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Computer Vision Group
TUM Department of Informatics
Technical University of Munich

Technical University of Munich



Convex Optimization for Computer Vision (IN2330) (4h + 2h, 8 ECTS)

Repeat Exam

The repeat exam is oral and will take place on October 5 - 6 in room 02.07.011B. In case you haven't reserved a slot yet, please send us a mail!

Important Announcements

NEWS: There will be no lecture and exercises in the week 27.6. - 1.6. due to CVPR 2016.

Important news: There will be no lecture on Monday, 16.5. because of Pfingsten and no lecture and exercises in the week 23.5. - 27.5. due to the SIAM Conference on Imaging Science.

Location for Friday's exercise class has changed. New room: Room 01.09.014!

Convex variational methods are one of the most powerful techniques for many computer vision and image processing problems, e.g. denoising, deblurring, inpainting, stereo matching, optical flow computation, segmentation, or super resolution. In this lecture we will discuss first order convex optimization methods to implement and solve the aforementioned problems efficiently. Particular attention will be paid to problems including constraints and non-differentiable terms, giving rise to methods that exploit the concept of duality such as the primal-dual hybrid gradient method or the alternating directions methods of multipliers. This lecture will cover the mathematical background needed to understand why the investigated methods converge as well as the efficient practical implementation.

We will cover the following topics:

Mathematical background

  • Convex sets and functions
  • Existence and uniqueness of minimizers
  • Subdifferentials
  • Convex conjugates
  • Saddle point problems and duality

Numerical methods

  • (Sub-)Gradient descent schemes
  • Proximal point algorithm
  • Primal-dual hybrid gradient method
  • Augmented Lagrangian methods
  • Acceleration schemes, adaptive step sizes, and heavy ball methods

Example applications in computer vision and signal processing problems, including

  • Image reconstruction (e.g. denoising, deblurring, inpainting)
  • Stereo and optical flow
  • Implementation in MATLAB


Location: Room 02.09.023
Time and Date: Monday 14:15 - 16:00, Wednesday 16:15 - 18:00
Lecturer: Dr. Michael Möller, Thomas Möllenhoff
Start: April 11th, 2016
The lecture is held in English.


Location: Room 01.09.014
Time and Date: Friday 09:15 - 11:00
Organization: Emanuel Laude
Start: April 15th, 2016
The exercise sheets consist of two parts, theoretical and programming exercises. The exercise sheets will be passed out in the lecture on Wednesday and you have one week to solve them. The solutions will be discussed in the Friday exercises two days later. Please submit the programming solutions as a zip file with filename "matriculationnumber_firstname_lastname.zip" only! containing your .m-files (no material files) via email to emanuel.laude@in.tum.de, and hand in the solutions to the theoretical exercises in Wednesday's lecture. Please remember to write clean, commented(!) code! You are allowed to work on the exercise sheets in groups of two students.

The exercise sheets can be accessed here.

Fast Optimization Challenge

During the course of the lecture, we will pose a challenge to solve an optimization problem as quickly as possible. The challenge ends on Tuesday 12.07 23:59 . The best solution to each problem will receive a prize. The challenges will be a good preparation for the final exam!

Submission instructions: The source code should be sent via e-mail to thomas.moellenhoff@in.tum.de.

The code is evaluated in MATLAB R2015b on a MacBook Pro with 2,8 GHz Intel Core i7 CPU and 16 GB RAM.

Challenge: Huber-TV Inpainting

Download the template code. The precise task is described on the slide with title "Fast optimization challenge I" in chapter 2.


Name Runtime Method
Zhenzhang 174.6 sec ADMM
Yumin 233.8 sec PDHG
- 621.1 sec Gradient Descent (Baseline implementation)

By achieving at least 60% of all possible points on the exercise sheets you can obtain a bonus of 0.3 in the final exam. Note that you can neither improve a 1.0 nor a 5.0.


The exam will be oral.

Lecture Material

Course material (slides and exercise sheets) can be accessed here.

Send us an email if you need the password.

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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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