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2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) (2005)
San Diego, California
June 20, 2005 to June 26, 2005
ISSN: 1063-6919
ISBN: 0-7695-2372-2
pp: 518-525
Ali Ghodsi , University of Waterloo
Jiayuan Huang , University of Waterloo
Finnegan Southey , University of Alberta
Dale Schuurmans , University of Alberta
<p>Images and other high-dimensional data can frequently be characterized by a low dimensional manifold (e.g. one that corresponds to the degrees of freedom of the camera). Recently, nonlinear manifold learning techniques have been used to map images to points in a lower dimension space, capturing some of the dynamics of the camera or the subjects. In general, these methods do not take advantage of any prior understanding of the dynamics we might have, relying instead on local Euclidean distances that can be misleading in image space.</p> <p>In practice, we frequently have some prior knowledge regarding the transformations that relate images (e.g. rotation, translation, etc). We present a method for augmenting existing embedding techniques with additional information derived from known transformations, either in the form of tangent spaces that locally characterize the manifold or distances derived from reconstruction errors. The extra information is incorporated directly into the cost function of the embedding technique. The techniques we augment are largely attractive because there is a closed form solution for their cost optimization. Our approach likewise produces a closed form solution for the augmented cost function. Experiments demonstrate the effectiveness of the approach on a variety of image data.</p>

D. Schuurmans, A. Ghodsi, J. Huang and F. Southey, "Tangent-Corrected Embedding," 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05)(CVPR), San Diego, CA, USA USA, 2005, pp. 518-525.
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