Recovering the shape of polyhedra using line-drawing analysis and complex reflectance models

Ilan Shimshoni; Jean Ponce

doi:10.1109/cvpr.1994.323875

Recovering the shape of polyhedra using line-drawing analysis and complex reflectance models

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

Abstract

Following Sugihara, we represent the geometric constraints imposed by the line-drawing of a polyhedron as a set of linear equalities and inequalities. Unlike him, we explicitly take into account the uncertainty in vertex position. This allows us to circumvent the superstrictness of the constraints without deleting any of them. For a given error bound, deciding whether a line-drawing is the correct projection of a polyhedron is reduced to linear programming, and SD shape recovery is reduced to optimization under linear constraints. Our method can be used for recovering the shape of polyhedral objects whose reflectance can be modelled accurately. We have implemented it for the Lambertian model and the Lambertian model with interreflections. We present results obtained using real images.

Original language	English
Title of host publication	Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
Publisher	Publ by IEEE
Pages	514-518
Number of pages	5
ISBN (Print)	0818658274, 9780818658273
DOIs	https://doi.org/10.1109/cvpr.1994.323875
State	Published - 1994
Externally published	Yes
Event	Proceedings of the 1994 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Seattle, WA, USA Duration: 21 Jun 1994 → 23 Jun 1994

Publication series

Name	Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
ISSN (Print)	1063-6919

Conference

Conference	Proceedings of the 1994 IEEE Computer Society Conference on Computer Vision and Pattern Recognition
City	Seattle, WA, USA
Period	21/06/94 → 23/06/94

Bibliographical note

Funding Information:
This work was supported in part by the Beckman Institute and the Center for Advanced Study of the University of Illinois at Urbana-Champaign, by the National Science Foundation under Grant IRI-9224815, and by the National Aeronautics and Space Administration under Grant NAG 1-613.

ASJC Scopus subject areas

Software
Computer Vision and Pattern Recognition

Access to Document

10.1109/cvpr.1994.323875

Cite this

Shimshoni, I., & Ponce, J. (1994). Recovering the shape of polyhedra using line-drawing analysis and complex reflectance models. In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (pp. 514-518). (Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition). Publ by IEEE. https://doi.org/10.1109/cvpr.1994.323875

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abstract = "Following Sugihara, we represent the geometric constraints imposed by the line-drawing of a polyhedron as a set of linear equalities and inequalities. Unlike him, we explicitly take into account the uncertainty in vertex position. This allows us to circumvent the superstrictness of the constraints without deleting any of them. For a given error bound, deciding whether a line-drawing is the correct projection of a polyhedron is reduced to linear programming, and SD shape recovery is reduced to optimization under linear constraints. Our method can be used for recovering the shape of polyhedral objects whose reflectance can be modelled accurately. We have implemented it for the Lambertian model and the Lambertian model with interreflections. We present results obtained using real images.",

author = "Ilan Shimshoni and Jean Ponce",

note = "Funding Information: This work was supported in part by the Beckman Institute and the Center for Advanced Study of the University of Illinois at Urbana-Champaign, by the National Science Foundation under Grant IRI-9224815, and by the National Aeronautics and Space Administration under Grant NAG 1-613.; Proceedings of the 1994 IEEE Computer Society Conference on Computer Vision and Pattern Recognition ; Conference date: 21-06-1994 Through 23-06-1994",

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language = "English",

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Shimshoni, I & Ponce, J 1994, Recovering the shape of polyhedra using line-drawing analysis and complex reflectance models. in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Publ by IEEE, pp. 514-518, Proceedings of the 1994 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Seattle, WA, USA, 21/06/94. https://doi.org/10.1109/cvpr.1994.323875

Recovering the shape of polyhedra using line-drawing analysis and complex reflectance models. / Shimshoni, Ilan; Ponce, Jean.
Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. Publ by IEEE, 1994. p. 514-518 (Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition).

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

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N2 - Following Sugihara, we represent the geometric constraints imposed by the line-drawing of a polyhedron as a set of linear equalities and inequalities. Unlike him, we explicitly take into account the uncertainty in vertex position. This allows us to circumvent the superstrictness of the constraints without deleting any of them. For a given error bound, deciding whether a line-drawing is the correct projection of a polyhedron is reduced to linear programming, and SD shape recovery is reduced to optimization under linear constraints. Our method can be used for recovering the shape of polyhedral objects whose reflectance can be modelled accurately. We have implemented it for the Lambertian model and the Lambertian model with interreflections. We present results obtained using real images.

AB - Following Sugihara, we represent the geometric constraints imposed by the line-drawing of a polyhedron as a set of linear equalities and inequalities. Unlike him, we explicitly take into account the uncertainty in vertex position. This allows us to circumvent the superstrictness of the constraints without deleting any of them. For a given error bound, deciding whether a line-drawing is the correct projection of a polyhedron is reduced to linear programming, and SD shape recovery is reduced to optimization under linear constraints. Our method can be used for recovering the shape of polyhedral objects whose reflectance can be modelled accurately. We have implemented it for the Lambertian model and the Lambertian model with interreflections. We present results obtained using real images.

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Shimshoni I, Ponce J. Recovering the shape of polyhedra using line-drawing analysis and complex reflectance models. In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. Publ by IEEE. 1994. p. 514-518. (Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition). doi: 10.1109/cvpr.1994.323875

Recovering the shape of polyhedra using line-drawing analysis and complex reflectance models

Abstract

Publication series

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Bibliographical note

ASJC Scopus subject areas

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