On 2015 Oct 27, Lydia Maniatis commented:

Perceived slant can be in any direction, not only around the horizontal.

On 2015 Aug 13, Lydia Maniatis commented:

The authors' claim here, that foreshortening is a "cue" to slant, is logically untenable. They define foreshortening as the change in the ratio of width to length (compression), i.e. the difference in the proportions of the object and the proportions of the projection of the object. More specifically, for each of their stimuli, they define this change with respect to a single one of the actually infinite number of 3D object shapes that could have produced the given projection (with some wiggle room since they are assuming orthographic and not perspective projection). But the viewer does not have access to this one object, and thus does not have access to the change in aspect ratio that the investigators have in mind. The shape of the object must be inferred from the projection, on the basis of shape constraints. Having been inferred, the degree of slant/foreshortening then follows as a secondary inference. It is in no way present as a cue in the stimulus/projection.

The reason that the investigators' predictions for the slant of single shapes were confirmed is that the 3D object on which they based their definition of foreshortening was the most regular shape that could have produced the given projection, that is, the 3D shape possessing the characteristics preferred by the visual system when interpreting a projection. If the visual system were partial to skew symmetrical rather than symmetrical shapes, then the stimulus would have been perceived as fronto-parallel with no foreshortening, and the prediction would have failed. Again, foreshortening is not a feature of the 2D stimulus.

The investigators' proposed dichotomy between single shapes and "textures" with respect to the role of the "foreshortening cue" is also false, and results from their failure to appreciate the role of shape constraints. The textures to which they refer were composed of rectangles subjected to orthographic projection. They were compressed/foreshortened, but the compressed projections were similarly rectangular, and thus would not have caused the visual system of the observer to infer a different shape (i.e. the shape based on which the investigators calculated the predicted degree of foreshortening), and thus a non-fronto-parallel orientation plus foreshortening. Rectangles just don't slant, even if they happen to be orthographic projections of taller rectangles.

Also, the discussion by Ivanov et al seems to take it for granted that the direction of foreshortening is from top to bottom as happened to be the case for their stimuli (since they treat it as a given), but the visual system may infer foreshortening in any direction, it just depends on the shape of the projection and what is required to regularise it as much as is consistent with the projection.

On 2015 Aug 13, Lydia Maniatis commented:

The authors' claim here, that foreshortening is a "cue" to slant, is logically untenable. They define foreshortening as the change in the ratio of width to length (compression), i.e. the difference in the proportions of the object and the proportions of the projection of the object. More specifically, for each of their stimuli, they define this change with respect to a single one of the actually infinite number of 3D object shapes that could have produced the given projection (with some wiggle room since they are assuming orthographic and not perspective projection). But the viewer does not have access to this one object, and thus does not have access to the change in aspect ratio that the investigators have in mind. The shape of the object must be inferred from the projection, on the basis of shape constraints. Having been inferred, the degree of slant/foreshortening then follows as a secondary inference. It is in no way present as a cue in the stimulus/projection.

The reason that the investigators' predictions for the slant of single shapes were confirmed is that the 3D object on which they based their definition of foreshortening was the most regular shape that could have produced the given projection, that is, the 3D shape possessing the characteristics preferred by the visual system when interpreting a projection. If the visual system were partial to skew symmetrical rather than symmetrical shapes, then the stimulus would have been perceived as fronto-parallel with no foreshortening, and the prediction would have failed. Again, foreshortening is not a feature of the 2D stimulus.

The investigators' proposed dichotomy between single shapes and "textures" with respect to the role of the "foreshortening cue" is also false, and results from their failure to appreciate the role of shape constraints. The textures to which they refer were composed of rectangles subjected to orthographic projection. They were compressed/foreshortened, but the compressed projections were similarly rectangular, and thus would not have caused the visual system of the observer to infer a different shape (i.e. the shape based on which the investigators calculated the predicted degree of foreshortening), and thus a non-fronto-parallel orientation plus foreshortening. Rectangles just don't slant, even if they happen to be orthographic projections of taller rectangles.

Also, the discussion by Ivanov et al seems to take it for granted that the direction of foreshortening is from top to bottom as happened to be the case for their stimuli (since they treat it as a given), but the visual system may infer foreshortening in any direction, it just depends on the shape of the projection and what is required to regularise it as much as is consistent with the projection.

On 2015 Oct 27, Lydia Maniatis commented:

Perceived slant can be in any direction, not only around the horizontal.