Search
March, 21-25 2011
Times: lectures: 13:00-14:30 in G205 and exercises: 16:15-17:45 in G3 (daily)
Location: Department of Cybernetics, Czech Technical University in Prague, Karlovo namesti 13, buiding G
Lectures of this intensive course 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.
Geometric computations in Computer Vision cover a large range of applications, such as calibration, orientation, reconstruction and grouping. They all are based on image features, mostly points or line segments. These are uncertain e. g. due to image noise, imperfection of their definition and possibly due to the suboptimality of the image analysis procedures. If this uncertainty is modelled statistically one can track the uncertainty of the basic features through the geometric reasoning chain, which consists of the derivation of new geometric entities and decisions based on expected geometric relations. As the tools from projective geometry ease geometric reasoning integrating projective geometry and statistics appears to be of great advantage. This integration conceptually is not straight forward: e. g. homogeneous entities have a free scale, fixing the scale leads to singular covariance matrices, the propagation of uncertainty of non-linear functions leads to distributions which, even when starting from a Gaussian distribution, are non-trivial, large estimation problems using homogeneous entities have to introduce constraints, directly or indirectly.
All lectures will take place during the week of March, 21-25 2011. Location: G205 Time: 13:00-14:30 daily
Lecturer: Wolfgang Förstner
All lectures in a single PDF, with corrections (last update: March 28, 2011)
All *annotated* lectures in a single PDF (last update: April 1, 2011)
The exercises will consist of exercises as a part of the intensive course. Answers to exercises are due the following date at the lecture. The student should collect at least 50% of points from each exercise to qualify for the exam.
Exercises:
Write a sugr-routine for ML-estimation of the essential matrix from point pairs similar ot the routine for estimating a homography in SUGR (copy and modify, including a test routine for checking the resultant covariance matrix of the five parameters)
The project is due by the end of the semester.
SUGR software (last update Mar 25, 2011)
wf@ipb.uni-bonn.de
sara@cmp.felk.cvut.cz