Locally isometric and conformal parameterization of image manifold

A. V. Bernstein; A. P. Kuleshov; Yu. A. Yanovich

doi:10.1117/12.2228741

8 December 2015 Locally isometric and conformal parameterization of image manifold

A. V. Bernstein, A. P. Kuleshov, Yu. A. Yanovich

Proceedings Volume 9875, Eighth International Conference on Machine Vision (ICMV 2015); 987507 (2015) https://doi.org/10.1117/12.2228741
Event: Eighth International Conference on Machine Vision, 2015, Barcelona, Spain

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.

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A. V. Bernstein, A. P. Kuleshov, and Yu. A. Yanovich "Locally isometric and conformal parameterization of image manifold", Proc. SPIE 9875, Eighth International Conference on Machine Vision (ICMV 2015), 987507 (8 December 2015); https://doi.org/10.1117/12.2228741

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KEYWORDS

Vector spaces

Reconstruction algorithms

Error analysis

Matrices

Data modeling

Image transmission

Machine vision

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