The quadric reference surface: applications in registering views of complex 3D objects

Amnon Shashua; Sebastian Toelg

doi:10.1007/bfb0028372

The quadric reference surface: applications in registering views of complex 3D objects

Amnon Shashua, Sebastian Toelg

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

2 Scopus citations

Abstract

The theoretical component of this work involves the following question: given any two views of some unknown textured opaque quadric surface in 3D, is there a finite number of corresponding points across the two views that uniquely determine all other correspondences coming from points on the quadric? A constructive answer to this question is then used to propose a transformation, we call a nominal quadratic transformation, that can be used in practice to facilitate the process of achieving full point-to-point correspondence between two grey-level images of the same (arbitrary) object.

Original language	American English
Title of host publication	Computer Vision—ECCV 1994 - 3rd European Conference on Computer Vision, Proceedings
Editors	Jan-Olof Eklundh
Publisher	Springer Verlag
Pages	407-416
Number of pages	10
ISBN (Print)	9783540579571
DOIs	https://doi.org/10.1007/bfb0028372
State	Published - 1994
Externally published	Yes
Event	3rd European Conference on Computer Vision, ECCV 1994 - Stockholm, Sweden Duration: 2 May 1994 → 6 May 1994

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	801 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	3rd European Conference on Computer Vision, ECCV 1994
Country/Territory	Sweden
City	Stockholm
Period	2/05/94 → 6/05/94

Bibliographical note

Funding Information:
Thanks to David Beymer for providingt he pair of imagesu sed for our ex-perimentsa, nd to Long Quan for providingt he code necessaryfo r recovering epipolesA. . Shashuais supportedb y a McDonnell-Pewp ostdoctorafel llowship from the Departmenotf Brain and CognitiveS ciencesS. . Toelg was supported by a postdoctorafle llowshipf rom the DeutscheF orschungsgemeinsehwahfitl e he was at MIT.

Funding Information:
Thanks to David Beymer for providing the pair of images used for our experiments, and to Long Quan for providing the code necessary for recovering epipoles. A. Shashua is supported by a McDonnell-Pew postdoctoral fellowship from the Department of Brain and Cognitive Sciences. S. Toelg was supported by a postdoctoral fellowship from the Deutsche Forschungsgemeinsehaft while he was at MIT.

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1994.

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10.1007/bfb0028372

Cite this

Shashua, A., & Toelg, S. (1994). The quadric reference surface: applications in registering views of complex 3D objects. In J-O. Eklundh (Ed.), Computer Vision—ECCV 1994 - 3rd European Conference on Computer Vision, Proceedings (pp. 407-416). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 801 LNCS). Springer Verlag. https://doi.org/10.1007/bfb0028372

Shashua, Amnon ; Toelg, Sebastian. / The quadric reference surface : applications in registering views of complex 3D objects. Computer Vision—ECCV 1994 - 3rd European Conference on Computer Vision, Proceedings. editor / Jan-Olof Eklundh. Springer Verlag, 1994. pp. 407-416 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "The theoretical component of this work involves the following question: given any two views of some unknown textured opaque quadric surface in 3D, is there a finite number of corresponding points across the two views that uniquely determine all other correspondences coming from points on the quadric? A constructive answer to this question is then used to propose a transformation, we call a nominal quadratic transformation, that can be used in practice to facilitate the process of achieving full point-to-point correspondence between two grey-level images of the same (arbitrary) object.",

author = "Amnon Shashua and Sebastian Toelg",

note = "Funding Information: Thanks to David Beymer for providingt he pair of imagesu sed for our ex-perimentsa, nd to Long Quan for providingt he code necessaryfo r recovering epipolesA. . Shashuais supportedb y a McDonnell-Pewp ostdoctorafel llowship from the Departmenotf Brain and CognitiveS ciencesS. . Toelg was supported by a postdoctorafle llowshipf rom the DeutscheF orschungsgemeinsehwahfitl e he was at MIT. Funding Information: Thanks to David Beymer for providing the pair of images used for our experiments, and to Long Quan for providing the code necessary for recovering epipoles. A. Shashua is supported by a McDonnell-Pew postdoctoral fellowship from the Department of Brain and Cognitive Sciences. S. Toelg was supported by a postdoctoral fellowship from the Deutsche Forschungsgemeinsehaft while he was at MIT. Publisher Copyright: {\textcopyright} Springer-Verlag Berlin Heidelberg 1994.; 3rd European Conference on Computer Vision, ECCV 1994 ; Conference date: 02-05-1994 Through 06-05-1994",

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Shashua, A & Toelg, S 1994, The quadric reference surface: applications in registering views of complex 3D objects. in J-O Eklundh (ed.), Computer Vision—ECCV 1994 - 3rd European Conference on Computer Vision, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 801 LNCS, Springer Verlag, pp. 407-416, 3rd European Conference on Computer Vision, ECCV 1994, Stockholm, Sweden, 2/05/94. https://doi.org/10.1007/bfb0028372

The quadric reference surface: applications in registering views of complex 3D objects. / Shashua, Amnon; Toelg, Sebastian.
Computer Vision—ECCV 1994 - 3rd European Conference on Computer Vision, Proceedings. ed. / Jan-Olof Eklundh. Springer Verlag, 1994. p. 407-416 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 801 LNCS).

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

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AU - Toelg, Sebastian

N1 - Funding Information: Thanks to David Beymer for providingt he pair of imagesu sed for our ex-perimentsa, nd to Long Quan for providingt he code necessaryfo r recovering epipolesA. . Shashuais supportedb y a McDonnell-Pewp ostdoctorafel llowship from the Departmenotf Brain and CognitiveS ciencesS. . Toelg was supported by a postdoctorafle llowshipf rom the DeutscheF orschungsgemeinsehwahfitl e he was at MIT. Funding Information: Thanks to David Beymer for providing the pair of images used for our experiments, and to Long Quan for providing the code necessary for recovering epipoles. A. Shashua is supported by a McDonnell-Pew postdoctoral fellowship from the Department of Brain and Cognitive Sciences. S. Toelg was supported by a postdoctoral fellowship from the Deutsche Forschungsgemeinsehaft while he was at MIT. Publisher Copyright: © Springer-Verlag Berlin Heidelberg 1994.

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AB - The theoretical component of this work involves the following question: given any two views of some unknown textured opaque quadric surface in 3D, is there a finite number of corresponding points across the two views that uniquely determine all other correspondences coming from points on the quadric? A constructive answer to this question is then used to propose a transformation, we call a nominal quadratic transformation, that can be used in practice to facilitate the process of achieving full point-to-point correspondence between two grey-level images of the same (arbitrary) object.

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ER -

Shashua A, Toelg S. The quadric reference surface: applications in registering views of complex 3D objects. In Eklundh J-O, editor, Computer Vision—ECCV 1994 - 3rd European Conference on Computer Vision, Proceedings. Springer Verlag. 1994. p. 407-416. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/bfb0028372

The quadric reference surface: applications in registering views of complex 3D objects

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