On 2015 Aug 20, Lydia Maniatis commented:

The author says that “If... [slant] judgments were based on scaling contrast or scaling gradients, then surfaces viewed under orthographic projection should all appear fronto-parallel. In order to evaluate these predictions, it is useful to consider the image of a planar surface under orthographic projection in Figure 3D.”

This is not a fair test. Figure 3D was constructed on the basis of a set of upright rectangles. Under orthographic projection, we still have upright rectangles, and the visual system treats projections shaped like rectangles as fronto-parallel, regardless of their source. If the rectangles had been tilted (resulting in parallelogram-shaped projections), or if we were dealing with circles instead of rectangles (producing elliptical projections), then the orthographic projection would not appear fronto-parallel.

The failure to take shape into account is typical of many studies on slant (e.g Ivanov et al 2014; Saunders and Chen 2015). But shape, whether collected in a “texture” or individually, is dispositive in slant perception and it needs to be explicitly considered, or else results will be inconsistent and uninterpretable.

The idea that foreshortening could even be a potential cue to slant is logically untenable, as I explain in a comment on Ivanov et al (2014).

I would also note that in the perspective projections in Figure 3, edges and objects are visually grouped to produce oblique lines, more so for the larger slants. It is known that obliques tend to be perceived as receding (e.g. Deregowski and Parker 1992). This presents a confound very difficult to disentangle from other suggestions.

On 2015 Aug 20, Lydia Maniatis commented:

The author says that “If... [slant] judgments were based on scaling contrast or scaling gradients, then surfaces viewed under orthographic projection should all appear fronto-parallel. In order to evaluate these predictions, it is useful to consider the image of a planar surface under orthographic projection in Figure 3D.”

This is not a fair test. Figure 3D was constructed on the basis of a set of upright rectangles. Under orthographic projection, we still have upright rectangles, and the visual system treats projections shaped like rectangles as fronto-parallel, regardless of their source. If the rectangles had been tilted (resulting in parallelogram-shaped projections), or if we were dealing with circles instead of rectangles (producing elliptical projections), then the orthographic projection would not appear fronto-parallel.

The failure to take shape into account is typical of many studies on slant (e.g Ivanov et al 2014; Saunders and Chen 2015). But shape, whether collected in a “texture” or individually, is dispositive in slant perception and it needs to be explicitly considered, or else results will be inconsistent and uninterpretable.

The idea that foreshortening could even be a potential cue to slant is logically untenable, as I explain in a comment on Ivanov et al (2014).

I would also note that in the perspective projections in Figure 3, edges and objects are visually grouped to produce oblique lines, more so for the larger slants. It is known that obliques tend to be perceived as receding (e.g. Deregowski and Parker 1992). This presents a confound very difficult to disentangle from other suggestions.