Contour Smoothing Based on Weighted Smoothing Splines

Abstract

Here we present a contour-smoothing algorithm based on weighted smoothing splines for contour extraction from a triangular irregular network (TIN) structure based on sides. Weighted smoothing splines are one-variable functions designed for approximating oscillatory data. Here some properties are derived from a small space of functions and working with few knots and special boundary conditions. However, in order to apply these properties to a two variable application such as contour smoothing, local reference frames for direct and inverse transformation are required. The advantage of using weighted smoothing splines as compared to pure geometric constructions such as the approximation by parabolic arcs or other type of spline function is the fact that these functions adjust better to the data and avoid the usual oscillations of spline functions. We note that Bezier and B-spline techniques are result in convenient, alternative representations of the same spline curves. While these techniques could be adapted to the weighted smoothing spline context, there is no advantage as our approach will be simple enough.