Using implicit polynomials for image compression

Implicit polynomials (IF) are being used to represent 2D curves and 3D surfaces. The zero-set of a 2D implicit polynomial of the form of p(x,y)=a/sub 1/x/sup N/+a/sub 2/x/sup N-1/y+...+ a/sub r/=0 can be used to describe data points making up a 2D curve. A similar 3D polynomial-p(x,y,z)=0 describes data points on a 3D surface. We describe a way to restrict the zero-set of the fitted polynomial so that correct restoration of the data from the polynomial's coefficients will be achieved.