Chair for Computer Aided Medical Procedures & Augmented Reality
Lehrstuhl für Informatikanwendungen in der Medizin & Augmented Reality

3D Computer Vision Summer Term 2010

Administrative Info

Lecture by Prof. Nassir Navab?
Exercises by Slobodan Ilic and Stefan Hinterstoisser
and Alexander Ladikos and Stefan Holzer and Juergen Sotke

Type: Lecture Module IN2057
Programs: Informatics (Bachelor, Master)
Informatics (Diploma, Wahlpflichtfach, Theoretische Informatik)
Information Systems (Bachelor), Computational Science and Engineering (Master)
Master Sports Engineering
SWS: 2+2
ECTS: 5 Credits
Course Language: English

Time, Location & Requirements

Lecture: Tuesday 10:00-11:30 MI 03.13.010

Exercises: Thursday 12:30-14:00 (the time announced on TUMOnline is not the correct time!) MI 03.13.010


  • The classes and exam are in English
  • Exams are to be written in English only
  • For the intermediate exam, only one handwritten Din A4 (front+back) page with notes is allowed; calculators are allowed (however, computers are not allowed!)
  • For the final exam, only one handwritten Din A4 page (front+back) with notes is allowed; calculators are allowed (however, computers are not allowed!)
  • The final exam contains 100 points, you need to have 50 points to pass it
  • Up to 40 bonus points can be earned from the homework and the intermediate exam

Site Content


The results of the re-examination have been added to the results list!

Final exam and final grades

The results of the final exam and Your final grades can be found here.

If you have questions concerning the exam or your final grade, please make an appointment by writing an email to Stefan or Jürgen.

Midterm exam

The results of the midterm exam can be found here.


Neither the class nor the exercises require any registration.


We will announce special dates on which students have to show their homework either on their own computer or on the computers of the CAMP-Lab. In these sessions, we will check the latest 3-5 homeworks.


In order to do the exercises students must know how to program in Matlab. A basic introduction is given on April 22nd from 14:30-16:00 in MI 03.13.010. The time of the exercise is a SINGLE EXCEPTION since it is hold jointly with the CAMP lecture. The regular time of the exercises is each Thursday between 12:30-14:00. Please read the Matlab tutorial/sheet given under Exercises if you want to attend!


Making a computer see was something that leading experts in the field of Artificial Intelligence thought to be at the level of difficulty of a summer student's project back in the sixties. Forty years later the task is still unsolved and seems formidable. A whole field, called Computer Vision, has emerged as a discipline in itself with strong connections to mathematics and computer science and looser connections to physics, the psychology of perception and the neuro sciences.

Over the past decade there has been a rapid development in the understanding and modeling of the geometry of multiple views in computer vision. The theory and practice have now reached a level of maturity where excellent results can be achieved for problems that were unsolved a decade ago, and often thought unsolvable. These tasks and algorithms include problems like:
Given two/three/multiple images, and no further information, compute/estimate:

  • matches between the images
  • the 3D position of the points that generate these matches
  • the cameras that generate the images

(Adapted form Hartley & Zisserman's "Multiple View Geometry in Computer Vision")

The fundamental mathematics and a profound comprehension of the basics of projective geometry as well as one-view geometry are the core of the lecture 3D Computer Vision.

Lecture Content

  1. Intro, motivation & Overview
  2. 2D Transformations
  3. Projective 2D Geometry
  4. 3D Transformations
  5. Projective 3D Geometry
  6. Parameter Estimation
  7. Camera Models
  8. Camera Calibration
  9. Conclusion & Discussion

Lecture Schedule

Date Conducted by Topic Material/Literature
Tue. 20.04.10 Prof. Nassir Navab Introduction and Motivation Introduction (without Videos)
Tue. 27.04.10 Prof. Nassir Navab Basic Transformations & 2D Projective Geometry Lecture 1
Tue. 04.05.10 Prof. Nassir Navab Transformations & 2D Projective Geometry Lecture 2
Tue. 11.05.10 Prof. Nassir Navab Parameter Estimation: Linear Estimation, DLT, Cost Functions Lecture 3 & 4
Tue. 18.05.10 Prof. Nassir Navab No Lecture due to SVV
Tue. 25.05.10 NO LECTURE (TUM „vorlesungsfreie Zeit“) NO LECTURE (TUM „vorlesungsfreie Zeit“)  
Tue. 01.06.10 Prof. Nassir Navab Parameter Estimation: Sampson Error, Statistical Cost Functions  
Tue. 08.06.10 Dr. Slobodan Ilic Non-linear Parameter Estimation Lecture 6
Tue. 15.06.10 Prof. Nassir Navab Algorithm Evaluation & Error Analysis Lecture 7
Tue. 22.06.10 Prof. Nassir Navab Projection and Camera Models Lecture 8
Tue. 29.06.10 Prof. Nassir Navab Computation of the Projection Matrix Lecture 9
Tue. 06.07.10 Prof. Nassir Navab Conics in Projective Geometry Lecture 10
Tue. 13.07.10 Prof. Nassir Navab Camera Models II Lecture 11
Tue. 20.07.10 Prof. Nassir Navab Modeling and Correction of Distortion  

