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)
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)