Robust Subspace Learning including
Robust Principal Component Analysis (PCA) and
Robust Singular Value Decomposition (SVD)

(with Fernando De la Torre, La Salle Univ. Ramon Llull, Barcelona, Spain.)

Many computer vision, signal processing and statistical problems can be posed as problems of learning low dimensional linear or multi-linear models. These models have been widely used for the representation of shape, appearance, motion, etc, in computer vision applications. Methods for learning linear models can be seen as a special case of subspace fitting. One drawback of previous learning methods is that they are based on least squares estimation techniques and hence fail to account for ``outliers'' which are common in realistic training sets. We review previous approaches for making linear learning methods robust to outliers and present a new method that uses an intra-sample outlier process to account for pixel outliers. We develop the theory of Robust Subspace Learning (RSL) for linear models within a continuous optimization framework based on robust M-estimation. The framework applies to a variety of linear learning problems in computer vision including eigen-analysis and structure from motion. Several synthetic and natural examples are used to develop and illustrate the theory and applications of robust subspace learning in computer vision.

Image data and a software implementation is available for download (click here).

Related Publications

A framework for robust subspace learning,
De la Torre, F. and Black, M. J.,
International Journal of Computer Vision. Vol. 54, Issue 1-3, pp. 117-142, Aug.-Oct. 2003.
(pdf). Software (Matlab).

Robust parameterized component analysis: Theory and applications to 2D facial appearance models,
De la Torre, F., and Black, M. J.,
Computer Vision and Image Understanding. Vol. 91, Issues 1-2, pp. 53-71, (July-August) 2003.

Robust principal component analysis for computer vision,
De la Torre, F. and Black, M. J.,
Int. Conf. on Computer Vision, ICCV-2001, Vancouver, BC, Vol. I, pp. 362-369.
(postscript, 1.0MB)(pdf, 0.36MB), (Software, demos, and data.)

Robust parameterized component analysis: Theory and applications to 2D facial modeling,
De la Torre, F. and Black, M. J.,
European Conf. on Computer Vision, ECCV 2002, A. Heyden, G. Sparr, M. Nielsen, and P. Johansen (Eds.), Springer-Verlag LNCS 2353, Vol. 4, pp. 653-669.

Dynamic coupled component analysis,
De la Torre, F. and Black, M. J.,
IEEE Proc. Computer Vision and Pattern Recognition, CVPR'01, Kauai, Hawaii, Vol. II, pp. 643-650, Dec. 2001.
(postscript), (pdf).

A framework for modeling the appearance of 3D articulated figures,
Sidenbladh, H., De la Torre, F., Black, M. J.,
Int. Conf. on Automatic Face and Gesture Recognition, Grenoble, France, pp. 368-375, March 2000.
(postscript), (abstract)