Global optimality for point set registration using semidefinite programming

Research output: Chapter in Book/Report/Conference proceedingPaper in conference proceeding

Standard

Global optimality for point set registration using semidefinite programming. / Iglesias, José Pedro; Olsson, Carl; Kahl, Fredrik.

Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. 2020. p. 8284-8292.

Research output: Chapter in Book/Report/Conference proceedingPaper in conference proceeding

Harvard

Iglesias, JP, Olsson, C & Kahl, F 2020, Global optimality for point set registration using semidefinite programming. in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. pp. 8284-8292, 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2020, Virtual, Online, United States, 2020/06/14. https://doi.org/10.1109/CVPR42600.2020.00831

APA

Iglesias, J. P., Olsson, C., & Kahl, F. (2020). Global optimality for point set registration using semidefinite programming. In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (pp. 8284-8292) https://doi.org/10.1109/CVPR42600.2020.00831

CBE

Iglesias JP, Olsson C, Kahl F. 2020. Global optimality for point set registration using semidefinite programming. In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. pp. 8284-8292. https://doi.org/10.1109/CVPR42600.2020.00831

MLA

Iglesias, José Pedro, Carl Olsson and Fredrik Kahl "Global optimality for point set registration using semidefinite programming". Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. 2020, 8284-8292. https://doi.org/10.1109/CVPR42600.2020.00831

Vancouver

Iglesias JP, Olsson C, Kahl F. Global optimality for point set registration using semidefinite programming. In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. 2020. p. 8284-8292 https://doi.org/10.1109/CVPR42600.2020.00831

Author

Iglesias, José Pedro ; Olsson, Carl ; Kahl, Fredrik. / Global optimality for point set registration using semidefinite programming. Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. 2020. pp. 8284-8292

RIS

TY - GEN

T1 - Global optimality for point set registration using semidefinite programming

AU - Iglesias, José Pedro

AU - Olsson, Carl

AU - Kahl, Fredrik

PY - 2020

Y1 - 2020

N2 - In this paper we present a study of global optimality conditions for Point Set Registration (PSR) with missing data. PSR is the problem of aligning multiple point clouds with an unknown target point cloud. Since non-linear rotation constraints are present the problem is inherently non-convex and typically relaxed by computing the Lagrange dual, which is a Semidefinite Program (SDP). In this work we show that given a local minimizer the dual variables of the SDP can be computed in closed form. This opens up the possibility of verifying the optimally, using the SDP formulation without explicitly solving it. In addition it allows us to study under what conditions the relaxation is tight, through spectral analysis. We show that if the errors in the (unknown) optimal solution are bounded the SDP formulation will be able to recover it.

AB - In this paper we present a study of global optimality conditions for Point Set Registration (PSR) with missing data. PSR is the problem of aligning multiple point clouds with an unknown target point cloud. Since non-linear rotation constraints are present the problem is inherently non-convex and typically relaxed by computing the Lagrange dual, which is a Semidefinite Program (SDP). In this work we show that given a local minimizer the dual variables of the SDP can be computed in closed form. This opens up the possibility of verifying the optimally, using the SDP formulation without explicitly solving it. In addition it allows us to study under what conditions the relaxation is tight, through spectral analysis. We show that if the errors in the (unknown) optimal solution are bounded the SDP formulation will be able to recover it.

U2 - 10.1109/CVPR42600.2020.00831

DO - 10.1109/CVPR42600.2020.00831

M3 - Paper in conference proceeding

AN - SCOPUS:85089134708

SP - 8284

EP - 8292

BT - Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition

T2 - 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2020

Y2 - 14 June 2020 through 19 June 2020

ER -