Binary and ternary textures containing higher-order spatial correlations

A quantitative method is presented for creating a large number of classes of binary (256) and ternary (7.62×10¹²) textures. The binary textures are presented as black and white (contrasts -1 and 1). The ternary textures have three levels: black, white and the mean luminance gray (contrasts -1, 0 and 1). The ternary patterns in particular display a wide variety of properties, including depth cues from disparity and lighting. Given the very large number of ternary patterns, we present guidelines and analytical methods for selecting sets of textures with particular image qualities and/or nonlinear relationships between pixels. The second- and third-order correlation functions of several thousand examples were examined to reveal patterns that are functionally isotrigon with other textures and or with uniformly distributed noise patterns.