Partial Smoothing Splines for Noisy +Boundaries with Corners

We have investigated the estimation of 2-D boundary functions from sampled data sets where both noise and corners are present. The approach is based on the partial smoothing spline in which the estimated boundary function consists of an ordinary smoothing spline and a parametric function that describes the discontinuities (i.e., corners of the boundary). Prior knowledge about the boundary, such as the number of corners, their locations, noise levels, and the amount of smoothness, is not required for the boundary estimate. The smoothing parameter and the corner locations of the spline, which are parts of the estimate, are determined by the generalized cross-validation method whereby statistical properties are gathered from the input sampled data rather than specified a priori. This approach enables the smoothing of a noisy boundary while retaining an accurate description of the boundary corners. Extensive experiments were conducted to verify its ability to smooth noise while retaining a good representation of boundary corners, and do not rely on any prior information.