Covariant-Conics Decomposition of Quartics for 2D Shape Recognition and Alignment
Abstract
This paper outlines a new geometric parameterization of 2D curves where
parameterization is in terms of geometric invariants and parameters
that determine intrinsic coordinate systems. This new
approach handles two fundamental problems: single-computation alignment,
and recognition of 2D shapes under Euclidean
or affine transformations. The approach is model-based: every
shape is first fitted by a quartic represented by a fourth degree 2D polynomial.
Based on the decomposition of this equation into three covariant conics,
we are able, in both the Euclidean and the affine cases, to define
a unique intrinsic coordinate system for non-singular bounded quartics
that incorporates usable
alignment information contained in the polynomial representation,
a complete set of geometric
invariants, and thus an associated canonical form for a quartic.
This representation permits shape recognition based on
11 Euclidean invariants, or 8 affine invariants. This is illustrated
in experiments with real data sets.
Reference
@ARTICLE{jpt-jmiv99,
author = {Tarel, J.-P. and Wolovich, W. A. and Cooper, D. B.},
title = {Covariant-Conics Decomposition of Quartics for 2D Shape Recognition and Alignment},
journal = {Journal of Mathematical Imaging and Vision},
volume = {19},
number = {3},
month = nov,
year = {2003},
pages = {255-273},
url = {http://perso.lcpc.fr/tarel.jean-philippe/publis/jmiv03.html}
}
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