Bootstrap Test Error Estimations of Polynomial Fittings in Surface Reconstruction

We propose the use of the bootstrap technique for estimating the test error in the context of surface reconstruction from noisy point sets. Validation experiments with polynomial fittings of locally parametrized neighborhoods of noisy point sets give evidence that, in agreement with the theory, the training error underestimates the test error while leave-one-out error overestimates it. Based on the same experiments, we show that the phenomenon of overfitting can be quantifiably detected in commonly used polynomial surface fitting settings. Finally, the bootstrap test error estimators are used to enhance a point set denoising application.