Abstract
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
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