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Authors:

Enqvist, Olof
;
Ask, Erik
;
Kahl, Fredrik
;
Åström, Karl

Editors:

Fitzgibbon, Andrew
;
Lazebnik, Svetlana
;
Perona, Pietro
;
Sato, Yoichi
;
Schmid, Cordelia

Department:

Mathematics (Faculty of Engineering)

Centre for Mathematical Sciences

Mathematical Imaging Group

Algebra

ELLIIT: the Linköping-Lund initiative on IT and mobile communication

Centre for Mathematical Sciences

Mathematical Imaging Group

Algebra

ELLIIT: the Linköping-Lund initiative on IT and mobile communication

Research Group:

Mathematical Imaging Group

Algebra

Algebra

Abstract:

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.

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.

Keywords:

geometry ;
optimization ;
computer vision

ISBN:

978-3-642-33717-8 (print)

ISSN:

1611-3349

LUP-ID:

981178b1-2700-4606-af41-534ee7ee2fdb | Link: https://lup.lub.lu.se/record/981178b1-2700-4606-af41-534ee7ee2fdb
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