1. Motivation and introduction to Variational Calculus
  2. Discretization (method of final elements and finite differences, Laplace equation)
  3. Image restoration (denoising, deblurring a superresolution)
  4. Bayesian approach (MAP, MLE, Variational Bayes, KL-divergence, parameter estimation, blind deconvolution)
  5. Sparse representation (soft&hard thresholding)
  6. Image registration as an optimization problem
  7. Segmentation and classification as an optimization problem (snakes, level sets, Chan-Vese a Mumford-Shah functional); version 2012: segmentation_part1, segmentation_part2 (segmentation as a problem of the minimum cut in graphs)
  8. Motion detection as an optimization problem (optical flow)
  9. Numerical methods solving optimization problems (SD, CG, Newton method, Lagrangian, etc.)


  • Mathematical problems in image processing, G. Aubert and P. Kornprobst, Springer, 2002.
  • Matrix Computations, Gene H. Golub, Charles F. Van Loan, Johns Hopkins University Press.
  • Blind Image Deconvolution, Ed. P. Campisi, K. Egiazarian, CRC Press, 2008.
  • Practical Optimization: Algorithms and Engineering Applications, Andreas Antoniou and Wu-Sheng Lu, 2007.
  • Pattern Recognition and Machine Learning, Christopher M. Bishop, Springer, 2006.


segmentation.pdf3.16 MB
segmentace.pdf1.44 MB
segmentace2.pdf1.55 MB
var_calculus.pdf4.45 MB
discretization.pdf925.62 KB
lecture_intro.pdf10.95 MB
optical_flow.pdf3.89 MB
restoration.pdf9.6 MB
Bayesian.pdf2.9 MB
Sparse.pdf767.85 KB
numerical.pdf2.27 MB