We found that the magnitude of the perceptual filling-in for the surface brightness was strongly affected by the edge filtering. As the filter increased, escalating the edge’s blurriness, the brightness for the central region for that circle also increased in a power function fashion. We could interpret it as a weakening of the edge influence on the surface’s brightness. The lower exponent (0.43) at 0.3 sigmas indicated a compressive brightness judgment—specifically an increase in the brightness judgment for lower luminance levels. This compression disappeared with greater smoothing, and at 1.5 sigmas the exponent is 0.97, reflecting a 1:1 match in the brightness judgments between the test conditions.
In our experiment, as we filtered the edges, we progressively eliminated the local, high-spatial frequencies as we increased the blurring values. The perceived brightness became more proportional to the lightness as the edge filtering increased. Since the filtering removes high spatial frequencies, the increase in the central region of the stimuli could be mediated predominantly by low spatial frequencies. In previous studies, similar conclusions have been reached in which luminance Chevreul-staircases were filtered for spatial frequencies (Peromaa & Laurinen, 2004). The authors found that only low spatial frequency components of edges were able to trigger brightness filling-in. In addition, they stated high spatial frequency components of edges do not produce a perceived brightness but only featured characteristics as lines. According to Perna and Moronne, the high-spatial-frequency filtering above 2 c/deg was never sufficient to raise the perceived difference of brightness above the threshold. Thus, the mechanism tuned to frequencies lower than 1 c/deg could mediate the filling-in brightness perceived. That is the case of our study, in which the stimuli were of .50 c/deg and lower as the filtering increased. Additionally, our results provide complementary information on brightness perception since evidence reported changes in the amount of brightness perceived as the edge filtering occurred. Future measurements using smaller and larger sigma should be performed to better comparisons with literature data.
Edges are also important for spatial location. In an alignment task targeting the changes in the blurriness of the edges of white bars, there was a consistent shift on edge location as it varied according to the level of stimulus’ contrast (Bex & Edgar, 1996). For well-defined edges, an increase in contrast did not change the alignment position; however, as the edge blurring increased, for raising contrast levels, there was also an increase in the shifting of the white stripes in a direction to the adjacent black region. It seems that with an increase in the contrast level as well as the edge blurring, there was an expansion of the total area perceived, which, in turn, shifted our perceptual location for the edges.
In some sense, our data complements those findings, since the blurriness of our stimuli generates an increase in the contrast perceived. One possible hypothesis for the contrast increasing could be related to the size enlargement. As we blurred the edges, there was an apparent increase in the apparent size of the circle. A possible mechanism which could compensate for the increase in size could be an increase in the contrast level. Indeed, our data could provide complementary information for the findings of Bex and Edgar (Bex & Edgar, 1996). Blurring the edges generated an expansion in the total area perceived, a consequent change in the edge location, and a compensatory increase in the perceived brightness. In our case, an additional effect was observed because the increase was polarity dependent, due to the fact that the bright grays appeared brighter and the dark grays appeared darker. Future measurements using multiple circle sizes with constant relative-size filtering would be a more appropriate approach to this question. Although, large sizes stimuli have been employed in different conditions than those we tested, it can give us support for hypotheses of what to expect from these future experiments. Recent studies using spatial complex stimuli in which contrast edges were embedded in a brown noise (1/f2) found that an edge detector profile with a peak to trough width of approx. 0.1 to 0.17° of difference between adjacent areas was needed for an edge to be detected (McIlhagga, 2018). Since authors used stimulus comprised of10° of visual angle, we could argue that an increase in size by changing the overall brightness altering the power law exponent could not be supported.
A consequence of the bright stimulus is that it becomes subjectively brighter; in addition, the dark stimulus is perceived as darker with the increase of the power law’s exponent. This increase in the contrast shifting relating it back to the edge blur affected the subjective contrast range, and, as a consequence, also increased in the exponent measured. Experimental evidence for the changes in the exponent regarding the range of the stimuli can be found in several studies (Lockhead & Hinson, 1986; Pradhan & Hoffman, 1963; Teghtsoonian, 1973). Our results provide support for the causal relation between our perceptual mechanisms and the range of the stimuli managing the edge filtering. A practical outcome of the brightness reduction to reach higher ranges is associated with the impairment in eyes’ saccadic movements, which reduces significantly the visual search precision (Gilchrist, Humphreys, Riddoch, & Neumann, 1997). In addition, as well as in the binocularity since there is an increase in the cortical disparity computation (Georgeson & Wallis, 2014).
The power law’s exponent was around 1.0 measured for the blurriness of 1.5 Gaussian sigma. This means that the magnitude of perceived brightness changed proportionally to the central region of the circle brightness and, thus, led to another important consequence of the phenomena, there were no edges’ influences on brightness perceived. These results suggest that surface brightness is a filling-in process more than an induction mechanism. As one increases the blurring of the edges, there is a perceptual shift of the edge to regions farther from the center of the circle. This displacement weakens the edge effect on the center which reduces its’ filling-in effect. Since the background was constant, the brightness induction remains the same for all the filtering conditions. Reducing the filtering enlarges the edge, and, consequently, the transition distance between the center of the circle and the surrounding would reduce as well—ultimately, the expected effect would be the opposite.
It is a worthwhile and open question as to why edge integration has evolved to be the favorite physiological mechanism to generate a representation of surface information. In addition, our study contributes to understanding an explanation of human blur vision. As we move away from the optimal edge detection condition, we have an exponential reduction of the brightness perception of spatial adjacent areas with a reduction in contrast detection and, consequently, in our spatial vision. Increases in blurring reduce the high structural complexity of visual scenes, decreases detection of high spatial frequencies, and negatively impacts local feature vision. As a direct consequence, spatial discrimination is reduced, negatively impacting elementary perceptual functions as a figure-ground organization (Ghose & Palmer, 2010).
This study used only three edge filters. It started with an edge detector size that was twice the limit found in previous studies, because we were interested in the brightness changes for different suprathreshold edge filtering, which could be a limitation of this study. Future investigations considering the transition between optimal edge filtering size 0.1–0.17 and ours, which started filtering at 0.30, would be important to model how brightness perception behaviors in this filtering range function. Also, future studies could integrate the findings of our work to improve computational modeling of visual neurons (Yedjour, Meftah, Lezoray, & Benyettou, 2017).