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Proceedings Paper

Locally isometric and conformal parameterization of image manifold
Author(s): A. V. Bernstein; A. P. Kuleshov; Yu. A. Yanovich
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Paper Abstract

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.

Paper Details

Date Published: 8 December 2015
PDF: 7 pages
Proc. SPIE 9875, Eighth International Conference on Machine Vision (ICMV 2015), 987507 (8 December 2015); doi: 10.1117/12.2228741
Show Author Affiliations
A. V. Bernstein, Institute for Information Transmission Problems (Russian Federation)
National Research Univ. Higher School of Economics (Russian Federation)
A. P. Kuleshov, Institute for Information Transmission Problems (Russian Federation)
National Research Univ. Higher School of Economics (Russian Federation)
Yu. A. Yanovich, Institute for Information Transmission Problems (Russian Federation)
National Research Univ. Higher School of Economics (Russian Federation)


Published in SPIE Proceedings Vol. 9875:
Eighth International Conference on Machine Vision (ICMV 2015)
Antanas Verikas; Petia Radeva; Dmitry Nikolaev, Editor(s)

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