On the reprojection of 3D and 2D scenes without explicit model selection

Amnon Shashua; Shai Avidan

doi:10.1007/3-540-45054-8_61

On the reprojection of 3D and 2D scenes without explicit model selection

Amnon Shashua, Shai Avidan

The Rachel and Selim Benin School of Engineering and Computer Science

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

2 Scopus citations

Abstract

It is known that recovering projection matrices from planar configurations is ambiguous, thus, posing the problem of model selection - is the scene planar (2D) or non-planar (3D)? For a 2D scene one would recover a homography matrix, whereas for a 3D scene one would recover the fundamental matrix or trifocal tensor. The task of model selection is especially problematic when the scene is neither 2D nor 3D - for example a “thin” volume in space. In this paper we show that for certain tasks, such as reprojection, there is no need to select a model. The ambiguity that arises from a 2D scene is orthogonal to the reprojection process, thus if one desires to use multilinear matching constraints for transferring points along a sequence of views it is possible to do so under any situation of 2D, 3D or “thin” volumes.

Original language	English
Title of host publication	Computer Vision - ECCV 2000 - 6th European Conference on Computer Vision, Proceedings
Editors	David Vernon
Publisher	Springer Verlag
Pages	936-949
Number of pages	14
ISBN (Print)	3540676856
DOIs	https://doi.org/10.1007/3-540-45054-8_61
State	Published - 2000
Event	6th European Conference on Computer Vision, ECCV 2000 - Dublin, Ireland Duration: 26 Jun 2000 → 1 Jul 2000

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	1842
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	6th European Conference on Computer Vision, ECCV 2000
Country/Territory	Ireland
City	Dublin
Period	26/06/00 → 1/07/00

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2000.

Access to Document

10.1007/3-540-45054-8_61

Cite this

Shashua, A., & Avidan, S. (2000). On the reprojection of 3D and 2D scenes without explicit model selection. In D. Vernon (Ed.), Computer Vision - ECCV 2000 - 6th European Conference on Computer Vision, Proceedings (pp. 936-949). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1842). Springer Verlag. https://doi.org/10.1007/3-540-45054-8_61

Shashua, Amnon ; Avidan, Shai. / On the reprojection of 3D and 2D scenes without explicit model selection. Computer Vision - ECCV 2000 - 6th European Conference on Computer Vision, Proceedings. editor / David Vernon. Springer Verlag, 2000. pp. 936-949 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

@inproceedings{227596075c5d433ca1dbb2d63ca6de48,

title = "On the reprojection of 3D and 2D scenes without explicit model selection",

abstract = "It is known that recovering projection matrices from planar configurations is ambiguous, thus, posing the problem of model selection - is the scene planar (2D) or non-planar (3D)? For a 2D scene one would recover a homography matrix, whereas for a 3D scene one would recover the fundamental matrix or trifocal tensor. The task of model selection is especially problematic when the scene is neither 2D nor 3D - for example a “thin” volume in space. In this paper we show that for certain tasks, such as reprojection, there is no need to select a model. The ambiguity that arises from a 2D scene is orthogonal to the reprojection process, thus if one desires to use multilinear matching constraints for transferring points along a sequence of views it is possible to do so under any situation of 2D, 3D or “thin” volumes.",

author = "Amnon Shashua and Shai Avidan",

note = "Publisher Copyright: {\textcopyright} Springer-Verlag Berlin Heidelberg 2000.; 6th European Conference on Computer Vision, ECCV 2000 ; Conference date: 26-06-2000 Through 01-07-2000",

year = "2000",

doi = "10.1007/3-540-45054-8_61",

language = "אנגלית",

isbn = "3540676856",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "936--949",

editor = "David Vernon",

booktitle = "Computer Vision - ECCV 2000 - 6th European Conference on Computer Vision, Proceedings",

address = "גרמניה",

}

Shashua, A & Avidan, S 2000, On the reprojection of 3D and 2D scenes without explicit model selection. in D Vernon (ed.), Computer Vision - ECCV 2000 - 6th European Conference on Computer Vision, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1842, Springer Verlag, pp. 936-949, 6th European Conference on Computer Vision, ECCV 2000, Dublin, Ireland, 26/06/00. https://doi.org/10.1007/3-540-45054-8_61

On the reprojection of 3D and 2D scenes without explicit model selection. / Shashua, Amnon; Avidan, Shai.
Computer Vision - ECCV 2000 - 6th European Conference on Computer Vision, Proceedings. ed. / David Vernon. Springer Verlag, 2000. p. 936-949 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1842).

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

TY - GEN

T1 - On the reprojection of 3D and 2D scenes without explicit model selection

AU - Shashua, Amnon

AU - Avidan, Shai

PY - 2000

Y1 - 2000

N2 - It is known that recovering projection matrices from planar configurations is ambiguous, thus, posing the problem of model selection - is the scene planar (2D) or non-planar (3D)? For a 2D scene one would recover a homography matrix, whereas for a 3D scene one would recover the fundamental matrix or trifocal tensor. The task of model selection is especially problematic when the scene is neither 2D nor 3D - for example a “thin” volume in space. In this paper we show that for certain tasks, such as reprojection, there is no need to select a model. The ambiguity that arises from a 2D scene is orthogonal to the reprojection process, thus if one desires to use multilinear matching constraints for transferring points along a sequence of views it is possible to do so under any situation of 2D, 3D or “thin” volumes.

AB - It is known that recovering projection matrices from planar configurations is ambiguous, thus, posing the problem of model selection - is the scene planar (2D) or non-planar (3D)? For a 2D scene one would recover a homography matrix, whereas for a 3D scene one would recover the fundamental matrix or trifocal tensor. The task of model selection is especially problematic when the scene is neither 2D nor 3D - for example a “thin” volume in space. In this paper we show that for certain tasks, such as reprojection, there is no need to select a model. The ambiguity that arises from a 2D scene is orthogonal to the reprojection process, thus if one desires to use multilinear matching constraints for transferring points along a sequence of views it is possible to do so under any situation of 2D, 3D or “thin” volumes.

UR - http://www.scopus.com/inward/record.url?scp=84944270677&partnerID=8YFLogxK

U2 - 10.1007/3-540-45054-8_61

DO - 10.1007/3-540-45054-8_61

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:84944270677

SN - 3540676856

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 936

EP - 949

BT - Computer Vision - ECCV 2000 - 6th European Conference on Computer Vision, Proceedings

A2 - Vernon, David

PB - Springer Verlag

T2 - 6th European Conference on Computer Vision, ECCV 2000

Y2 - 26 June 2000 through 1 July 2000

ER -

Shashua A, Avidan S. On the reprojection of 3D and 2D scenes without explicit model selection. In Vernon D, editor, Computer Vision - ECCV 2000 - 6th European Conference on Computer Vision, Proceedings. Springer Verlag. 2000. p. 936-949. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-45054-8_61

On the reprojection of 3D and 2D scenes without explicit model selection

Abstract

Publication series

Conference

Bibliographical note

Access to Document

Other files and links

Fingerprint

Cite this