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Technical University of Munich

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Computer Vision I: Variational Methods

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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.

Summary

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.

Prerequisites

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.

Videos

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

Lecture Material

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Informatik IX
Chair of Computer Vision & Artificial Intelligence

Boltzmannstrasse 3
85748 Garching info@vision.in.tum.de

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