Robust Fitting for Multiple View Geometry

Summary, in English

How hard are geometric vision problems with outliers? We show that for most fitting problems, a solution that minimizes the num- ber of outliers can be found with an algorithm that has polynomial time- complexity in the number of points (independent of the rate of outliers). Further, and perhaps more interestingly, other cost functions such as the truncated L2 -norm can also be handled within the same framework with the same time complexity. We apply our framework to triangulation, relative pose problems and stitching, and give several other examples that fulfill the required condi- tions. Based on efficient polynomial equation solvers, it is experimentally demonstrated that these problems can be solved reliably, in particular for low-dimensional models. Comparisons to standard random sampling solvers are also given.

• Author: Olof Enqvist; Erik Ask; Fredrik Kahl; Karl Åström
• Editor: Andrew Fitzgibbon; Svetlana Lazebnik; Pietro Perona; Yoichi Sato; Cordelia Schmid
• Department/s: Mathematics (Faculty of Engineering); Centre for Mathematical Sciences; Mathematical Imaging Group; Algebra; ELLIIT: the Linköping-Lund initiative on IT and mobile communication
• Publishing year: 2012
• Language: English
• Pages: 738-751
• Publication/Series: Lecture Notes in Computer Science (Computer Vision - ECCV 2012, Proceedings of the 12th European Conference on Computer Vision, Florence, Italy, October 7-13, 2012, Part I )
• Volume: 7572
• Links: http://dx.doi.org/10.1007/978-3-642-33718-5_53
• Document type: Conference paper
• Publisher: Springer
• Topic: Mathematics
• Keywords: geometry; optimization; computer vision
• Conference name: 12th European Conference on Computer Vision (ECCV 2012)
• Conference date: 2012-10-07 - 2012-10-13
• Conference place: Florence, Italy
• Status: Published
• Research group: Mathematical Imaging Group; Algebra
• ISBN/ISSN/Other: ISSN: 0302-9743; ISSN: 1611-3349; ISBN: 978-3-642-33717-8 (print); ISBN: 978-3-642-33718-5 (online)