## An Adaptive and Stable Method for Fitting Implicit Polynomial Curves and Surfaces

- Bo Zheng, Jun Takamatsu, Katsushi Ikeuchi
- IEEE Transactions on Pattern Analysis and Machine…
- 2010

Highly Influenced

4 Excerpts

- Published 1998 in IEEE Trans. Pattern Anal. Mach. Intell.

A new method is presented for identifying and comparing closed, bounded, free-form curves that are defined by even implicit polynomial (IP) equations in the Cartesian coordinates x and y. The method provides a new expression for an IP involving a product of conic factors with unique conic factor centers. The critical points for an IP curve also are defined. The conic factor centers and the critical points are shown to be useful related points that directly map to one another under affine transformations. In particular, the explicit determination of such points implies both a canonical form for the curves and the transformation matrix which relates affine equivalent curves.

@article{Wolovich1998TheDO,
title={The Determination of Implicit Polynomial Canonical Curves},
author={William A. Wolovich and Mustafa Unel},
journal={IEEE Trans. Pattern Anal. Mach. Intell.},
year={1998},
volume={20},
pages={1080-1090}
}