Global optimality for point set registration using semidefinite programming
(2020) 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2020 p.8284-8292- Abstract
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... (More)
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.
(Less)
- author
- Iglesias, José Pedro ; Olsson, Carl LU and Kahl, Fredrik LU
- organization
- publishing date
- 2020
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
- pages
- 9 pages
- conference name
- 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2020
- conference location
- Virtual, Online, United States
- conference dates
- 2020-06-14 - 2020-06-19
- external identifiers
-
- scopus:85089134708
- DOI
- 10.1109/CVPR42600.2020.00831
- language
- English
- LU publication?
- yes
- id
- 5b60b4a0-2fe9-4bc3-9b01-a87acea4bbf8
- date added to LUP
- 2021-01-13 15:31:57
- date last changed
- 2022-05-12 17:32:16
@inproceedings{5b60b4a0-2fe9-4bc3-9b01-a87acea4bbf8, abstract = {{<p>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.</p>}}, author = {{Iglesias, José Pedro and Olsson, Carl and Kahl, Fredrik}}, booktitle = {{Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition}}, language = {{eng}}, pages = {{8284--8292}}, title = {{Global optimality for point set registration using semidefinite programming}}, url = {{http://dx.doi.org/10.1109/CVPR42600.2020.00831}}, doi = {{10.1109/CVPR42600.2020.00831}}, year = {{2020}}, }