A linear least-squares solution to elastic Shape-from-Template

Abed Malti; Adrien Bartoli; Richard Hartley

doi:10.1109/CVPR.2015.7298771

A linear least-squares solution to elastic Shape-from-Template

Abed Malti, Adrien Bartoli, Richard Hartley

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

21 Citations (Scopus)

Abstract

We cast SfT (Shape-from-Template) as the search of a vector field (X, δX), composed of the pose X and the displacement δX that produces the deformation. We propose the first fully linear least-squares SfT method modeling elastic deformations. It relies on a set of Solid Boundary Constraints (SBC) to position the template at X in the deformed frame. The displacement is mapped by the stiffness matrix to minimize the amount of force responsible for the deformation. This linear minimization is subjected to the Reprojection Boundary Constraints (RBC) of the deformed shape X + δX on the deformed image. Compared to state-of-the-art methods, this new formulation allows us to obtain accurate results at a low computation cost.

Original language	English
Title of host publication	IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2015
Publisher	IEEE Computer Society
Pages	1629-1637
Number of pages	9
ISBN (Electronic)	9781467369640
DOIs	https://doi.org/10.1109/CVPR.2015.7298771
Publication status	Published - 14 Oct 2015
Event	IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2015 - Boston, United States Duration: 7 Jun 2015 → 12 Jun 2015

Publication series

Name	Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
Volume	07-12-June-2015
ISSN (Print)	1063-6919

Conference

Conference	IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2015
Country/Territory	United States
City	Boston
Period	7/06/15 → 12/06/15

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10.1109/CVPR.2015.7298771

Cite this

Malti, A., Bartoli, A., & Hartley, R. (2015). A linear least-squares solution to elastic Shape-from-Template. In IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2015 (pp. 1629-1637). Article 7298771 (Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition; Vol. 07-12-June-2015). IEEE Computer Society. https://doi.org/10.1109/CVPR.2015.7298771

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abstract = "We cast SfT (Shape-from-Template) as the search of a vector field (X, δX), composed of the pose X and the displacement δX that produces the deformation. We propose the first fully linear least-squares SfT method modeling elastic deformations. It relies on a set of Solid Boundary Constraints (SBC) to position the template at X in the deformed frame. The displacement is mapped by the stiffness matrix to minimize the amount of force responsible for the deformation. This linear minimization is subjected to the Reprojection Boundary Constraints (RBC) of the deformed shape X + δX on the deformed image. Compared to state-of-the-art methods, this new formulation allows us to obtain accurate results at a low computation cost.",

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Malti, A, Bartoli, A & Hartley, R 2015, A linear least-squares solution to elastic Shape-from-Template. in IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2015., 7298771, Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol. 07-12-June-2015, IEEE Computer Society, pp. 1629-1637, IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2015, Boston, United States, 7/06/15. https://doi.org/10.1109/CVPR.2015.7298771

A linear least-squares solution to elastic Shape-from-Template. / Malti, Abed; Bartoli, Adrien; Hartley, Richard.
IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2015. IEEE Computer Society, 2015. p. 1629-1637 7298771 (Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition; Vol. 07-12-June-2015).

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

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N2 - We cast SfT (Shape-from-Template) as the search of a vector field (X, δX), composed of the pose X and the displacement δX that produces the deformation. We propose the first fully linear least-squares SfT method modeling elastic deformations. It relies on a set of Solid Boundary Constraints (SBC) to position the template at X in the deformed frame. The displacement is mapped by the stiffness matrix to minimize the amount of force responsible for the deformation. This linear minimization is subjected to the Reprojection Boundary Constraints (RBC) of the deformed shape X + δX on the deformed image. Compared to state-of-the-art methods, this new formulation allows us to obtain accurate results at a low computation cost.

AB - We cast SfT (Shape-from-Template) as the search of a vector field (X, δX), composed of the pose X and the displacement δX that produces the deformation. We propose the first fully linear least-squares SfT method modeling elastic deformations. It relies on a set of Solid Boundary Constraints (SBC) to position the template at X in the deformed frame. The displacement is mapped by the stiffness matrix to minimize the amount of force responsible for the deformation. This linear minimization is subjected to the Reprojection Boundary Constraints (RBC) of the deformed shape X + δX on the deformed image. Compared to state-of-the-art methods, this new formulation allows us to obtain accurate results at a low computation cost.

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A linear least-squares solution to elastic Shape-from-Template

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