Abstract

Observers were shown images that had luminance variations in the vertical direction (y) and constant luminance in the horizontal direction (x). Variance of the difference of the luminance at any two ys was proportional to the differences in the ys to some fractional power. The fractional power is related to the fractal dimension. Discrimination thresholds were measured using the second alternative six-level forced choice paradigm. Thresholds were found to be insensitive to changes in the fractal dimension, viewing time, change in width of the image beyond 8 arcmin, and to noise flanking the vertical strip containing the fractal statistics. Thresholds increased rapidly when the height of the image decreased below 1 arc deg. Identical statistics were also used to generate a pattern of spatial displacement in the horizontal direction of a vertical line. Thresholds for luminance variations were found to be two to three times worse than those obtained for spatial displacement. The thresholds for spatial displacement varied among observers and were between 0.015 and 0.03 in the fractal dimension scale. Although an ideal observer can be invented that would give superior performance, human observers perform better than the traditional methods used to determine fractal dimensions like the box counting method or the power spectral method.

© 1991 Optical Society of America