Geometry of Computer Vision and Graphics

The course is not on the list Without time-table
Code Completion Credits Range Language
A4M33GVG Z,ZK 6 2P+2C Czech
The course cannot be taken simultaneously with:
Theoretical foundations of computer vision, graphics, and interaction (A4M33TZ)
Geometry of Computer Vision and Graphics (BE4M33GVG)
The course is a substitute for:
Theoretical foundations of computer vision, graphics, and interaction (A4M33TZ)
Department of Cybernetics

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.


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

Further information:
No time-table has been prepared for this course
The course is a part of the following study plans:
Data valid to 2022-08-18
For updated information see http://bilakniha.cvut.cz/en/predmet1962706.html