A Framework for robust subspace learning
(with Michael J. Black,  Computer Science Department. Brown University. USA)



ABSTRACT: 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








De la Torre, F. and Black, M. J., A framework for robust subspace learning.
Accepted for publication in International Journal of Computer Vision.
Pre-print (pdf, 1.39MB).




De la Torre, F. and Black, M. J., Robust principal component analysis for computer vision
Int. Conf. on Computer Vision, ICCV-2001, Vancouver,
 (postscript, 1.0MB)(pdf, 0.36MB).



Sidenbladh, H., De la Torre, F., Black, M. J., A framework for modeling the appearance of 3D articulated figures
Int. Conf. on Automatic Face and GestureRecognition, Grenoble, France, April 2000.
(postscript 0.98MB) (pdf, 0.36MB)














Learning a Subspace of illumination









Original data    (MPEG-0.68Mb) 




Standard Principal Component Analysis (PCA)  (MPEG-0.55Mb




Robust Principal Component Analysis (RPCA) (MPEG-0.43Mb








Preliminary results on structure from motion (SFM)









A toy problem of SFM (GIF-0.13Mb












Robust Principal Component Analysis /
Robust Singular Value Decomposition 
                  (17 Mb)