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Course, academic year 2019/2020
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Geometry of Computer Vision - NMMB440
Title in English: Geometrie počítačového vidění
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2019 to 2019
Semester: summer
E-Credits: 6
Hours per week, examination: summer s.:2/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: English, Czech
Teaching methods: full-time
Guarantor: doc. Ing. Tomáš Pajdla, Ph.D.
Class: M Mgr. MMIB > Povinně volitelné
Classification: Mathematics > Geometry
Annotation -
Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (14.05.2019)
We will introduce a model of the perspective camera, explain how images change when moving a camera and show how to find the camera pose from images. We will demonstrate the theory in practical tasks of panorama construction, finding the camera pose, adding a virtual object to a real scene and reconstructing a 3D model of a scene from its images. We will be building on our previous knowledge of Linear algebra and will provide fundamentals of geometry The course may not be taught every academic year, it will be taught at least once every two years.
Course completion requirements - Czech
Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (11.06.2019)

Předmět je zakončen ústní zkouškou.

Literature -
Last update: T_KA (30.04.2015)

R. Hartley, A.Zisserman. Multiple View Geometry in Computer Vision. Cambridge University Press, 2000

Requirements to the exam - Czech
Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (11.06.2019)

Zkouška má ústní formu. Její požadavky odpovídají obsahu přednesené látky.

Syllabus -
Last update: T_KA (29.04.2016)

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.

 
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