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# Computer Vision I: Variational Methods

## Module IN2246

This Module is offered by TUM Department of Informatics.

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

### Module version of SS 2015

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions
WS 2015/6SS 2015WS 2011/2

### Basic Information

IN2246 is a semester module in English language at Master’s level which is offered irregular.

This Module is included in the following catalogues within the study programs in physics.

• Catalogue of non-physics elective courses
240 h 90 h 8 CP

### Content, Learning Outcome and Preconditions

#### Content

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.
Exemples include denoising, deblurring, image segmentation, tracking, optical flow estimation, depth estimation from stereo images or 3D reconstruction from multiple views.
In this class, the basic concepts of variational methods will be introduced :
- The Euler-Lagrange calculus and partial differential equations
- Formulation of computer vision and image analysis challenges as variational problems
- Efficient solution of variational problems
- Discussion of convex formulations and convex relaxations to compute optimal or near-optimal solutions in the variational setting
The key concepts will be implemented in Matlab to provide hands-on experience.

#### Learning Outcome

Upon successful completion of the module the participants understand the basic concepts of variational methods on a fundamental, scientific and practical level.
They are able to efficiently solve variational problems and to implement the solution with Matlab.

#### Preconditions

MA0901 Linear Algebra for Informatics
MA0902 Analysis for Informatics

### Courses, Learning and Teaching Methods and Literature

#### Courses and Schedule

VI 6 Computer Vision I: Variational Methods (IN2246) Cremers, D. Demmel, N. Tue, 10:00–12:00, Interims I 102
Thu, 10:00–12:00, Interims I 102
Wed, 10:30–12:30, Interims II 004

#### Learning and Teaching Methods

The main concepts will be presented in the lecture. During the tutorial, related exercises and discussions will deepen the understanding. Besides theoretical exercises, there will be programming exercises.

#### Media

Tutor presentation, interactive problem solving, discussion

#### Literature

Mathematical Image Processing (Bredies, Lorenz)

### Module Exam

#### Description of exams and course work

The exam takes the form of a 120 minutes written test. In the written exam students should prove that they understood the basic concepts of variational methods. The questions will focus on the key concepts which have been discussed during the lecture and the tutorials. Mathematical proofs of the central concepts and questions about the implementation in Matlab assess acquaintance with the concepts in variational image processing.

#### Exam Repetition

The exam may be repeated at the end of the semester.

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