Spline Smoothing on Surfaces

Spline Smoothing on Surfaces

We present a method for estimating functions on topologically and/or geometrically complex surfaces from possibly noisy observations. Our approach is an extension of spline smoothing, using a Þnite element method. The paper has a substantial tutorial component: we start by reviewing smoothness measures for functions deÞned on surfaces, simplicial surfaces and differentiable structures on such s...

Smoothing Spline Curves and Surfaces for Sampled Data

We consider the problem of designing optimal smoothing spline curves and surfaces for a given set of discrete data. For constructing curves and surfaces, we employ normalized uniform B-splines as the basis functions. First we derive concise expressions for the optimal solutions in the form which can be used easily for numerical computations as well as mathematical analyses. Then, assuming that ...

Smoothing by Spline Functions

Smoothing an arc spline

Arc splines are G continuous curves made of circular arcs and straight-line segments. They have the advantages that the curvature of an arc spline is known and controlled at all but a finite number of points, and that the offset curve of an arc spline is another arc spline. Arc splines are used by computer-controlled machines as a natural curve along which to cut and are used by highway route p...

Monotone B-spline Smoothing

Estimation of growth curves or item response curves often involves monotone data smoothing. Methods that have been studied in the literature tend to be either less exible or more diicult to compute when constraints such as monotonicity are incorporated. Built upon the ideas of Ramsay (1988) and Koenker, Ng and Portnoy (1994), we propose monotone B-spline smoothing based on L 1 optimization. It ...