\(L_1C^1\) polynomial spline approximation algorithms for large data sets
The authors propose a new strategy of \( L_1 \) approximation. The main idea is to minimize a shape functional based on the second derivative in an a priori fixed neighborhood of the data set. This functional enables to control locally the deviation between the data set and the resulting curve contrary to \( L_1 \) smoothing splines or \( L_1 \) spline fits. They introduce a new approximating strategy to create an iterative local \( L_1C^1 \) spline approximation extending to the bicubic spline approximation over \( 3D \) data grids and using this result for the image cases. Rich literature and some conclusion and supporting examples are provided at the end of the paper.
scientific article; zbMATH DE number 6376434
scientific article