Continuous representations are fundamental for modeling sampled data and performing computations and numerical simulations directly on the model or its elements. To effectively and efficiently address the approximation of 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 the data noise can be represented as a probabilistic distribution: from the point of view of non-parametric regression, the wQISA estimator is robust to random perturbations, 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.

连续表示对于建模采样数据以及直接在模型或其元素上执行计算和数值模拟至关重要。为了有效且高效地解决点云的逼近问题，我们提出了加权拟插值样条曲线逼近方法（wQISA）。我们提供了该方法的全局和局部边界，并讨论了该方法如何仍保留经典准插值方案的形状属性。当数据噪声可以表示为概率分布时，此方法特别有用：从非参数回归的角度来看，wQISA估计器对于随机扰动（如噪声和异常值）具有鲁棒性。最后，我们通过对真实数据进行的几种数值模拟（包括对图像的曲线拟合，