Implications of triple correlation uniqueness for texture statistics and the Julesz conjecture

Abstract

Triple correlation uniqueness refers to the fact that every monochromatic image of finite size is uniquely determined up to translation by its triple correlation function. Here that fact is used to prove that every finite image composed of discrete colors is determined up to translation by its third-order statistics. Consequently, if two texture samples have identical third-order statistics, they must be physically identical images and thus visually nondiscriminable by definition. It follows that a third-order version of Julesz’s long-abandoned conjecture about spontaneous texture discrimination is necessarily true (notwithstanding such well-known counterexamples as the odd and even textures). The second-order (i.e., original) version of that conjecture is not necessarily true: physically distinct finite images with identical second-order statistics can be constructed, so counterexamples are possible. However, the counterexamples that one finds in the literature are either nonexact or difficult to reconstruct. A new principle is described that permits the easy construction of discriminable black and white texture samples that have strictly identical second-order statistics and thus provide exact counterexamples to the Julesz conjecture.

Ähnliche Arbeiten