On 2015 Sep 10, Lydia Maniatis commented:

The authors say that “we assessed whether the highest luminance is mapped onto a fixed surface reflectance (“white”) independently of target reflectance, illumination level (real or simulated), or luminance. ”

Evidently, by “illumination level” they are referring to the collection of luminances of their “Mondrians,” and by “luminance” they are referring to the luminance of individual target surfaces. It may be that, in relatively low luminance conditions, observers experienced a sense of low illumination, but neither the authors nor anyone else has, to my knowledge, tested whether such an impression does, in fact, arise. The fact that “low illumination” conditions resulted in lower lightness matches for targets actually implies the opposite, since impressions that surfaces are “in shadow” typically cause them to appear lighter than equiluminant. apparently plain view surfaces. So average luminance (regardless of how the investigators achieve this) and contrast are the variables being looked at,

As is typical in experiments using “Mondrians” or checkerboard stimuli, the authors seem to overlook the fact that these stimuli are capable of producing differential illumination, transparency, luminosity effects, despite the absence of the usual “cues.” This is evident, for example, in checkerboard stimuli used by Allred, Radonjic, Gilchrist & Brainard (2012), who tentatively acknowledge (but do not test for) some but not all of the (self-evident) effects. Anderson et al cite Radonjic, Allred, Gilchrist and Brianard (2011) as having shown that “a stimulus ratio of 5905:1 could be mapped onto an extended lightness ratio of 100:1 and concluded that such results ruled out theories that predict perceived lightness from luminance ratios or Weber contrast” and suggest that “these data cast significant doubt on the view that the visual system has any understanding of the range of reflectance values that populate natural environments.” However, it is not clear that the high-range stimuli in Radonjic et al's experiments did not produce luminosity effects. Their observers did, in fact, report luminosity for the highest luminance values in those stimuli, but the authors discounted those reports as being due to the stimuli having been presented on an “emissive screen.” However, this explanation does not seem credible given that the same luminance values did not produce luminosity reports in lower-range situations.

If there were apparent scission effects going on in Anderson et al's stimuli, then observer reports would have been affected. When a surface is completed “beneath” a shadow, and seen as homogeneous in its lightness, this does not mean that we can't see that it is also darker at the shadowed place, in the same way that amodally completed surfaces are seen and not seen at the same time. You can't disprove that an amodal completion is occurring simply on the basis of asking an observer to report on the local color in the image at an “obstructed” location. Similarly, simply asking a naive observer to make a lightness match where scission is occurring is problematic.

It is always important for readers of perception papers to be able to see the stimuli used, so it would have been good if all of the Mondrians, and not just the one, were made available.

On 2015 Sep 10, Lydia Maniatis commented:

The authors say that “we assessed whether the highest luminance is mapped onto a fixed surface reflectance (“white”) independently of target reflectance, illumination level (real or simulated), or luminance. ”

Evidently, by “illumination level” they are referring to the collection of luminances of their “Mondrians,” and by “luminance” they are referring to the luminance of individual target surfaces. It may be that, in relatively low luminance conditions, observers experienced a sense of low illumination, but neither the authors nor anyone else has, to my knowledge, tested whether such an impression does, in fact, arise. The fact that “low illumination” conditions resulted in lower lightness matches for targets actually implies the opposite, since impressions that surfaces are “in shadow” typically cause them to appear lighter than equiluminant. apparently plain view surfaces. So average luminance (regardless of how the investigators achieve this) and contrast are the variables being looked at,

As is typical in experiments using “Mondrians” or checkerboard stimuli, the authors seem to overlook the fact that these stimuli are capable of producing differential illumination, transparency, luminosity effects, despite the absence of the usual “cues.” This is evident, for example, in checkerboard stimuli used by Allred, Radonjic, Gilchrist & Brainard (2012), who tentatively acknowledge (but do not test for) some but not all of the (self-evident) effects. Anderson et al cite Radonjic, Allred, Gilchrist and Brianard (2011) as having shown that “a stimulus ratio of 5905:1 could be mapped onto an extended lightness ratio of 100:1 and concluded that such results ruled out theories that predict perceived lightness from luminance ratios or Weber contrast” and suggest that “these data cast significant doubt on the view that the visual system has any understanding of the range of reflectance values that populate natural environments.” However, it is not clear that the high-range stimuli in Radonjic et al's experiments did not produce luminosity effects. Their observers did, in fact, report luminosity for the highest luminance values in those stimuli, but the authors discounted those reports as being due to the stimuli having been presented on an “emissive screen.” However, this explanation does not seem credible given that the same luminance values did not produce luminosity reports in lower-range situations.

If there were apparent scission effects going on in Anderson et al's stimuli, then observer reports would have been affected. When a surface is completed “beneath” a shadow, and seen as homogeneous in its lightness, this does not mean that we can't see that it is also darker at the shadowed place, in the same way that amodally completed surfaces are seen and not seen at the same time. You can't disprove that an amodal completion is occurring simply on the basis of asking an observer to report on the local color in the image at an “obstructed” location. Similarly, simply asking a naive observer to make a lightness match where scission is occurring is problematic.

It is always important for readers of perception papers to be able to see the stimuli used, so it would have been good if all of the Mondrians, and not just the one, were made available.