The “Structure” of the Visual Environment and Perception 113“relative” to indicate that it was normalized such that the
highest probability in the plot was 1.0). Figure 4.19B, which
shows such orientation differences, demonstrates that for
6 distances and 36 directions of the test element, the edge
elements are likely to be roughly parallel to the reference
element. Geisler et al. (2001, p. 713) concluded,
This result shows that there is a great deal of parallel structure in
natural images, presumably due to the effects of growth and
erosion (e.g., the parallel sides of a branch, parallel geological
strata, etc.), perspective projection (e.g., the elongation of sur-
face markings due to slant), shading (e.g., the illumination of a
branch often produces a shading contour parallel to the side of
the branch), and so on.Now consider Figure 4.19C, which shows the most fre-
quent directions for the same set of distances and directions of
A BC DE FRelative Probability
1.1
.01 90 0 90 0d 1.23d 1.23Likelihood Ratio
100
10
1
.1
.01 90 0d 1.23Relative Probability
1.1
.01Figure 4.19 Statistics of edge co-occurrence in the sample images shown in Figure 4.18. Source:Copyright
2001 by Elsevier Science Ltd. Reprinted with permission. See insert for color version of this figure.reference
dFigure 4.20 Parameters of the relationship between two edge elements:
distanced, direction , and orientation difference . Source: Copyright
2001 by Elsevier Science Ltd. Reprinted with permission.edge element pairs as in Figure 4.19B. To understand this plot,
imagine you choose a test element under an orientation differ-
enceand a distancedand rotate it around the center of polar
coordinates (i.e., along a circumference with radiusd) until it
finds itself at the most likely directionfor the given distance
and orientation difference. Figure 4.19C shows that in the re-
sulting pattern the test elements are approximately cocircular