Robust Principal Component 
Analysis for Computer Vision
(with Michael J. Black,  Computer Science Department. Brown University. USA)

ABSTRACT: Principal Component Analysis (PCA) has been widely used for the representation of shape, appearance, and motion. One drawback of typical PCA methods is
that they are least squares estimation techniques and hence fail to account for ``outliers'' which are common in realistic training sets. In computer vision applications, outliers typically occur within a sample (image) due to pixels that are corrupted by noise, alignment errors, or occlusion. We review previous approaches for making PCA 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 Principal Component Analysis (RPCA) and describe a robust M-estimation algorithm for learning linear multivariate representations of high dimensional data such as images. Quantitative comparisons with traditional PCA and previous robust algorithms illustrate the benefits of RPCA when outliers are present. Details of the algorithm are described and a software implementation is being made publically available. 


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)