Coefficients a and b control the low and high frequency ranges that the watermark affects. Because of the watermark invariant properties, we embed the watermark only in the Fourier descr iptor magnitude. We use the inverse Fourier transform of the Fourier coefficients to produce the watermarked curve L . This watermarking method is also applicable in the control points of B-spline contour representations. In both polygonal curves and in B-spline curves, watermark embedding can create curve discontinuities or curve self-crossing.