A regularization approach for surface reconstruction from point clouds

Ill-posed inverse problems arise in many branches of science and engineering. In the typical situation one is interested in recovering a whole function given a finite number of noisy measurements on functionals. Regularization approach is one of the solutions for this kind of problems among which we find surface reconstruction from point clouds. In this article we present a classification of methods for surface reconstruction and its solution in the framework of classical regularization, in terms of linear combinations of the reproducing kernel in certain proper space for reconstruction. We evaluate the quality of this solution to approximate 3D data and some examples for computational implementation are also shown in order to complete a user’s guide for an efficient employment of kernel methods in the reconstruction of multivariate functions.