On 2016 Mar 31, Lydia Maniatis commented:

Todd, Egan & Kallie (2015) provide more demonstrations of violations of the "darker-is-deeper" rule. They note that the rule is already falsified by literature: "the evidence is overwhelming that observers' judgments of 3D shape from shading do not conform to the predictions of [the rule]" (Of course - the possible falsifying cases are infinite in number).

They also note that the rule was falsified by Langer and Bulthoff (2000), who concluded from their observations that "the perception of shape from shading must be based on a process that is more sophisticated that a simple darker-is-deeper heuristic." (Todd et al, 2015).

I wondered whether Chen and Tyler (2015) had cited Langer & Bulthoff (2000) in this paper. Indeed, they do, but the implication is the opposite of the description cited above:

"Langer & Bülthoff (2000) showed that the observer can indeed discriminate between “hills” and “valleys” on a surface with this “dark-is-deep” rule" (Chen and Tyler, 2015). This description conveys a very different and misleading (I would prefer to describe it as dishonest) impression of the results of the cited reference, papering over complications and contradictions to smooth the way to a preferred but non-viable argument.

On 2015 Nov 27, Lydia Maniatis commented:

I just want to expand a little on my previous comment, with regard to the direction of the light source. As I said, the implied direction of the light is front-parallel to the corrugations, but my suggestion that the shadowing is consistent with attenuation due to distance along the normal seems inadequate. I want to add that the putative peaks of the corrugations would tend to reflect light from all directions, not only light coming along the normal, and that the troughs would receive less light because, from some directions, it would be blocked by the protruding sections. (I realise now that this is the point the author was trying to make with the north-south wall example. He is correct but again, that does not mean that the light is not directional, only that it comes from a number of directions. I think that my assumption of fronto-parallel lighting may be more consistent with the patterns than his assumption that the directions form the surface of a half-sphere (the sky), but they might be equivalent.)

On 2015 Nov 27, Lydia Maniatis commented:

In his comment above, CCC says that “The issue of diffuse illumination is a rather minor aspect of the paper...” However, based on the abstract, confirming the “diffuse illumination assumption" is presented as central goal: “These results validate the idea that human observers can use the diffuse illumination assumption to perceived depth from luminance gradients alone without making an assumption of light direction.”

In the authors' stimuli, light does, in fact, have an implied direction – the light source is fronto-parallel to the (apparent) corrugations, such that its intensity is attenuated with distance in the direction along the normal.

As a general fact, the greater weighting of what we could call pictorial cues over binocular disparity in the perception of depth did not require more corroboration. It is evident in the fact that very convincing pictorial depth effects are easy to achieve, despite the zero disparity. Also, with regard to the presence of positive (rather than zero) disparity cues, a relevant reference that was not included is Pizlo, Zygmunt, Yunfeng Li, and Robert M. Steinman. "Binocular disparity only comes into play when everything else fails; a finding with broader implications than one might suppose." Spatial Vision 21.6 (2008): 495-508. (Update 12/2: I apologise, the authors do cite this paper).

In their abstract Langer and Buelthoff (2000) conclude that “overall performance in the depth-discrimination task was superior to that predicted by a dark-means-deep model. This implies that humans use a more accurate model than dark-means-deep to perceive shape-from-shading under diffuse lighting.”

On 2015 Nov 23, Chien-Chung Chen commented:

First of all, it should be noted that this paper is about cue combination, not shape-from-shading per se. The issue of diffuse illumination is a rather minor aspect of the paper, to which most of the discussion in the thread is quite irrelevant.

The commenter’s argument that no shadows are generated under diffuse illumination is a serious misunderstanding of the properties of diffuse illumination. Although, the light comes from every direction, it does not reach everywhere. For instance, suppose one erects a wall running from north to south on an otherwise flat surface. Immediately to the west of the wall, all the light from the east would be blocked by the wall. Thus, this location would receive less light and in turn appear darker than it would be without the wall, effectively forming a diffuse shadow. In short, the light received at a position on a surface depends on the extent of the sky it is exposed to. On an uneven surface, a position in a “valley” would “see” less of the sky than a position on a “hill” and thus would appear darker. This is why under diffuse illumination, darker implies deeper. Notice that, deeper means deeper than the surrounding surface, not from the source of light as the commenter erroneously states.

The difference between the “light-from-above” but with “darker-is-deeper” assumptions is one of the range of scenes to which they apply. It is indeed an empirical issue whether an interpretation that applies to many scenes is a true default or is cued by some aspect of the scene. Our claim is that the directional lighting assumption that is so common in computer graphics is typically cued by the discrepancy between symmetric contour information and asymmetric shading information. (In the case of Ramachandran’s disks, the contour information is circularly symmetric.) This particular discrepancy is a narrow subset of all possible arrangements of contours and shading in images. If this discrepancy is removed, either by making the shading (circularly) symmetric or by making the contours asymmetric, the prediction is that the visual system will not maintain the “light-from-above” assumption but will default to the “darker-is-deeper” assumption. The “darker-is-deeper” assumption is considered the more basic default because it can apply to images with any degree of symmetry or asymmetry. Of all possible visual scenes generated at random, only a small subset will contain symmetries and an even smaller subset will have contour/shading discrepancies consistent with any kind of oblique lighting direction. It is only in the presence of such discrepancies that a default for the lighting direction could come into play.

