M2. Optimization and Inference techniques in Computer Vision (31819)

The aim of this module is to learn about numerical optimization algorithms that are behind many tasks in computer vision. Main concepts will include energy minimization, numerical techniques for variational problems, convex optimization and graphical models. These techniques will be applied in the project in the context of image segmentation and restoration (denoising and inpainting).
Project title: 
Removing objects in urban scenes
The goal of this project is to gain practical experience with the basic optimization methods used in computer vision. The methods will be studied in the context of image segmentation and restoration (denoising and inpainting), with special emphasis on the formulation of the optimization problem and its resolution. The tools learnt along this project are generic and present in a majority of computer vision applications (as found in other modules, e.g. in clutter removal for improved 3D scene reconstruction, M6).
Module lectures: 


Academic Year 2018-2019         
Week Date Time Lecture Lecturer University Building Room
1 Tue. Oct. 2nd  16:00 -18:00 Introduction to optimization problems and energy minimization methods. Examples and Overview of varational formulation. Numerical techniques for variational problems (I).

Juan Fco. Garamendi 

UPF  Roc Boronat  52.329 
Thu. Oct. 4th 16:00 -18:00 Numerical techniques for variational problems (II): Gateaûx derivate, Euler-Lagrange equation and gradient methods. Applications: denoising, image inpainting and Poisson editing. Review of numerical linear algebra (I). Juan Fco. Garamendi UPF Roc Boronat 52.223
Thu. Oct. 4th 18:00 - 19:00

Project Introduction

Karim Lekadir

UPF Roc Boronat


2 Tue. Oct. 9th 16:00 -18:00 Review of numerical linear algebra (II): lesat squares methods and singular value decomposition. The Backpropagation strategy for gradient computation. 
Juan Fco. Garamendi UPF Roc Boronat 52.S31 
Thu. Oct. 11th 16:00 -18:00 Convex optimization (I). Constrained and unconstrained optimization. Duality principles and methods. Applications: Total Variation restoration, disparity computation, optical flow computation,... Coloma Ballester UPF Roc Boronat 52.223
Thu. Oct. 11th 18:00 - 19:00 Project follow-up Karim Lekadir  UPF Roc Boronat   52.223
 3 Tue. Oct. 16th  16:00 -18:00

Convex optimization (II):  Duality principles and methods. Non-convex problems and convex relaxation. Segmentation with variational models. The Mumford and Shah Functional and the Level sets framework. 

Coloma Ballester UPF Roc Boronat  52.329
Thu. Oct. 18th  16:00 -18:00 Bayesian networks and MRFs. Inference Types. Examples: stereo, denoising.  Joan Serrat  UPF Roc Boronat    52.223 
Thu. Oct. 18th 18:00 - 19:00 Project follow-up Karim Lekadir UPF  Roc Boronat     52.223 
4 Tue. Oct. 23rd 16:00 -18:00 Inference algorithms (I): belief propagation (sum-product and max-sum) and generalizations. Examples: blob tracking, video synchronization. Guidelines for PGM exercises.  Oriol Ramos UPF  Roc Boronat 52.S31 
Thu. Oct. 25th 16:00 - 18:00 Inference algorithms (II): Graph cuts, linear programming relaxation, Monte Carlo methods. Examples: co-segmentation Oriol Ramos UPF Roc Boronat   52.223 
Thu. Oct. 25th 18:00 - 19:00 Project follow-up

Karim Lekadir

UPF  Roc Boronat   52.223  


Tue. Oct. 30th   HOMEWORK        
Thu. Nov. 1st   HOLIDAY        
6 Tue. Nov. 7th  16:00-18:00 Learning of graphical models.Structured SVMs Joan Serrat UPF Roc Boronat 52.S31 
Thu. Nov. 9th 16:00-18:00 PGM exercises: inference for segmentation and learning for labeling

Oriol Ramos 

Joan Serrat

UPF Tallers



Thu. Nov. 9th 18:00 -19:00 Project follow-up

Karim Lekadir

UPF Roc Boronat


7 Tue. Nov. 13th   HOMEWORK        
Thu. Nov. 15th   HOMEWORK        
8 Thu. Nov. 22nd 16:00-19:00 Project Presentations  Karim Lekadir UPF Roc Boronat 52.121
9 Tue. Nov. 27th   HOMEWORK        
9 Thu. Nov. 29th 16:00-18:00 HOMEWORK        
10 Tue.Dec. 4th 16:00 -19:00 EXAM Coloma Ballester UPF Roc Boronat  52.023

 M2 Student Guide [here]