Estimation of Planar Curves, Surfaces, and Nonplanar Space Curves Defined by Implicit Equations with Applications to Edge and Range Image Segmentation

@article{Taubin1991EstimationOP,
title={Estimation of Planar Curves, Surfaces, and Nonplanar Space Curves Defined by Implicit Equations with Applications to Edge and Range Image Segmentation},
author={Gabriel Taubin},
journal={IEEE Trans. Pattern Anal. Mach. Intell.},
year={1991},
volume={13},
pages={1115-1138}
}

This paper addresses the problem of parametric representation and estimation of complex planar curves in 2-D, surfaces in 3-D and nonplanar space curves in 3-D. Curves and surfaces can be defined either parametrically or implicitly, and we use the latter representation. A planar curve is the set of zeros of a smooth function of two variables X-Y, a surface is the set of zeros of a smooth function of three variables X-~-Z, and a space curve is the intersection of two surfaces, which are the set… CONTINUE READING