Robust Fitting for Multiple View Geometry

Olof Enqvist; Erik Ask; Fredrik Kahl; Karl Åström

doi:10.1007/978-3-642-33718-5_53

Robust Fitting for Multiple View Geometry

Olof Enqvist, Erik Ask, Fredrik Kahl, Karl Åström

Research output: Chapter in Book/Report/Conference proceeding › Paper in conference proceeding › peer-review

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.

Original language	English
Title of host publication	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 )
Editors/authors	Andrew Fitzgibbon, Svetlana Lazebnik, Pietro Perona, Yoichi Sato, Cordelia Schmid
Publisher	Springer
Pages	738-751
Number of pages	14
Volume	7572
ISBN (Print)	978-3-642-33717-8 (print), 978-3-642-33718-5 (online)
DOIs	https://doi.org/10.1007/978-3-642-33718-5_53
Publication status	Published - 2012
Event	12th European Conference on Computer Vision (ECCV 2012) - Florence, Italy Duration: 2012 Oct 7 → 2012 Oct 13

Publication series

Name
Volume	7572
ISSN (Print)	1611-3349
ISSN (Electronic)	0302-9743

Conference

Conference	12th European Conference on Computer Vision (ECCV 2012)
Country/Territory	Italy
City	Florence
Period	2012/10/07 → 2012/10/13

Subject classification (UKÄ)

Mathematical Sciences

Free keywords

geometry
optimization
computer vision

Access to Document

10.1007/978-3-642-33718-5_53

Cite this

Enqvist, O., Ask, E., Kahl, F., & Åström, K. (2012). Robust Fitting for Multiple View Geometry. In A. Fitzgibbon, S. Lazebnik, P. Perona, Y. Sato, & C. Schmid (Eds.), 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 ) (Vol. 7572, pp. 738-751). Springer. https://doi.org/10.1007/978-3-642-33718-5_53

Enqvist, Olof ; Ask, Erik ; Kahl, Fredrik et al. / Robust Fitting for Multiple View Geometry. 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 ). editor / Andrew Fitzgibbon ; Svetlana Lazebnik ; Pietro Perona ; Yoichi Sato ; Cordelia Schmid. Vol. 7572 Springer, 2012. pp. 738-751

@inproceedings{981178b127004606af41534ee7ee2fdb,

title = "Robust Fitting for Multiple View Geometry",

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.",

keywords = "geometry, optimization, computer vision",

author = "Olof Enqvist and Erik Ask and Fredrik Kahl and Karl {\AA}str{\"o}m",

year = "2012",

doi = "10.1007/978-3-642-33718-5\_53",

language = "English",

isbn = "978-3-642-33717-8 (print)",

volume = "7572",

publisher = "Springer",

pages = "738--751",

editor = "Andrew Fitzgibbon and Svetlana Lazebnik and Pietro Perona and Yoichi Sato and Cordelia Schmid",

booktitle = "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 )",

address = "Germany",

note = "12th European Conference on Computer Vision (ECCV 2012) ; Conference date: 07-10-2012 Through 13-10-2012",

}

Enqvist, O, Ask, E, Kahl, F & Åström, K 2012, Robust Fitting for Multiple View Geometry. in A Fitzgibbon, S Lazebnik, P Perona, Y Sato & C Schmid (eds), 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 ). vol. 7572, Springer, pp. 738-751, 12th European Conference on Computer Vision (ECCV 2012), Florence, Italy, 2012/10/07. https://doi.org/10.1007/978-3-642-33718-5_53

Robust Fitting for Multiple View Geometry. / Enqvist, Olof; Ask, Erik; Kahl, Fredrik et al.
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 ). ed. / Andrew Fitzgibbon; Svetlana Lazebnik; Pietro Perona; Yoichi Sato; Cordelia Schmid. Vol. 7572 Springer, 2012. p. 738-751.

Research output: Chapter in Book/Report/Conference proceeding › Paper in conference proceeding › peer-review

TY - GEN

T1 - Robust Fitting for Multiple View Geometry

AU - Enqvist, Olof

AU - Ask, Erik

AU - Kahl, Fredrik

AU - Åström, Karl

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

KW - geometry

KW - optimization

KW - computer vision

UR - https://www.scopus.com/pages/publications/84867878992

U2 - 10.1007/978-3-642-33718-5_53

DO - 10.1007/978-3-642-33718-5_53

M3 - Paper in conference proceeding

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

SN - 978-3-642-33718-5 (online)

VL - 7572

SP - 738

EP - 751

BT - 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 )

A2 - Fitzgibbon, Andrew

A2 - Lazebnik, Svetlana

A2 - Perona, Pietro

A2 - Sato, Yoichi

A2 - Schmid, Cordelia

PB - Springer

T2 - 12th European Conference on Computer Vision (ECCV 2012)

Y2 - 7 October 2012 through 13 October 2012

ER -

Enqvist O, Ask E, Kahl F, Åström K. Robust Fitting for Multiple View Geometry. In Fitzgibbon A, Lazebnik S, Perona P, Sato Y, Schmid C, editors, 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 ). Vol. 7572. Springer. 2012. p. 738-751 doi: 10.1007/978-3-642-33718-5_53

Robust Fitting for Multiple View Geometry

Abstract

Publication series

Conference

Subject classification (UKÄ)

Free keywords

Access to Document

Other files and links

Fingerprint

Mathematical Imaging Group

Algebra

Cite this

Robust Fitting for Multiple View Geometry

Abstract

Publication series

Conference

Subject classification (UKÄ)

Free keywords

Access to Document

Other files and links

Fingerprint

Projects

Mathematical Imaging Group

Algebra

Cite this