Surface reconstruction with discontinuities

Thin-plate spline fitting is often applied to fitting smooth surfaces to a collection of data. However, discontinuities in the data are smoothed by this technique. This occurs because of several underlying assumptions of spline fitting that do not hold when discontinuities are present. The theory of robust statistics can be used to deal with these outliers. In this paper, we present one way to apply the theory of robust statistics to the problem of discontinuous surface fitting.

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