On 2017 Mar 29, Lydia Maniatis commented:

This explanation of the Cornsweet effect, in terms of the assumption of uneven illumination, has fundamental theoretical problems.

The explanation involves a particular variant of the figure, in which the luminance gradient occurs after a stretch of homogeneous luminance. The authors construct a figure that looks like a pair of adjacent, curved and receding surfaces. Each surface contains the luminance pattern of one rectangle of the Cornsweet. The pictorial context in which the authors have embedded them produces a percept in which the luminance changes are explicitly (that is, perceptually) attributed to illumination changes occurring over two differently-colored surfaces. The authors argue that this more complex context and the physical situation corresponding to the associated percept is the most “probable” cause of the simpler, two-rectangle version, and that the visual system therefore interprets it as such. There are several serious problems with this argument.

First, Purves et al's (1999) figure can be described as anything but "probable." I have rarely or never seen anything structured remotely like it in the human or natural environment. And, while in the published images the apparently brightly-lit side is oriented either upwards or sideways, the apparent colors of the two sides DON"T CHANGE if we view it upside-down, even though illumination from directly below is, of course, highly improbable. So the argument from probability doesn't seem valid on its face. (Also, see below)

Second, the Purves et al (1991) figure is very different in form from the two simple Cornsweet rectangles lying side-by-side. To say that this pair of rectangles is being interpreted as a very different structure - while continuing to look just the way they do - e.g. flat and coplanar, rather than curved and sharply bent at the common edge - is awkward. We are in effect dealing with the converse of the notion of “unnoticed sensations.” Here, it is a complex, 3D figural interpretation which is supposed occur but go unnoticed. And it is supposed occur even though the right angles and parallel sides of the Cornsweet figures are not typically perceived as, and as retinal projections do not typically correspond to, receding surfaces. Here, the probability argument works against the authors account; in their figure, they take care to use converging edges.

Third, Purves et al still haven’t addressed, let alone explained, the Kersten-Knill (1991) version of the Cornsweet illusion, which, within each rectangle, grades evenly from left-to-right and is perfectly consistent with two half-cylinders lit from one side (as is evidenced by the right half of the Kersten-Knill demonstration). Luminance variations consistent with cylindrical surfaces are typically perceived as such, even when lacking the type of formal cues added by Kersten and Knill. We see this in the case of the "sinusoidal patches" commonly employed in the vision literature, sometimes referred to as "sinusoidally-corrugated surfaces" (e.g. Chen and Tyler 2015, PLOS one) because of the strong impression of 3D relief they create. On the basis of Purves et al's explanation of their Cornsweet variant, the two halves of the Kersten-Knill variant should appear similarly-colored. But they don't.

It should be clear that the explanation offered by Purves et al (1999) is no explanation at all, but a purely ad hoc account, a pictorial bagatelle which simply turns a blind eye to theoretical difficulties and inconsistencies.

On 2017 Mar 29, Lydia Maniatis commented:

This explanation of the Cornsweet effect, in terms of the assumption of uneven illumination, has fundamental theoretical problems.

The explanation involves a particular variant of the figure, in which the luminance gradient occurs after a stretch of homogeneous luminance. The authors construct a figure that looks like a pair of adjacent, curved and receding surfaces. Each surface contains the luminance pattern of one rectangle of the Cornsweet. The pictorial context in which the authors have embedded them produces a percept in which the luminance changes are explicitly (that is, perceptually) attributed to illumination changes occurring over two differently-colored surfaces. The authors argue that this more complex context and the physical situation corresponding to the associated percept is the most “probable” cause of the simpler, two-rectangle version, and that the visual system therefore interprets it as such. There are several serious problems with this argument.

First, Purves et al's (1999) figure can be described as anything but "probable." I have rarely or never seen anything structured remotely like it in the human or natural environment. And, while in the published images the apparently brightly-lit side is oriented either upwards or sideways, the apparent colors of the two sides DON"T CHANGE if we view it upside-down, even though illumination from directly below is, of course, highly improbable. So the argument from probability doesn't seem valid on its face. (Also, see below)

Second, the Purves et al (1991) figure is very different in form from the two simple Cornsweet rectangles lying side-by-side. To say that this pair of rectangles is being interpreted as a very different structure - while continuing to look just the way they do - e.g. flat and coplanar, rather than curved and sharply bent at the common edge - is awkward. We are in effect dealing with the converse of the notion of “unnoticed sensations.” Here, it is a complex, 3D figural interpretation which is supposed occur but go unnoticed. And it is supposed occur even though the right angles and parallel sides of the Cornsweet figures are not typically perceived as, and as retinal projections do not typically correspond to, receding surfaces. Here, the probability argument works against the authors account; in their figure, they take care to use converging edges.

Third, Purves et al still haven’t addressed, let alone explained, the Kersten-Knill (1991) version of the Cornsweet illusion, which, within each rectangle, grades evenly from left-to-right and is perfectly consistent with two half-cylinders lit from one side (as is evidenced by the right half of the Kersten-Knill demonstration). Luminance variations consistent with cylindrical surfaces are typically perceived as such, even when lacking the type of formal cues added by Kersten and Knill. We see this in the case of the "sinusoidal patches" commonly employed in the vision literature, sometimes referred to as "sinusoidally-corrugated surfaces" (e.g. Chen and Tyler 2015, PLOS one) because of the strong impression of 3D relief they create. On the basis of Purves et al's explanation of their Cornsweet variant, the two halves of the Kersten-Knill variant should appear similarly-colored. But they don't.

It should be clear that the explanation offered by Purves et al (1999) is no explanation at all, but a purely ad hoc account, a pictorial bagatelle which simply turns a blind eye to theoretical difficulties and inconsistencies.