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Multilinear analysis of image ensembles: TensorFaces. (English) Zbl 1034.68693

Heyden, Anders (ed.) et al., Computer vision - ECCV 2002. 7th European conference, Copenhagen, Denmark, May 28–31, 2002. Proceedings. Part 1. Berlin: Springer (ISBN 3-540-43745-2). Lect. Notes Comput. Sci. 2350, 447-460 (2002).
Summary: 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.
For the entire collection see [Zbl 0992.68526].

MSC:

68U99 Computing methodologies and applications
68T45 Machine vision and scene understanding
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