ABSTRACT
Over the past three decades a good deal of research on visual texture perception has been motivated by the hope that the discriminability of textures could be predicted on the basis of the global statistical properties of images. An early and especially influential expression of that hope was Bela Julesz's (1962) famous conjecture that textures cannot be discriminated without point-by-point scrutiny if they have the same “second-order statistics.” Second-order statistics are descriptors applicable to images composed of a small number of distinct colors, and Julesz's conjecture takes its simplest form in the context of binary (black and white) images. The second-order statistics of a binary image are the probabilities, for all oriented line segments, that when any given segment is dropped at random onto the image (preserving its orientation), both ends land on the foreground color—for example, both on black. When this definition is formalized, the Julesz conjecture for binary textures proves to be equivalent to the hypothesis that two such textures cannot be discriminated (“preattentively,” that is) if they have the same autocorrelation function. Figure 7.1 illustrates some perceptual facts that might lead one to such a hypothesis. On the left is an 8 × 8 array composed of four texture samples: The upper right quadrant is a 4 × 4 array of down-pointing arrows, and the other three quadrants are identical 4 × 4 arrays of up-pointing arrows. Considered as separate binary images, all four quadrants have the same autocorrelation function, and at first glance one does not notice that the upper right quadrant is different from the rest of the figure. In general, a 180° rotation of the micropatterns (here, the arrows) of a texture does not alter its autocorrelation function (for reasons spelled out in the section titled Autocorrelation and Second-Order Statistics), and it appears to be generally true that we cannot instantaneously discriminate between binary textures composed of micro-patterns that are 180° rotations of one another. This fact gains significance when one realizes that the same is not true of 90° rotations. The right side of Fig. 7.1 shows another 4 × 4 arrangement of texture samples, but here the upper right quadrant is composed of right-pointing arrows. In this case the autocorrelation function of the upper right quadrant image is not the same as that of the other three quadrants, and perceptually, that quadrant is immediately seen to be different.
