Image manifolds

A collection of related N by M images, such asa set of faces, may be modeled by a manifold embedded in an NM-dimensional Euclidean space called an image manifold. With the modeling of image spaces as manifolds, geometric properties of image manifolds can be studied either theoretically or experimentally A practical result of the investigation of image manifolds provides an insight into image source entropy (i.e., image compressibility), a subject about which, oddly, little is known. The investigation begins with the most basic properties of a manifold, its dimension and its curvature. The study of dimensionality reveals a high embedding ratio, which gives promise of very high compression rates. The curvature of image manifolds is shown to be large indicating that application of traditional Linear transform techniques may not fulfill this promise.