Perceptual Coherence : Hearing and Seeing

The Transition Between Noise and Structure 155
K = 1: The first-order statistic is the probability that any dot in the array
will have a certain brightness or luminance. In B. F. J. Green et al. (1957),
there were only two levels of brightness (i.e., white or black) so that
Pr(white) = 1 − Pr(black). Julesz (1962) used two to four levels of brightness
(black, dark gray, light gray, white). Different probability distributions
vary the overall brightness and contrast of the array, and this variable has
been termed spatial density or tonal quality. Three random textures based
on different probability distributions of 10 different gray levels are shown
in figure 4.1. Different probability distributions create textures that yield
easy segregation.
K = 2: The second-order statistic is the conditional probability between
pairs of dots. Simply put, given the brightness of one dot, is the probability
of the brightness of a second dot different than its probability of occurrence
according to the K = 1 statistic? In figure 4.2, three examples of K = 2
Figure 4.1. Texture differences due to K = 1 statistics of the reflectance of the
individual squares in each 12 × 12 matrix. The y axis gives the percentages of each
of the 10 different reflectance values. Differences in the K = 1 statistic generate
rapid segmentation between the three matrices arrayed vertically, although the
boundary is soft.