AN INTERPOLATION METHOD FOR STOCHASTIC MODELS

Abstract

This paper presents a method using stochastic models for the simulation and interpolation of natural phenomena. These models are based on the general concept of random functions with stationary increments, to which the fbm belongs. The consideration of this family of stochastic processes, instead of just considering the fractal one, leads to greater diversity and realism. Another way to enhance realism is to combine analysis and interpolation. We suggest calculating the stochastic parameters from the analysis of existing natural surfaces and to use them as input data for the interpolation algorithm. We propose an interpolation algorithm which respects the stochastic behavior of this class of processes. This method provides a better understanding of the interpolation mechanisms. One can thus study the influence of the stochastic parameters and the data points localization on the interpolated valued. A final advantage of this algorithm is to interpolate surfaces defined by irregular data points. This type of representation is actually often encountered in cartography (contour lines, spot elevations, ...). This possibility is also very interesting for image synthesis applications, since it allows specifying with ease the rough shape of a given image.