DocumentCode :
3426787
Title :
Unifying Nuclear Norm and Bilinear Factorization Approaches for Low-Rank Matrix Decomposition
Author :
Cabral, Ricardo ; De la Torre, Fernando ; Costeira, Joao P. ; Bernardino, Alexandre
Author_Institution :
ISR - Inst. Super. Tecnico, Lisbon, Portugal
fYear :
2013
fDate :
1-8 Dec. 2013
Firstpage :
2488
Lastpage :
2495
Abstract :
Low rank models have been widely used for the representation of shape, appearance or motion in computer vision problems. Traditional approaches to fit low rank models make use of an explicit bilinear factorization. These approaches benefit from fast numerical methods for optimization and easy kernelization. However, they suffer from serious local minima problems depending on the loss function and the amount/type of missing data. Recently, these low-rank models have alternatively been formulated as convex problems using the nuclear norm regularizer, unlike factorization methods, their numerical solvers are slow and it is unclear how to kernelize them or to impose a rank a priori. This paper proposes a unified approach to bilinear factorization and nuclear norm regularization, that inherits the benefits of both. We analyze the conditions under which these approaches are equivalent. Moreover, based on this analysis, we propose a new optimization algorithm and a "rank continuation\´\´ strategy that outperform state-of-the-art approaches for Robust PCA, Structure from Motion and Photometric Stereo with outliers and missing data.
Keywords :
image representation; matrix decomposition; optimisation; principal component analysis; bilinear factorization; low-rank matrix decomposition; nuclear norm approach; nuclear norm regularization; optimization algorithm; photometric stereo; rank continuation; robust PCA; Algorithm design and analysis; Computational modeling; Computer vision; Numerical models; Optimization; Principal component analysis; Robustness;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Computer Vision (ICCV), 2013 IEEE International Conference on
Conference_Location :
Sydney, NSW
ISSN :
1550-5499
Type :
conf
DOI :
10.1109/ICCV.2013.309
Filename :
6751420
Link To Document :
بازگشت