A Procedural Description of Geometric Textures by Spectral and Spatial Analysis of Profiles

In this paper we describe a method for automatically generating procedural ”geometric” textures, using a hybrid (spectral and spatial) analysis of profiles (1D curves). The profile describes a certain height variation for a certain abscissa. We call ”geometric” textures a class of textures including ”Bump” textures and ”hypertextures”. In dealing with this challenge (automatic synthesis), we introduce two new key ideas. The first is to compute efficiently a compact and procedural description of the texture, by using a spectral (Fourier transform based) and spatial (histogram based) analytical approach of profiles. The resulting texture is defined as a sum of elementary random functions. This sum is generated according to the profile. The procedural description allows the direct computation of the texture values at any co-ordinates in the Euclidean space and the stochastic aspect of the elementary functions also allows for the processing of highly random textures, with no considerable increase of computation time. The second key idea consists of using analysis in the particular and more complex case of geometric textures. For most analytical methods, underlying geometry is never considered. Using profiles as models, the resulting geometric texture is obtained by extending this profile to 2D or 3D space. The resulting texture directly matches the supplied 1D model. Hence, our method promises to be a very useful tool for easily and efficiently ”modelling” any kind of geometric textures including rocks, bumps, peaks, fur, cotton and so on.