Covariant Conics Decomposition of Quartics for 2D Object
Recognition and Affine Alignment
Abstract
This paper outlines a geometric parameterization of 2D curves where
the parameterization is in terms of geometric invariants and terms
that determine an intrinsic coordinate system. Thus, we present a new
approach to handle two fundamental
problems: single-computation alignment and recognition of 2D shapes under
affine transformations. The approach is model-based, and every
shape is first fit by an implicit fourth degree (quartic) polynomial.
Based on the decomposition of this equation into
three covariant conics,
we are able to define
a unique intrinsic reference system that can incorporates all the useable
alignment information contained in the implicit polynomial representation,
a complete set of geometric
invariants, and thus an associated canonical form for a quartic.
This representation permits shape recognition based on 8 invariants.
This is illustrated in experiments with real data sets.
Reference
@inproceedings{jpt-icip98,
author = {Tarel, J.-P. and Wolovich, W. and Cooper, D. B.},
title = {Covariant Conics Decomposition of Quartics for 2D Object Recognition and Affine Alignment},
booktitle = {Proceedings of the International Conference on Image Processing (ICIP'98)},
address = {Chicago, Illinois, USA},
date = {4-7},
month = {October},
pages = {818-822},
year = {1998},
note = {http://perso.lcpc.fr/tarel.jean-philippe/publis/icip98.html}
}
Pdf file (137 Kb)
(c) IEEE