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Regular version of the site

Book chapter

Locally isometric and conformal parameterization of image manifold

P. 1-7.
Bernstein A., Kuleshov A. P., Yanovich Y.

Images can be represented as vectors in a high-dimensional Image space with components specifying light intensities at image pixels. To avoid the ‘curse of dimensionality’, the original high-dimensional image data are transformed into their lower-dimensional features preserving certain subject-driven data properties. These properties can include ‘information-preserving’ when using the constructed low-dimensional features instead of original high-dimensional vectors, as well preserving the distances and angles between the original high-dimensional image vectors. Under the commonly used Manifold assumption that the high-dimensional image data lie on or near a certain unknown low-dimensional Image manifold embedded in an ambient high-dimensional ‘observation’ space, a constructing of the lower-dimensional features consists in constructing an Embedding mapping from the Image manifold to Feature space, which, in turn, determines a low-dimensional parameterization of the Image manifold. We propose a new geometrically motivated Embedding method which constructs a low-dimensional parameterization of the Image manifold and provides the information-preserving property as well as the locally isometric and conformal properties. © (2015) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.

In book

Edited by: A. Verikas, P. Radeva, D. Nikolaev. Barcelona: SPIE, 2015.