Multilinear Analysis of Image Ensembles: TensorFaces

  • M. Alex O. Vasilescu
  • Demetri Terzopoulos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2350)


Natural images are the composite consequence of multiple factors related to scene structure, illumination, and imaging. Multilinear algebra, the algebra of higher-order tensors, offers a potent mathematical framework for analyzing the multifactor structure of image ensembles and for addressing the difficult problem of disentangling the constituent factors or modes. Our multilinear modeling technique employs a tensor extension of the conventional matrix singular value decomposition (SVD), known as the N-mode SVD. As a concrete example, we consider the multilinear analysis of ensembles of facial images that combine several modes, including different facial geometries (people), expressions, head poses, and lighting conditions. Our resulting “TensorFaces” representation has several advantages over conventional eigenfaces. More generally, multilinear analysis shows promise as a unifying framework for a variety of computer vision problems.


Singular Value Decomposition Independent Component Analysis Facial Image Independent Component Analysis Multilinear Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • M. Alex O. Vasilescu
    • 1
    • 2
  • Demetri Terzopoulos
    • 1
    • 2
  1. 1.Courant InstituteNew York UniversityUSA
  2. 2.Department of Computer ScienceUniversity of TorontoCanada

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