Theoretical foundations of computer vision, graphics, and interaction
Code  Completion  Credits  Range  Language 

AD4M33TZ  Z,ZK  6  14KP+6KC  Czech 
 Garant předmětu:
 Lecturer:
 Tutor:
 Supervisor:
 Department of Cybernetics
 Synopsis:

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.
 Requirements:

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, atest
24Linear algebra and optimization tools for computing with geometrical objects
56Cameras in affine space  assignment I
78Geometry of objects and cameras in projective space  assignment II
910Principles of randomized algorithms  assignment III.
1114Randomized 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
 Note:
 Further information:
 No timetable has been prepared for this course
 The course is a part of the following study plans: