## COURSE DESCRIPTION

### In-depth Study of Image Processing through Variational Problems and Optimization Solutions

The course broadens topics of the image processing course NPGR002, and it is aimed at students eager to gain deeper knowledge in the field. The majority of image processing tasks can be formulated as a variational problem. We introduce the calculus of variations and numerical methods for solving optimization problems. Then, we focus on problems from image processing, which one can formulate as an optimization problem, and we illustrate possible solutions for various practical applications.

This course is taught in the same form at the MFF CUNI and FJFI CTU.

### COURSE SCHEDULE

Summer semester 2023/24:

Lectures are every Thursday from 9am to 12am starting Feb 29 in UTIA, room 203.

### COURSE OUTLINE

• 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)

• 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)

### COURSE HANDOUTS

The files contain most of the slides used during the lectures.

### RECOMMENDED 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.

# EXAMS

#### Connect with us

Pod Vodárenskou věží 4, Prague 8, Czechia