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The Determination of Implicit Polynomial Canonical Curves
October 1998 (vol. 20 no. 10)
pp. 1080-1090

Abstract—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.

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Index Terms:
Implicit polynomials, affine transformations, object recognition, pose estimation, canonical curves.
Citation:
William A. Wolovich, Mustafa Unel, "The Determination of Implicit Polynomial Canonical Curves," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 20, no. 10, pp. 1080-1090, Oct. 1998, doi:10.1109/34.722620
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