Image distance functions for manifold learning

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.