A power law study of the edge influence on the perceived filling-in brightness magnitude

Edge plays a special role in spatial perception and as well as in determining the brightness of a surface within borders. The aim of our study was to measure threshold brightness in different levels of edges thickness.

Steven's power law for circles modulating in luminance was estimated for 30 subjects (mean age 24 years, SD 3.3, 13 female). Stimuli were presented on the iMac display using the 11-bit graphic board and consisted of two circles of 3° of visual angle, separated by 10°. We tested 7 levels of Michelson contrast: 7, 8, 10, 15, 26, 50, and 100. Three edges filtering were tested (0.3, 0.8, and 1.5° of smoothing). The subjects' task was to judge the brightness of the edge filtered circle compared with the circle of the hard edge which was considered the modulus and received an arbitrary level of 50, representing the amount of brightness perception. In each trial, the same contrast level was presented in both circles. Five judgments were performed for each contrast level in edge filtering.

We found an increase in the power law exponent as the increase of the edge filtering (for sigma of 0.3 = 0.43, sigma of 0.8 = 0.73, and sigma 1.5 = 0.97). All power function fitting had high correlation coefficients (r² = .94, r² = .95, r² = .97, respectively to sigma 0.3, 0.8, and 1.5) passing to the model's adhesion criteria.

There was a progressive distortion on the figure brightness perception as increasing the edge filtering suggesting the control of edges on the polarity of the overall brightness. Also, perceived brightness was increasingly veridical with increased filtering, approaching 1:1 correspondence at 1.5 sigmas.