SubjectsSubjects(version: 941)
Course, academic year 2022/2023
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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
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 -
Last update: RNDr. Tomáš Holan, Ph.D. (30.04.2019)
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.
Course completion requirements -
Last update: doc. Ing. Filip Šroubek, Ph.D., DSc. (10.06.2018)
  • visiting lectures (exceptions possible if previously negotiated)
  • taking an oral exam
Literature -
Last update: doc. RNDr. Tomáš Dvořák, CSc. (30.04.2019)

G. Aubert, P. Kornprobst: Mathematical problems in image processing, Springer, 2002

C.M. Bishop: Pattern Recognition and Machine Learning, Springer, 2006

A. Antoniou, W.-S. Lu: Practical Optimization: Algorithms and Engineering Applications, Springer, 2007

Syllabus -
Last update: doc. Ing. Filip Šroubek, Ph.D., DSc. (01.02.2022)
  • calculus of variations (history, Euler-Lagrange equation, brachistochrone problem, Lagrangien, functions of bounded variation)
  • numerical methods (partial differential equations, finite elements, finite differences, steepest descent, conjugate gradients, quadratic programming)
  • approximation of functions
  • image registration (TPS - thin plate spline)
  • image reconstruction (denoising, deconvolution, regularization with total variation, reconstruction of medical data)
  • image segmentation (Mumford-Shah functional, active contours, method of level-sets, classification)
  • motion detection (optical flow)
  • clustering, feature selection

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

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