Uncertain geometric reasoning in computer vision

Lecturer:

Radim Šára (gar.)

Tutor:

Radim Šára (gar.)

Supervisor:

Department of Cybernetics

Synopsis:

The lectures provide an introduction into the concepts of uncertain geometric reasoning using projective entities with applications in Computer Vision. They cover aspects such as the representation of uncertain projective entities, the uncertainty propagation, performing statistical testing of geometric relations and optimal estimation of geometric entities and transformations.

Five lectures per 90 minutes will be given during a single week of 21-25. March 2011. Software, short exercises parallel to the lectures and a project will be provided. The lectures will be given by a leading expert in the field, Prof. Wolfgang Förstner, University of Bonn, Germany.

More details on the course web page at http://cw.felk.cvut.cz/doku.php/courses/ae4m33ugr/start

Requirements:

Linear algebra

- eigenvalues, singular values,

- determinants, null space

- Kronecker product and vec-operator

Probability theory and statistics

- continuous pdf's (Gauss, chi-square)

- covariance propagation

- classical hypothesis testing

Projective geometry

- homogeneous representation of 2D points and lines, 3D points and planes

- spatial relations, constructions and transformations

- algebraic solutions for transformations from correspondences

Multi-view geometry

- projection matrix and its properties

- epipolar geometry

- fundamental and essential matrix

Image analysis

- least squares matching (Lucas-Kanade/Ackermann)

- key point extraction, structure tensor (Harris)

- line extraction

Syllabus of lectures:

1. Maximum likelihood estimation in the Gauss-Markov model

2. Maximum likelihood estimation in a Gauss-Helmert (GH) model with constraints

3. Uncertainty of projective geometric entities

4. Estimation of geometric entities

5. Estimation of transformations

6. Pitfalls in uncertain reasoning (conceptual lecture)

7. Uncertainty of minimal solutions

8. Orientation of a camera

9. Optimally estimating parametric curves and surfaces

10. Reasoning with uncertain 3D lines

Syllabus of tutorials:

The exercises will consist of hands-on exercises as a part of the intensive course and a homework project on Relative orientation of two calibrated omnidirectional cameras.

Study Objective:

Study materials:

Förstner, Wolfgang: Minimal Representations for Uncertainty and Estimation in Projective Spaces, In: Proceedings of the Asian Conference on Computer Vision. Queenstown, New Zealand 2010.

Förstner, Wolfgang: Optimal Vanishing Point Detection and Rotation Estimation of Single Images of a Legoland Scene, In: Proceedings of the ISPRS Symposium Commission III PCV. Paris 2010.

Meidow, Jochen; Beder, Christian; Förstner, Wolfgang:

Reasoning with uncertain points, straight lines, and straight line segments in 2D

In: ISPRS Journal of Photogrammetry and Remote Sensing, 64. Jg. 2009, Heft: 2, S. 125-139.

Förstner, Wolfgang: Uncertainty and Projective Geometry, In: Bayro Corrochano, Eduardo (Hg.): Handbook of Geometric Computing. 2005, S. 493-535.

McGlone, Chris, Bethel, Jim, Mikhail, Ed M. (Eds): Manual of Photogrammetry, ASPRS, 2004

Koch, Karl-Rudolf: Parameter Estimation and Hypothesis Testing in Linear Models, 2. Edition, Bonn (1999)(German Version from 1997)

Förstner, Wolfgang: Reliability Analysis of Parameter Estimation in Linear Models with Applications to Mensuration Problems in Computer Vision, In: CVGIP - Computer Vision, Graphics, and Image Processing. 1987, S. 273-310.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: