Bilinear Parameterization for Non-Separable Singular Value Penalties
(2021) 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2021 In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition p.3896-3905- Abstract
Low rank inducing penalties have been proven to successfully uncover fundamental structures considered in computer vision and machine learning; however, such methods generally lead to non-convex optimization problems. Since the resulting objective is non-convex one often resorts to using standard splitting schemes such as Alternating Direction Methods of Multipliers (ADMM), or other subgradient methods, which exhibit slow convergence in the neighbourhood of a local minimum. We propose a method using second order methods, in particular the variable projection method (VarPro), by replacing the nonconvex penalties with a surrogate capable of converting the original objectives to differentiable equivalents. In this way we benefit from... (More)
Low rank inducing penalties have been proven to successfully uncover fundamental structures considered in computer vision and machine learning; however, such methods generally lead to non-convex optimization problems. Since the resulting objective is non-convex one often resorts to using standard splitting schemes such as Alternating Direction Methods of Multipliers (ADMM), or other subgradient methods, which exhibit slow convergence in the neighbourhood of a local minimum. We propose a method using second order methods, in particular the variable projection method (VarPro), by replacing the nonconvex penalties with a surrogate capable of converting the original objectives to differentiable equivalents. In this way we benefit from faster convergence. The bilinear framework is compatible with a large family of regularizers, and we demonstrate the benefits of our approach on real datasets for rigid and non-rigid structure from motion. The qualitative difference in reconstructions show that many popular non-convex objectives enjoy an advantage in transitioning to the proposed framework.
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- author
- Örnhag, Marcus Valtonen LU ; Iglesias, José Pedro and Olsson, Carl LU
- organization
- publishing date
- 2021
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- Proceedings - 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2021
- series title
- Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
- pages
- 10 pages
- publisher
- IEEE - Institute of Electrical and Electronics Engineers Inc.
- conference name
- 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2021
- conference location
- Virtual, Online, United States
- conference dates
- 2021-06-19 - 2021-06-25
- external identifiers
-
- scopus:85123192020
- ISSN
- 1063-6919
- ISBN
- 9781665445092
- DOI
- 10.1109/CVPR46437.2021.00389
- language
- English
- LU publication?
- yes
- id
- 9a5dc39f-ed92-499d-acb4-f5e7c782b802
- date added to LUP
- 2022-03-24 15:19:46
- date last changed
- 2022-05-02 18:15:07
@inproceedings{9a5dc39f-ed92-499d-acb4-f5e7c782b802, abstract = {{<p>Low rank inducing penalties have been proven to successfully uncover fundamental structures considered in computer vision and machine learning; however, such methods generally lead to non-convex optimization problems. Since the resulting objective is non-convex one often resorts to using standard splitting schemes such as Alternating Direction Methods of Multipliers (ADMM), or other subgradient methods, which exhibit slow convergence in the neighbourhood of a local minimum. We propose a method using second order methods, in particular the variable projection method (VarPro), by replacing the nonconvex penalties with a surrogate capable of converting the original objectives to differentiable equivalents. In this way we benefit from faster convergence. The bilinear framework is compatible with a large family of regularizers, and we demonstrate the benefits of our approach on real datasets for rigid and non-rigid structure from motion. The qualitative difference in reconstructions show that many popular non-convex objectives enjoy an advantage in transitioning to the proposed framework.</p>}}, author = {{Örnhag, Marcus Valtonen and Iglesias, José Pedro and Olsson, Carl}}, booktitle = {{Proceedings - 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2021}}, isbn = {{9781665445092}}, issn = {{1063-6919}}, language = {{eng}}, pages = {{3896--3905}}, publisher = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}}, series = {{Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition}}, title = {{Bilinear Parameterization for Non-Separable Singular Value Penalties}}, url = {{http://dx.doi.org/10.1109/CVPR46437.2021.00389}}, doi = {{10.1109/CVPR46437.2021.00389}}, year = {{2021}}, }