Nonparametric Estimation and Simulation of Two-Dimensional Gaussian Image Textures

Abstract

The work to be described is motivated by the need to simulate a variety of real–world image textures, all of which can be well approximated by stationary Gaussian random fields (SGRFs). Specifically, given an observed SGRF T, we wish to simulate SGRFs which look like and possess similar statistical properties to T. The main contribution of this paper is the development of an automatic and nonparametric spectrum estimation procedure which is able to produce an estimated spectrum of Tin such a way that SGRFs simulated from this estimated spectrum have these desirable characteristics. Two special features of the procedure are: (i) it relies on a different risk function to that commonly used in nonparametric spectrum estimation, and (ii) it chooses its smoothing parameters by the technique of unbiased risk estimation. Results from a simulation study and a practical example demonstrate the good performance of the procedure. The practical example also illustrates how the proposed procedure can be combined with Monte Carlo testing to tackle target testing problems. Finally, the procedure is applied to the synthesis of some Brodatz textures, with some success.