Special Functions and Transformations in Image Analysis
Code | Completion | Credits | Range | Language |
---|---|---|---|---|
01SFTO | ZK | 2 | 2+0 | Czech |
- Garant předmětu:
- Lecturer:
- Tutor:
- Supervisor:
- Department of Mathematics
- Synopsis:
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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:
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passing of ROZ1 and ROZ2
- Syllabus of lectures:
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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:
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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:
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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:
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- Matematické inženýrství (elective course)
- Aplikované matematicko-stochastické metody (compulsory elective course)
- Matematická informatika (elective course)