Discontinuity preserving surface reconstruction

A two-stage algorithm for visual surface reconstruction while preserving discontinuities is presented. The primary contribution is the second stage, a weighted bicubic spline as a surface descriptor. The weighted bicubic spline has a factor in the regularizing term that adapts the behavior of the spline across the discontinuity. The weighted bicubic interpolating spline is able to interpolate data with step discontinuities with no discernible distortion (such as Gibbs phenomena) in the interpolated surface. Since regularization is related to spline approximation, extensions to this work should suggest ideas for solving ill-posed problems in vision. Experiments with weighted bicubic spline interpolation are presented