Surface interpolation by adaptive Neuro-Fuzzy Inference System based local Ordinary Kriging

A new approach to the Ordinary Kriging interpolation method based on the combination of local interpolation and variogram modelling with Adaptive Neuro-Fuzzy Inference System (ANFIS) is proposed for surface interpolation. In this method, the experimental variogram is modelled by ANFIS and this model is used to interpolate the unknown values of specific points in a new local manner. In this local way, all the unknown points are grouped based on each reference point. As the study data, two types of data sets coming from mathematical functions and a 3D scanning system are used. The tests show that the proposed method produces better performances for all data sets in comparison to the well known and highly approved interpolation methods; Ordinary Kriging, Triangle Based Cubic and Radial Basis Function-Multiquadric. Moreover, by the proposed method the computational complexity impressively decreases compared to the global Ordinary Kriging.