Visual textures are statistical structures, and must be considered as such to interpret the Julesz conjecture and related notions properly. Yellott presents a result concerning the statistics of individual images, but this result is of limited relevance to the study of texture perception because of the distinction between spatially-finite samples of a texture (an image) and the ensemble from which the sample is drawn. This distinction makes sense both logically and empirically. The assumptions and approximations that are required to link the mathematical notion of a texture ensemble to laboratory practice are no more severe or unnatural than those required in the application of other useful mathematical structures to biology. Interpretation of texture perception in terms of images rather than ensembles leads to an impoverished experimental and theoretical analysis.
Julesz, B., Gilbert, E.N., Shepp, L.A., and Frisch, H.L. (1973)
Inability of humans to discriminate between
visual textures that agree in second-order statistics -- revisited.
Perception 2, 391-405.
Yellott, J. (1993)
Implications of triple correlation uniqueness for
texture statistics and the Julesz
conjecture. J. Opt. Soc. Amer. A10, 777-793.