Theoretical foundations of computer vision, graphics, and interaction

The course cannot be taken simultaneously with:

Theoretical foundations of computer vision, graphics, and interaction (A4M33TZ)

The course is a substitute for:

Theoretical foundations of computer vision, graphics, and interaction (A4M33TZ)

Lecturer:

Tomáš Pajdla (gar.)

Tutor:

Tomáš Pajdla (gar.), Michal Havlena, Martin Matoušek

Supervisor:

Department of Cybernetics

Synopsis:

We will explain fundamentals of image and space geometry including Euclidean, affine and projective geometry, the model of a perspective camera, image transformations induced by camera motion, and image normalization for object recognition. The theory will be demonstrated on practical task of creating mosaics from images, measuring the geometry of objects by a camera, and reconstructing geometrical properties of objects from their projections. We will build on linear algebra and optimization and lay down foundation for other subjects such as computational geometry, computer vision, computer graphics, digital image processing and recognition of objects in images.

Requirements:

A standard course in Linear Algebra.

Syllabus of lectures:

1. Geometry of computer vision and graphics and how to study it.

2. Linear and affine spaces.

3. Position and its representation.

4. Mathematical model for perspective camera.

5. Perspective camera calibration and pose computatation.

6. Homography.

7. Invariance and covariant constructions.

8. Projective plane, ideal points and ideal line, vanishing points and horizon.

9. Camera calibration from vanishing points and from planar homography.

10. Projective space. Points, lines, planes.

11. Angle and distace in the projective space.

12. Auticalibration of perspective camera.

13. Epipolar geometry.

14. 3D reconstruction from images.

Syllabus of tutorials:

1Introduction, a-test

2-4Linear algebra and optimization tools for computing with geometrical objects

5-6Cameras in affine space - assignment I

7-8Geometry of objects and cameras in projective space - assignment II

9-10Principles of randomized algorithms - assignment III.

11-14Randomized algorithms for computing scene geometry - assignment IV.

Study Objective:

The goal is to present the theoretical background for modeling of perspective cameras and solving tasks of measurement in images and scene reconstruction.

Study materials:

[1] P. Ptak. Introduction to Linear Algebra. Vydavatelstvi CVUT, Praha, 2007.

[2] E. Krajnik. Maticovy pocet. Skriptum. Vydavatelstvi CVUT, Praha, 2000.

[3] R. Hartley, A.Zisserman. Multiple View Geometry in Computer Vision.

Cambridge University Press, 2000.

[4] M. Mortenson. Mathematics for Computer Graphics Applications. Industrial Press. 1999

Note:

Time-table for winter semester 2011/2012:

Time-table is not available yet

Time-table for summer semester 2011/2012:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon	roomKN:E-126 Pajdla T. 09:15–10:45 (lecture parallel1) Karlovo nám. Trnkova posluchárna K5roomKN:E-220 Matoušek M. Havlena M. 12:45–14:15 (lecture parallel1 parallel nr.101) Karlovo nám. Laboratoř BIOroomKN:E-220 Matoušek M. Havlena M. 16:15–17:45 (lecture parallel1 parallel nr.102) Karlovo nám. Laboratoř BIOroomKN:E-220 Matoušek M. Havlena M. 18:00–19:30 (lecture parallel1 parallel nr.103) Karlovo nám. Laboratoř BIO
Tue
Fri
Thu
Fri

The course is a part of the following study plans:

• Otevřená informatika - Počítačové vidění a digitální obraz (compulsory course of the specialization)