International Journal of Computer Vision

, Volume 54, Issue 1–3, pp 117–142

A Framework for Robust Subspace Learning

  • Fernando De la Torre
  • Michael J. Black


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 draw-back 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.

principal component analysis singular value decomposition learning robust statistics subspace methods structure from motion robust PCA robust SVD 


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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Fernando De la Torre
    • 1
  • Michael J. Black
    • 2
  1. 1.Department of Communications and Signal Theory, La Salle School of EngineeringUniversitat Ramon LLullBarcelonaSpain
  2. 2.Department of Computer ScienceBrown UniversityProvidence

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