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Theoretical foundations of computer vision, graphics, and interaction

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Code Completion Credits Range Language
A4M33TZ Z,ZK 6 2P+2C Czech
It is not possible to register for the course A4M33TZ if the student is concurrently registered for or has already completed the course A4M33GVG (mutually exclusive courses).
During a review of study plans, the course A4M33GVG can be substituted for the course A4M33TZ.
It is not possible to register for the course A4M33TZ if the student is concurrently registered for or has previously completed the course A4M33GVG (mutually exclusive courses).
The requirement for course A4M33TZ can be fulfilled by substitution with the course A4M33GVG.
Garant předmětu:
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. Then we will study methods of calculating geometrical objects in images and space, estimating geometrical models from observed data, and for calculating geometric and physical properties of observed objects. The theory will be demonstrated on practical task of creating mosaics from images, measuring the geometry of objects by a camera, and reconstructing geometrical and physical properties of objects from their projections. We will build on linear algebra, probability theory, numerical mathematics 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. Computer vision, graphics, and interaction - the discipline and the subject.

2. Modeling world geometry in the affine space.

3. The mathematical model of the perspective camera.

4. Relationship between images of the world observed by a moving camera.

5. Estimation of geometrical models from image data.

6. Optimal approximation using points and lines in L2 and minimax metric.

7. The projective plane.

8. The projective, affine and Euclidean space.

9. Transformation of the projective space. Invariance and covariance.

10. Random numbers and their generating.

11. Randomized estimation of models from data.

12. Construction of geometric objects from points and planes using linear programming.

13. Calculation of spatial object properties using Monte Carlo simulation.

14. Review.

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 2024-05-27
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