Image manifolds

Haw-minn Lu; Yeshaiahu Fainman; Robert Hecht-Nielsen

doi:10.1117/12.304659

1 April 1998 Image manifolds

Haw-minn Lu, Yeshaiahu Fainman, Robert Hecht-Nielsen

Proceedings Volume 3307, Applications of Artificial Neural Networks in Image Processing III; (1998) https://doi.org/10.1117/12.304659
Event: Photonics West '98 Electronic Imaging, 1998, San Jose, CA, United States

Abstract

A collection of related N by M images, such as a 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, geometrical 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.

Citation Download Citation

Haw-minn Lu, Yeshaiahu Fainman, and Robert Hecht-Nielsen "Image manifolds", Proc. SPIE 3307, Applications of Artificial Neural Networks in Image Processing III, (1 April 1998); https://doi.org/10.1117/12.304659

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