Exercise Schedule

Date Conducted by Topic Exercises Solutions Homework due
Thu 22.04.10 Slobodan Ilic,Stefan Hinterstoisser, Juergen Sotke no exercise - there is a Matlab tutorial - see anouncements  MATLAB Workshop,
 MATLAB Primer,
no solution
no homework
Thu 29.04.10 Slobodan Ilic,Stefan Hinterstoisser, Juergen Sotke Homogeneous Coordinates; Hierarchy of Transformations (2D);
Duality of Points and Lines (also under Transformations)
Exercise 1
Thu 06.05.10 Slobodan Ilic,Stefan Hinterstoisser 3D Rigid Transformations; Rotation representations; Rodrigues Angles; Representing Projective Geometry in R3 Exercise 2 tba.
Thu 13.05.10 no lecture due to holiday (Christi Himmelfahrt)   no exercise sheet no solution no homework
Thu 20.05.10 Stefan Hinterstoisser, Juergen Sotke Cross-Ratio of Points and Lines, DLT, Mosaicing Exercise 3 Attention: we changed this exercise sheet due to the modified lecture!
Thu 27.05.10 Slobodan Ilic,Alexander Ladikos tba. Exercise 4 tba.
Thu 03.06.10 no exercise due to holiday (Fronleichnam)        
Thu 10.06.10 Stefan Hinterstoisser Error Models, Homography Exercise 5 tba.
Thu 17.06.10 Alexander Ladikos, Hauke Heibel, Juergen Sotke Maximum Likelihood Estimation, Non-linear estimation methods Exercise 6 tba.
Thu 24.06.10 Slobodan Ilic,Alexander Ladikos Error Propagation Exercise 7
(im1.png, im2.png, error_ellipse.m)
Thu 01.07.10 Slobodan Ilic,Stefan Holzer Projection Matrices, Camera Calibration Exercise 8 tba.
Thu 08.07.10 Slobodan Ilic,Stefan Holzer Planar Camera Calibration, Radial Distortion Exercise 9
Calibration data: fx = 3133, fy = 3139, s = 0, u0 = 1509, v0 = 1177
Thu 15.07.10 Slobodan Ilic,Stefan Holzer tba. tba.


  • Midterm Exam: the midterm exam will be at Fri. 11.06.10: 9:30am-11:30am.
  • Final Exam: the final exam will start on Sat. 24.07.10: 9:00am


  • Primary Reading
    • Multiple View Geometry in Computer Vision by Richard Hartley & Andrew Zisserman

  • General Introduction to 3D Computer Vision
    • Three-Dimensional Computer Vision by Olivier Faugeras
    • Computer Vision: A Modern Approach by David A. Forsyth & Jean Ponce
    • Introductory Techniques for 3-D Computer Vision by Emanuele Trucco & Alessandro Verri

  • More Specific Readings
    • The Geometry of Multiple Images: The Laws That Govern the Formation of Multiple Images of a Scene and Some of Their Applications by Olivier Faugeras, Quang-Tuan Luong, Theodore H. Papadopoullos; MIT Press; 2001

Title: 3D Computer Vision
Professor: Nassir Navab
Tutors: Slobodan Ilic, Stefan Hinterstoisser, Alexander Ladikos, Stefan Holzer, Juergen Sotke
Type: Lecture
Information: 2+2 SWS, 5 ECTS, Theoretische Informatik, Wahlpflichtfach
Term: 2010SoSe
Abstract: The class covers projective and one-view geometry for Computer Vision Applications.

Edit | Attach | Refresh | Diffs | More | Revision r1.86 - 05 May 2011 - 12:37 - StefanHolzer

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