[Statlist] Talk on statistics

[Christina Kuenzli]

                  ETH and University of Zurich 

                           Proff. 
         A.D. Barbour - P. Buehlmann - F. Hampel - L. Held
            H.R. Kuensch - M. Maathuis - S. van de Geer

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           We are glad to announce the following talk
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     February 22, 2008     15.15-17.00    LEO C 6

     Random Sampling Consensus for Quasi-Degenerate Data
     Marc Pollefeys, ETH Zürich

  The computation of image relations from a number of potentially 
corresponding points is a major task in computer vision.  When those 
correspondences are computed automatically from images, the initial set
of potential correspondences is often contaminated with a high fraction
of gross outliers.  Often the Random Sampling Consensus (RANSAC) is 
employed for the robust computation of such relations.   While RANSAC is 
robust to many different issues, it typically fails when a large 
fraction of the correct correspondences only partially constrain the 
solution (e.g. in some cases this happens when the scene is (close to) 
planar).  The computed relation is always consistent with the data but 
RANSAC does not verify that it is unique. Our approach proposes a 
framework that estimates the correct relation with the same robustness 
as RANSAC even for (quasi-)degenerate data. The approach is based on a 
hierarchical RANSAC which tries to estimate a gradually larger and 
larger family of solutions while keeping a large fraction of the inliers 
to fit all solutions in the family.  In contrast to previous algorithms
for (quasi-)degenerate data our technique does not require problem 
specific tests or models to deal with degenerate configurations. 
Accordingly it can be applied for the estimation of any linear relation
on any data and is not limited to a special type of relation as some 
previous approaches.  More in general this approach can be seen as 
determining the robust rank of a matrix in the sense that it estimates 
the smallest rank that can be obtained while only removing a small 
fraction of the rows.  Our approach will be illustrated with examples 
from computer vision where the camera motion is robustly computed for 
image sequences even in presence of quasi-degenerate data.

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Christina Kuenzli            <kuenzli at stat.math.ethz.ch>
Seminar fuer Statistik      
Leonhardstr. 27,  LEO D11      phone: +41 (0)44 632 3438         
ETH-Zentrum,                   fax  : +41 (0)44 632 1228 
CH-8092 Zurich, Switzerland        http://stat.ethz.ch/~    
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