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 nonlinear 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.