A two-stage algorithm for discontinuity-preserving surface reconstruction

A two-stage algorithm for visual surface reconstruction from scattered data while preserving discontinuities is presented. The first stage consists of a robust local approximation algorithm (the moving least median of squares (MLMS) of error) to 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 can approximate data with step discontinuities with no discernible distortion in the approximating surface. The combination of robust surface fitting and WBSs removes outliers and reduces Gaussian noise. Either stage by itself would not effectively remove both kinds of noise. Experimental results with the two-stage algorithm are presented