Bilinear Parameterization for Non-Separable Singular Value Penalties
Paper i proceeding, 2021

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.


Marcus Valtonen Örnhag

Lunds universitet

José Pedro Lopes Iglesias

Chalmers, Elektroteknik, Signalbehandling och medicinsk teknik

Carl Olsson

Chalmers, Elektroteknik, Signalbehandling och medicinsk teknik

Lunds universitet

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

10636919 (ISSN)

9781665445092 (ISBN)

2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)
Nashville, TN, USA,

Integrering av geometri och semantik i datorseende

Vetenskapsrådet (VR) (2016-04445), 2017-01-01 -- 2020-12-31.

Optimeringsmetoder med prestandagarantier för maskininlärningsmetoder

Vetenskapsrådet (VR) (2018-05375), 2019-01-01 -- 2022-12-31.



Datavetenskap (datalogi)

Datorseende och robotik (autonoma system)



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