Covariant Conics Decomposition of Quartics for 2D Object Recognition and Affine Alignment

Jean-Philippe Tarel, William Wolovich and David Cooper

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}
}

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