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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2024/2025

Variational Methods in Image Processing

The course is not on the list Without time-table
Code Completion Credits Range
D01VMSO ZK
Garant předmětu:
Lecturer:
Tutor:
Supervisor:
Department of Mathematics
Synopsis:

The course broadens topics of the image processing course and it is aimed for students eager to gain deeper knowledge in the field. The majority of image processing tasks can be formulated as a variational problem. We give an introduction to the calculus of variations and numerical methods solving optimization problems. Then we focus on problems from image processing, which one can formulate as an optimization problem and we illustrate possible solutions on a wide variety of practical applications.

Requirements:
Syllabus of lectures:

- Calculus of variations (history, Euler-Lagrange equation, brachistochrone problem, Lagrangien, functions of bounded variation)

- image reconstruction (denoising, deconvolution, regularization with total variation, reconstruction of medical data)

- implicit neural representation, deep image prior

- image segmentation (Mumford-Shah functional, active contours, method of level-sets, classification)

- optical flow (Lucas-Kanade, parametrizace)

- Variational Bayes (MLE, MAP, KL-divergence, parameter estimation)

- sparse representation (soft&hard thresholding)

- numerical methods (partial differential equations, finite elements, finite differences, steepest descent, conjugate gradients, quadratic programming)

- image registration (TPS - thin plate spline)

Syllabus of tutorials:
Study Objective:
Study materials:

[1] Mathematical problems in image processing, G. Aubert and P. Kornprobst, Springer, 2002.

[2] Matrix Computations, Gene H. Golub, Charles F. Van Loan, Johns Hopkins University Press.

[3] Blind Image Deconvolution, Ed. P. Campisi, K. Egiazarian, CRC Press, 2008.

[4] Practical Optimization: Algorithms and Engineering Applications, Andreas Antoniou and Wu-Sheng Lu, 2007.

[5] Pattern Recognition and Machine Learning, Christopher M. Bishop, Springer, 2006.

Note:
Further information:
https://zoi.utia.cas.cz/index.php/teaching/lecture-courses/npgr029
No time-table has been prepared for this course
The course is a part of the following study plans:
Data valid to 2024-05-18
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