Stochastic Image Models and Texture Synthesis

This chapter explores the mathematical and algorithmic properties of two sample-based texture models: random phase noise (RPN) and asymptotic discrete spot noise (ADSN). These models permit to synthesize random phase textures. They arguably derive from linearized versions of two early Julesz texture discrimination theories. The ensuing mathematical analysis shows that, contrarily to some statements in the literature, RPN and ADSN are different stochastic processes. Nevertheless, numerous experiments also suggest that the textures obtained by these algorithms from identical samples are perceptually similar. The relevance of this study is enhanced by three technical te l-0 05 95 28 3, v er si on 1 24 M ay 2 01 1 20 Chapter 2. Random Phase Textures contributions providing solutions to obstacles that prevented the use of RPN or ADSN to emulate textures. First, RPN and ADSN algorithms are extended to color images. Second, a preprocessing is proposed to avoid artifacts due to the non-periodicity of real-world texture samples. Finally, the method is extended to synthesize textures with arbitrary size from a given sample. The content of this chapter is mostly from [61].