A review of point sets parameterization methods for curve fitting

Parametric curve fitting which includes curve approximation and interpolation is a critical topic in many fields, such as medical images, 3D reconstruction and data visualization, etc. To approximate or interpolate point sets with a curve, parameterization of points is usually a key step, which has a great impact on the final result. Many methods that have been proposed to tackle this problem. To our best knowledge, there is not any review paper about point set parameterization for curve fitting. In this paper, we will review the proposed techniques of parameterizing point sets for curve fitting. These methods will be divided into two categories. In the first category, the parameterization of point sets and curve fitting are treated as two separable and successive steps, specifically, the parameters obtained using some techniques in the first step are used for the curve fitting process in the second step. The two steps are solved together in the second category using more complex techniques. Methods in each of the two types will be reviewed in this paper.