Covariant-Conics Decomposition of Quartics for 2D Shape Recognition and Alignment

Jean-Philippe Tarel, William Wolovich and David Cooper

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-jmiv03,
  author  = {J.-P. Tarel and W. A. Wolovich and D. B. Cooper},
  title   = {Covariant-Conics Decomposition of Quartics for 2D Shape Recognition and Alignment},
  journal = {Journal of Mathematical Imaging and Vision},
  volume  = {19},
  number  = {3},
  month   = {November},
  pages   = {255-273},
  year 	  = {2003},
  note    = {http://perso.lcpc.fr/tarel.jean-philippe/jmiv03.html}
}

Compressed postscript file (292 Kb)
Pdf file (486 Kb)
(c) Kluwer Academic Publishers