Theoretical foundations of computer vision, graphics, and interaction
Kód | Zakončení | Kredity | Rozsah | Jazyk výuky |
---|---|---|---|---|
AE4M33TZ | Z,ZK | 6 | 2+2c | česky |
- Přednášející:
- Cvičící:
- Předmět zajišťuje:
- katedra kybernetiky
- Anotace:
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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 calculations with 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 and determining camera positions in space. We will build on linear algebra, probability theory and numerical mathematics and lay down foundation for other subjects such as computational geometry, computer vision, computer graphics, digital image processing and recognition of objects in images.
- Požadavky:
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A standard course in Linear Algebra.
- Osnova přednášek:
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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.
- Osnova cvičení:
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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.
- Cíle studia:
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The goal is to present the theoretical background for
modeling of perspective cameras and solving tasks of
measurement in images and scene reconstruction.
- Studijní materiály:
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[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
- Poznámka:
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Rozsah výuky v kombinované formě studia: 14p+6c
- Další informace:
- Pro tento předmět se rozvrh nepřipravuje
- Předmět je součástí následujících studijních plánů:
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- Open Informatics - Computer Vision and Image Processing (povinný předmět oboru)
- Open Informatics - Computer Graphics and Interaction (povinný předmět oboru)