A 2-STAGE ALGORITHM FOR DISCONTINUITY-PRESERVING SURFACE RECONSTRUCTION

This paper presents a new two-stage algorithm for visual surface reconstruction from scattered data while preserving discontinuities. The basic paradigm is to clean, grid (the first stage), and then fit the data with a discontinuity preserving spline (the second stage). The first stage consists of a robust local approximation algorithm (the moving least median of squares (MLMS) of error) to both clean the data and create a grid from the original scattered data points. This process is discontinuity preserving. The second stage introduces a weighted bicubic spline (WBS) as a surface descriptor. The WBS has a factor in the regularizing term that adapts the behavior of the spline across discontinuities. The weighted bicubic approximating spline is able to approximate data with step discontinuities with no discernible distortion, such as Gibbs phenomena, in the approximating surface. The combination of robust surface fitting and WBS's removes outliers and reduces Gaussian noise. Either stage by itself would not effectively remove both kinds of noise. Experiments with the two-stage algorithm are presented.