Weighted Quasi Interpolant Spline Approximations: Properties and Applications
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Continuous representations are fundamental for modeling sampled data so that computations and numerical simulations can be performed directly on the model or its elements. To effectively and efficiently address the approximation of perturbed point clouds we propose the Weighted Quasi Interpolant Spline Approximation method (wQISA). We provide global and local bounds of the method and discuss how it still preserves the shape properties of the classical quasi-interpolation scheme. This approach is particularly useful when data noise can be represented as a probabilistic distribution: from the point of view of nonparametric regression, the wQISA estimator is robust to random data perturbation such as noise and outliers. Finally, we show the effectiveness of the method with several numerical simulations on real data, including curve fitting on images, surface approximation and simulation of rainfall precipitations.
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