On Interactive Object Shape Modeling Using Algebraic Curves
Journal of VLSI Signal Processing Systems - special issue on multimedia signal processing
Stable Fitting of 2D Curves and 3D Surfaces by Implicit Polynomials
IEEE Transactions on Pattern Analysis and Machine Intelligence
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Denote a point in the plane by z=(z,y) and a polynomial of nth degree in z by f(z) /spl Sigma//sub i,j//spl ges/o/sub 1/i+j/spl les/n(a/sub ij/x/sup i/y/sup j/). Denote by Z(f) the set of points for which f(z)=0. Z(f) is the 2D curve represented by f(z). In this paper, we present a new approach to fitting 2D curves to data in the plane (or 3D surfaces to range data) which has significant advantages over presently known methods. It requires considerably less computation and the resulting curve can be forced to lie close to the data set at prescribed points provided that there is an nth degree polynomial that can reasonably approximate the data. Linear programming is used to do the fitting. The approach can incorporate a variety of distance measures and global geometric constraints.