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Course, academic year 2023/2024
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Variational methods in image processing - NPGR029
Title: Variační metody ve zpracování obrazu
Guaranteed by: Department of Software and Computer Science Education (32-KSVI)
Faculty: Faculty of Mathematics and Physics
Actual: from 2017
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, English
Teaching methods: full-time
Teaching methods: full-time
Guarantor: doc. Ing. Filip Šroubek, Ph.D., DSc.
Class: DS, softwarové systémy
Informatika Mgr. - volitelný
M Mgr. MMIB > Povinně volitelné
Classification: Informatics > Computer Graphics and Geometry
Co-requisite : NPGR002
Annotation -
The course broadens topics of the image processing course NPGR002: Digital Image Processing 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.
Last update: Holan Tomáš, RNDr., Ph.D. (30.04.2019)
Course completion requirements -
  • visiting lectures (exceptions possible if previously negotiated)
  • taking an oral exam
Last update: Šroubek Filip, doc. Ing., Ph.D., DSc. (10.06.2018)
Literature -

[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.

Last update: Šroubek Filip, doc. Ing., Ph.D., DSc. (14.02.2024)
Syllabus -
  • 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)

More information (study materials, exams, diploma thesis) is available at NPGR029

Last update: Šroubek Filip, doc. Ing., Ph.D., DSc. (14.02.2024)
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