Subject description - A4M33GVG

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A4M33GVG Geometry of Computer Vision and Graphics Extent of teaching:2P+2C
Guarantors:  Roles:PO Language of
teaching:
CS
Teachers:  Completion:Z,ZK
Responsible Department:13133 Credits:6 Semester:L

Anotation:

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 modeling 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:

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.

Literature:

[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

Requirements:

A standard course in Linear Algebra.

Webpage:

https://cw.fel.cvut.cz/b182/courses/gvg/start

Subject is included into these academic programs:

Program Branch Role Recommended semester
MPOI3 Computer Vision and Image Processing PO 2
MPOI4NEW Computer Graphics and Interaction PO 2


Page updated 18.10.2019 07:53:05, semester: Z,L/2020-1, L/2018-9, Z,L/2019-20, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)