Abstract

A pair of repetitive textures with the same Fourier spectra can be discriminated based on the relative phases of the components. We have found that for some pairs of textures phase discrimination is easy while for other pairs phase discrimination is impossible. A scheme for classifying textures based on autocorrelation functions greater than second order is able to account for these results. The autocorrelation scheme allows one to generate patterns with statistical constraints of any order, in one and two dimensions. We show that without scrutiny by foveal attention, discrimination fails at about the level of fourth-order constraints. This autocorrelation analysis also can account for why certain phases are easier to discriminate than others. For example, Rentschler and Treutwein¹ showed that in the periphery the threshold phase ϕ for discriminating cos(fx) + cos(3fx + ϕ) vs cos(fx) + cos(3fx − ϕ) is much larger than the phase threshold of sin(fx) + sin(3fx + ϕ) vs sin(fx) + sin(3fx − ϕ). The autocorrelation analysis is in agreement with this result. The autocorrelation approach may provide a general metric for phase discrimination of repetitive textures in peripheral vision.

© 1985 Optical Society of America