passing of ROZ1 and ROZ2

Syllabus of 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

Syllabus of tutorials:

Study Objective:

theory of moments and its application in digital image processing. An introduction to vavelet theory and an application of wavelets in digital image processing. An practical application of introduced algorithms (edge detection, denoising, image registration, object recognition, compression).

Study materials:

Key references:

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)

Recommended references:

S. Mallat: A Wavelet Tour of Signal Processing, Academic Press, 2008

Media and tools: a complete set of lecture slides and excersises are available at http://zoi.utia.cas.cz/ PGR013

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Matematické inženýrství (elective course)
• Aplikované matematicko-stochastické metody (compulsory elective course)
• Matematická informatika (elective course)