Subject description - BE4M33GVG

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BE4M33GVG Geometry of Computer Vision and Graphics
Roles:PO Extent of teaching:2P+2C
Department:13133 Language of teaching:EN
Guarantors:Pajdla T. Completion:Z,ZK
Lecturers:Pajdla T., Sattler T. Credits:6
Tutors:Korotynskiy V., Matoušek M., Pajdla T., Pánek V. Semester:L

Web page:


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.

Study targets:

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

Course outlines:

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.

Exercises outline:

1 Introduction, a-test 2-4 Linear algebra and optimization tools for computing with geometrical objects 5-6 Cameras in affine space - assignment I 7-8 Geometry of objects and cameras in projective space - assignment II 9-10 Principles of randomized algorithms - assignment III. 11-14 Randomized algorithms for computing scene geometry - assignment IV.


[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


A standard course in Linear Algebra


Computer vision and graphics, Euclidean, affine, projective geometry, perspective camera, random numbers, randomized algorithms, Monte Carlo simulation, linear programming.

Subject is included into these academic programs:

Program Branch Role Recommended semester
MEOI5_2018 Computer Vision and Image Processing PO 2
MEOI3_2018 Computer Graphics PO 2

Page updated 19.5.2024 15:51:18, semester: Z/2024-5, Z,L/2023-4, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)