Approximation of the Distance from a Point to an Algebraic Manifold

Alexei Yu. Uteshev; Marina V. Goncharova

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Paper

Approximation of the Distance from a Point to an Algebraic Manifold

Topics: Shape Representation

In Proceedings of the 8th International Conference on Pattern Recognition Applications and Methods ICPRAM - Volume 1, 715-720, 2019 , Prague, Czech Republic

Authors: Alexei Yu. Uteshev and Marina V. Goncharova

Affiliation: Faculty of Applied Mathematics, St. Petersburg State University, 7/9 Universitetskaya nab., St. Petersburg, 199034 and Russia

Keyword(s): Algebraic Manifold, Distance Approximation, Discriminant, Level Set.

Related Ontology Subjects/Areas/Topics: Applications ; Pattern Recognition ; Shape Representation ; Software Engineering

Abstract: The problem of geometric distance d evaluation from a point X0 to an algebraic curve in R2 or manifold G(X) = 0 in R3 is treated in the form of comparison of exact value with two its successive approximations d(1) and d(2). The geometric distance is evaluated from the univariate distance equation possessing the zero set coinciding with that of critical values of the function d2(X0), while d(1)(X0) and d(2)(X0) are obtained via expansion of d2(X0) into the power series of the algebraic distance G(X0). We estimate the quality of approximation comparing the relative positions of the level sets of d(X), d(1)(X) and d(2)(X).

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Paper citation in several formats:

Uteshev, A. and Goncharova, M. (2019). Approximation of the Distance from a Point to an Algebraic Manifold. In Proceedings of the 8th International Conference on Pattern Recognition Applications and Methods - ICPRAM; ISBN 978-989-758-351-3; ISSN 2184-4313, SciTePress, pages 715-720. DOI: 10.5220/0007483007150720

@conference{icpram19,
author={Alexei Yu. Uteshev and Marina V. Goncharova},
title={Approximation of the Distance from a Point to an Algebraic Manifold},
booktitle={Proceedings of the 8th International Conference on Pattern Recognition Applications and Methods - ICPRAM},
year={2019},
pages={715-720},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0007483007150720},
isbn={978-989-758-351-3},
issn={2184-4313},
}

TY - CONF

JO - Proceedings of the 8th International Conference on Pattern Recognition Applications and Methods - ICPRAM
TI - Approximation of the Distance from a Point to an Algebraic Manifold
SN - 978-989-758-351-3
IS - 2184-4313
AU - Uteshev, A.
AU - Goncharova, M.
PY - 2019
SP - 715
EP - 720
DO - 10.5220/0007483007150720
PB - SciTePress