The mathematical framework for studies of texture perception is discussed. Textures correspond to statistical ensembles, whereas images are spatially finite samples of a texture. The main ideas underlying the use of visual textures in experimental and theoretical analyses of preattentive vision are summarized, with an emphasis on the distinction between texture ensembles and images. The Julesz conjecture [ Perception 2, 391 ( 1973)] is that preattentive discrimination of textures is possible only for textures that have different second-order correlation statistics. Recently Yellot [ J. Opt. Soc. Am. A 10, 777 ( 1993)] claimed that the triple correlation uniqueness (TCU) theorem, a mathematical result that every monochromatic image of finite size is uniquely determined (up to translation) by its third-order statistics, makes higher-order variants of the Julesz conjecture trivial. However, the TCU theorem applies to individual images, and not to texture ensembles, and thus is of limited relevance to the study of texture perception.
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