RBF interpolation and Gaussian process regression through an RKHS formulation

Radial Basis Function (RBF) interpolation is a common approach to scattered data interpolation. Gaussian Process regression is also a common approach to estimating statistical data. Both techniques play a central role, for example, in statistical or machine learning, and recently they have been increasingly applied in other fields such as computer graphics. In this survey we describe the formulation of both techniques as instances of functional regression in a Reproducing Kernel Hilbert Space. We then show that the RBF and Gaussian Process techniques can in some cases be reduced to an identical formulation, differing primarily in their assumptions on when the data locations and values are known, as well as in their (respectively) deterministic and stochastic perspectives. The scope and effectiveness of the RBF and Gaussian process techniques are illustrated through several applications in computer graphics.