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by M. Alex, O. Vasilescu, Demetri Terzopoulos
In Proceedings of the European Conference on Computer Vision
http://mrl.nyu.edu/~dt/papers/eccv02/eccv02.pdf
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Abstract:
Abstract. 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. 1
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