Syllabus
- 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)
More information (study materials, exams, diploma thesis) is available at NPGR029
Annotation
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.