Department of Image Processing

 Slides:

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.)

Literatura:

• 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.