Terrain texture synthesis with an extended self-similar model
Lance Kaplan, C.‐C. Jay Kuo · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1995
We propose a new method for terrain texture synthesis by using a generalized two dimensional fractional Brownian motion (fBm) model called the extended self-similar (ESS) process. The utility of 2-D fBm for terrain texture modeling has been examined by some researchers. Although the fBm may provide a good model for landscapes for some scales, it will not capture the behavior of the terrain at all scales. We introduce the ESS process to model terrains at all scales where the parameters of the ESS model provide a multiscale roughness representation of the landscape. Specifically, we define a generalized Hurst parameter which changes with respect to scales. To validate the usefulness of the new model, we show how to estimate the generalized Hurst parameters from 2-D data and how to synthesize an ESS process. The generation method is based on Fourier synthesis of the stationary ESS increments, and the algorithm has a complexity of O[N2 log(N)] for an image of size N X N. Then, we demonstrate the relation between the generalized Hurst parameter and visual roughness through examples of synthesized images. Finally, we examine the ability of the ESS process to render real terrain data.