Image distance functions for manifold learning

Authors:
Richard Souvenir;Robert Pless
Affiliations:
Department of Computer Science and Engineering, Washington University, One Brookings Drive, Campus Box 1045, St Louis, MO 63130, USA;Department of Computer Science and Engineering, Washington University, One Brookings Drive, Campus Box 1045, St Louis, MO 63130, USA
Venue:
Image and Vision Computing
Year:
2007

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Abstract

Many natural image sets are samples of a low-dimensional manifold in the space of all possible images. When the image data set is not a linear combination of a small number of basis images, linear dimensionality reduction techniques such as PCA and ICA fail and non-linear dimensionality reduction techniques are required to automatically determine the intrinsic structure of the image set. Recent techniques such as ISOMAP and LLE provide a mapping between the images and a low-dimensional parameterization of the images. This paper specializes general manifold learning by considering a small set of image distance measures that correspond to key transformation groups observed in natural images. This results in more meaningful embeddings for a variety of applications.