TeachingSs08CV2

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

3D Computer Vision II Summer Term 2008

Administrative Info

Lecture by Prof. Nassir Navab
Exercises by Dr. Selim Benhimane and Hauke Heibel

2+2 SWS, 5 ECTS, Theoretische Informatik, Wahlpflichtfach

Time, Location & Requirements

Tuesday 10:30-12:00 MI 03.13.010
Exercises: Thursday 13:00-14:30 MI 03.13.010
Office hours: Wednesday 13:00-14:30 (MI 03.13.043 or MI 03.13.061)

Course information and certificate requirements:

  • The classes as well as the exercises will be held in English.
  • The lecture consists of one intermediate exam and a final exam.
  • All exams are hand written and only notes are allowed (no book, no calculator)
  • The final exam contains 100 points and the intermediate exam contains 40 points.
  • 50 out of 140 (100+40) are required to pass the class.

Office hours:

  • Whenever a student has a question regarding the lecture or exercises, he is welcome to drop by during our office hours!

Site Content

Announcements

Neither the class nor the exercises require any registration.

Overview

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"

This tasks and algorithms as well as the methods which allow us to reason about the quality of our results are the core of the lecture 3D Computer Vision II. This lecture deals with multiple view geometry problems and having attended 3D Computer Vision I is of great benefit, however, it is not, in any case, compulsory.

Content

  1. Intro, motivation & overview
  2. Projective geometry and 2D, 3D transformations
  3. Parameter estimation
  4. Camera model
  5. Two-View: Epipolar Geometry, 3D reconstruction, Fundamental Matrix, Structure computation
  6. Two-View: Mixed Camera Models: Perspective and Orthographic, Combined Othrographic and Perspective (COP) Images
  7. Three-View: The Trifocal Tensor
  8. Multi-View: Factorization Method, Multi-view Reconstruction, Motion and Structure from Motion

Course Schedule

Date Topic Conducted by Material/Literature
Tue, Apr 15, 2008 Introduction and Overview Prof. Dr. N. Navab Introduction
Tue, Apr 22, 2008 Reminder: Projective Geometry Prof. Dr. N. Navab Projective Geometry
Tue, Apr 29, 2008 No class due to CAMP Chair internal meeting    
Tue, May 6, 2008 Reminder: Parameter estimation Prof. Dr. N. Navab Parameter Estimation
Tue, May 13, 2008 No class due to Pentecost    
Tue, May 20, 2008 No class due to Studentische Vollversammlung    
Tue, May 27, 2008 One-View Geometry & Camera Models Prof. Dr. N. Navab One-View Geometry & Camera Models
Tue, Jun 3, 2008 Two-View Geometry: Introduction Prof. Dr. N. Navab Epipolar Geometry 1
Tue, Jun 10, 2008 Invited Talk: Multiple-camera reconstruction Dr. Radu Horaud  
Tue, Jun 17, 2008 The optimal triangulation method (ALERT! Exercises) Dr. Selim Benhimane Exercise 07
Exercise 07Solution
Tue, Jun 24, 2008 Two-View Geometry: 3D Reconstruction Prof. Dr. N. Navab 3d_CV_Lecture06_01.pdf
Tue, Jul 1, 2008 Two-View Geometry & Trifocal Tensor Prof. Dr. N. Navab 3d_CV_Lecture06_02.pdf
3d_CV_TriFocalTensor.pdf
Tue, Jul 8, 2008 Invited Talk: Multiple View Geometry Prof. Richard Hartley  
Tue, Jul 15, 2008 Invited Talk Dr. Mirko Appel  

Exercises

Date Topic Conducted by Material/Literature Assignment/Solution
Thu, Apr 17, 2008 Introduction to numerical computing with Matlab
Linear Algebra Basic for Computer Vision
Vector Notation
Hauke Heibel Basic Vector Algebra
Exercise 01
 
Thu, Apr 24, 2008 Homogeneous Representation of Points and Lines in Projective Space
Hierarchy of Transformations
Simple Coordinate Transformations (2D/3D)
Transformation Invariants
Hauke Heibel Exercise 02  
Thu, May 1, 2008 No exercises due to May Day      
Thu, May 8, 2008 Cross-Ratio of Angles
The Cross-Ratio in Needle Placement
The Cross-Ratio for Depth-Recovery
Hauke Heibel Exercise 03  
Thu, May 15, 2008 Non-linear Parameter Estimation Dr. Selim Benhimane Exercise 04  
Thu, May 22, 2008 No exercises due to Feast of Corpus Christi      
Thu, May 29, 2008 Camera Models and Projection Matrices Dr. Selim Benhimane Exercise 05  
Thu, Jun 5, 2008 Intermediate Exam in MI 03.13.010 (90 min.)
No book, no lecture slides allowed.
Only a two-sided written A4 paper is allowed during the test.
It contains your own notes and should be hand written.
     
Thu, Jun 12, 2008 Epipolar Geometry Hauke Heibel Exercise 06  
Thu, Jun 19, 2008 Two-View Geometry: Fundamental Matrix (ALERT! Lecture) Prof. Dr. N. Navab Epipolar Geometry 2  
Thu, Jun 26, 2008 Exam Correction Dr. Selim Benhimane    
Thu, Jul 3, 2008 Homography and Fundamental matrix linear computations Dr. Selim Benhimane Exercise 08  
Thu, Jul 10, 2008 Image Rectification Hauke Heibel Exercise 09 - Matlab Code
Paper
 
Thu, Jul 17, 2008 Final Exam in MI 03.13.010 (90 min.)
No book, no lecture slides allowed.
Only a two-sided written A4 paper is allowed during the test.
It contains your own notes and should be hand written.
     

Readings

  • 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

TeachingForm
Title: 3D Computer Vision II
Professor: Prof. Dr. Nassir Navab
Tutors: Dr. Selim Benhimane and Hauke Heibel
Type: Lecture
Information: 2+2 SWS, 5 ECTS, Theoretische Informatik, Wahlpflichtfach
Term: 2008SoSe
Abstract: 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 modelling 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" This tasks and algorithms as well as the methods which allow us to reason about the quality of our results are the core of the lecture 3D Computer Vision II. This lecture deals with multiple view geometry problems and having attended 3D Computer Vision I is of great benefit, however, it is not, in any case, compulsory.


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