1. Multiple View Geometry
Ilan Shimshoni
Dept of Management Information Systems
University of Haifa

2. Examples of Applications
Visual robot navigation
3D reconstruction from video
Was there a goal in a game from two video cameras?

3. What do we know? Camera parameters
Camera position with respect to the scene
Relative camera position (known or constrained)
Objects in the scene
Their positions
Characteristics of objects in the scene
Nothing!!!

4. The more we know the easier it is.
The more we need to know the harder it is to perform the experiment.
Example stereo reconstruction
Camera parameters known
Relative camera positions known and constrained
Goal: reconstruct scene. Find for each point in the first image its corresponding point in the second image.
How can we make the task easier?

5. Another example: scene reconstruction from a video sequence
Camera parameters not known
Camera positions not known
Much easier for the user
Something in between: Scene reconstruction from a set of images taken by a plane (geodesic dept)
Position of plane known quite accurately
High quality camera which has been accurately calibrated

6. How do we solve problems?
Example: Pose estimation
The algorithm is given:
A model of a 3D object
The geometric imaging parameters of the camera
An image of the object
Goal:
Calculate accurately the position of the camera with respect to the object

7. Applications
A robot would like to grab an object with its gripper using a camera which is positioned on the robot
A robot would like to know where it is. The object is the room.
A satellite would like to know its orientation in space from an image it took of the stars. The object is the universe

8. The input:

9. Steps in developing an algorithm
Define f(X,x,)
Find a method to compute 
such that f(X,x,) = 0
What should we do if there is measurement noise in x?
How do we match x to X?
How do we deal with incorrect matches (outliers)?
Build a full system.

11. Criminisi

14. MIT city scanning project
Produce image hemispheres
Localize hemispheres using GPS
Match hemispheres using vision methods
Find accurate positions of cameras
Reconstruct buildings
Reconstruct fine details

15. 3D reconstruction from image sequence

17. Cipolla 2008

18. Elections November 2008