On 2015 Aug 12, Lydia Maniatis commented:

There are many problems with this paper, but the most concrete is that the authors' theoretical position is contradicted by fact.

They are assuming that, if we replace a black check on a checkerboard with a grey one, such that the latter is adjacent to white checks, it will be subject to contrast, and thus appear darker than a grey check replacing a white check, which will (supposedly) lighten due to the adjacent black checks.

Simply based on the fact that contrast tends to occur in the context of a figure-ground relationship, which here is lacking, we might question and test this assumption, rather than treating it as given. DeValois and DeValois (1975) created the corresponding demonstration, which may be viewed here http://www.shapirolab.net/Graphics/Icons/Checker Board Icon.jpg. The check surrounded by white checks lightens, and vice versa. The fact that the checks that the authors' are assuming are undergoing contrast are actually undergoing assimilation completely undermines their arguments.

(Adelson makes the same incorrect assumption about checkerboard contrast here: http://web.mit.edu/persci/people/adelson/checkershadow_description.html)

Beyond this, the authors are attributing the relative lightness of pair of checks appearing to differ in illumination to contrast (incorrectly, as discussed above) and of a pair ellipses to assimilation, when both effects can (only) be explained by the same process of compensation for illumination.

On 2015 Aug 12, Lydia Maniatis commented:

There are many problems with this paper, but the most concrete is that the authors' theoretical position is contradicted by fact.

They are assuming that, if we replace a black check on a checkerboard with a grey one, such that the latter is adjacent to white checks, it will be subject to contrast, and thus appear darker than a grey check replacing a white check, which will (supposedly) lighten due to the adjacent black checks.

Simply based on the fact that contrast tends to occur in the context of a figure-ground relationship, which here is lacking, we might question and test this assumption, rather than treating it as given. DeValois and DeValois (1975) created the corresponding demonstration, which may be viewed here http://www.shapirolab.net/Graphics/Icons/Checker Board Icon.jpg. The check surrounded by white checks lightens, and vice versa. The fact that the checks that the authors' are assuming are undergoing contrast are actually undergoing assimilation completely undermines their arguments.

(Adelson makes the same incorrect assumption about checkerboard contrast here: http://web.mit.edu/persci/people/adelson/checkershadow_description.html)

Beyond this, the authors are attributing the relative lightness of pair of checks appearing to differ in illumination to contrast (incorrectly, as discussed above) and of a pair ellipses to assimilation, when both effects can (only) be explained by the same process of compensation for illumination.