Note: As a TUM student, if you are planning to take the exam and get credits, you are encouraged to participate in current course iteration during the semester.

Variational Methods are among the most classical techniques for optimization of cost functions in higher dimension. Many challenges in Computer Vision and in other domains of research can be formulated as variational methods. Examples include denoising, deblurring, image segmentation, tracking, optical flow estimation, depth estimation from stereo images or 3D reconstruction from multiple views.

In this class, I will introduce the basic concepts of variational methods, the Euler-Lagrange calculus and partial differential equations. I will discuss how respective computer vision and image analysis challenges can be cast as variational problems and how they can be efficiently solved. Towards the end of the class, I will discuss convex formulations and convex relaxations which allow to compute optimal or near-optimal solutions in the variational setting.

The requirements for the class are knowledge in basic mathematics, in particular multivariate analysis and linear algebra. Some prior knowledge on optimization is a plus but is not necessary.

Lecture recordings from 2013/14 can be found on YouTube.

Slides from 2019/20 can be found below. These are for the most part compatible with the recorded lectures, but contain a few minor corrections and additions.