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

Authors:
Jean-Philippe Tarel;William A. Wolovich;David B. Cooper
Affiliations:
INRIA, Domaine de Voluceau, Rocquencourt, B.P. 105, 78153 Le Chesnay Cedex, France. Jean-Philippe.Tarel@inria.fr;Division of Engineering, Brown University, Box D, Providence, RI 02912–9104, USA. WaW@lems.brown.edu;Division of Engineering, Brown University, Box D, Providence, RI 02912–9104, USA. Cooper@lems.brown.edu
Venue:
Journal of Mathematical Imaging and Vision
Year:
2003

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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.