A Statistical Criterion to Judge the Goodness of Fit of LR B-Splines Surface Approximation

AbstractThe surface approximation obtained with adaptive strategies using locally refined (LR) B-splines depends on the degrees of freedom of the spline space, the tolerance from which the refinement is performed, the noise level of the scattered observations, the refinement strategy and the bidegree of the spline space. The choice of the best model is a challenging task that can be partially answered with statistical criteria, such as the Akaike Information Criterion (AIC). Here we relax the assumption that the approximation error should be normally distributed and with equal variance and propose the use of the student distribution to compute the AIC. We apply the AIC to decide which tolerance, refinement level, or polynomial bidegree are the most adequate for an optimal fitting. We highlight how the resulting AIC can be combined with more usual criteria to judge the goodness of fit of the surface approximation.