Finally, it is true that is difficult to separate “darker-is-deeper” and “darker-is-darker-colored” from one instance. However, such heuristics do not depend on one instance but the statistics of nature scenes. In a complex scene, one does not just use one visual cue. “Good shape” is not a necessary condition for darker-is-deeper rule as the complex random stimuli used by Langer & Buelthoff (2000) showed.

On 2015 Sep 26, Lydia Maniatis commented:

You say in the article that under diffuse illumination "light comes from every direction." In that case, there should be no shadows; a uniformly-colored surface should appear uniformly-colored in the image and unevenness (bumps, etc) will not be evident. The fact that you postulate a “darker-deeper” rule indicates that illumination is directional – “deeper” being equivalent to “farther from the source.”

When you say that diffuse illumination is “the default assumption when there is not strong enough evidence to support other interpretations of the scene,” how is this different from my saying that “light from the top right” is the default assumption when there is not strong enough evidence to support other interpretations of the scene?

The information available to the visual system is simply a luminance pattern, which could derive from an infinite number of reflectance/illumination combinations at each point. A “diffuse illumination” assumption – or any illumination assumption – cannot drive a solution to this problem, because it actually cannot decide between the possibilities: “darker is deeper” and “darker-is-darker-colored.” The drivers of the solution are good shape assumptions, combined with the assumption that good shapes have uniform reflectance. So if we have a good shape, (e.g. the Ramachandran bumps) then we assume that the luminance differences are illumination-based, and the illumination assumption follows.

(I would like to add that my earlier comment was deleted by moderators b/c it was a duplication, not b/c it was inappropriate!)

On 2015 Sep 25, Chien-Chung Chen commented:

The commenter seemed to confuse the concept of “default” with “predominate”. The default assumption is like a null hypothesis in statistics. The visual system uses the default assumption when there is not strong enough evidence to support other interpretations of the scene. The commenter seemed to take it that the default assumption meant that the observer would always make this assumption about the scene over other possible interpretations (thus, her statement that we “could not explain why we often perceive illumination to be directional”). With this clarification, it should be clear that in our paper, there is no logical contradiction in our claim that diffused illumination is a visual system default.

On 2015 Aug 18, Lydia Maniatis commented:

The authors claim to their results a. "validate the idea that human observers can use the diffuse illumination assumption to perceive depth from luminance gradients alone without making an assumption of light direction and b. confirm that "observers can recover shape from shading under diffuse illumination on the basis of the “dark-is-deep” rule."

There is a logical problem with the idea that the visual system has a "diffuse illumination assumption," on the basis of which it applies a dark is deep rule.

In viewing a scene, we perceive both the quality of the illumination (including direction) and the albedo of surfaces. Both of these qualities are constructed by the visual system, which must resolve the reflectance/illumination ambiguity. There is no default assumption as to either the reflectance of a particular patch nor the quality of the illumination. Both are inferred on the basis of structural constraints.

For example, in the case of the Ramachandran bumps demonstration, the fundamental choice is between seeing concave or convex circles with a homogeneous reflectance, or seeing part moon shapes of varying reflectances (some dark, some light, some in-between). In the Chen/Tyler stimuli, structural assumptions as to the "best" shape consistent with the stimulus produce a percept consistent with a homogeneously coloured surface under diffuse illumination. If the diffuse illumination assumption came first, we could not explain why we see the corrugations in the obviously flat picture, and we could not explain why we often perceive illumination to be directional. In addition, we can create cartoonish versions of corrugations, in which the deeper dark region is not signalled by a gradient, and still produce a similar impression of dark is deep. If structural assumptions don't favour it, however, dark will not be deep, it will just be dark.

In order to defend an a priori diffuse illumination assumption, the authors would need to explain why the assumption is made only sometimes (i.e. only when structural constraints demand it. )

I would add that their stimuli are not really consistent with diffuse illumination conditions, in the sense that both the upper and lower edges are straight, and thus we must be seeing the corrugated surfaces through a rectangular aperture. The concave sections of the surface would be at some distance from the edge of this aperture and I assume the luminance profile would indicate this in some way, with shadowing, or black holes in the gaps, something.

When it comes to 3D perception, shading follows shape, not vice versa.

On 2015 Aug 18, Lydia Maniatis commented:

The authors claim to their results a. "validate the idea that human observers can use the diffuse illumination assumption to perceive depth from luminance gradients alone without making an assumption of light direction and b. confirm that "observers can recover shape from shading under diffuse illumination on the basis of the “dark-is-deep” rule."

There is a logical problem with the idea that the visual system has a "diffuse illumination assumption," on the basis of which it applies a dark is deep rule.

In viewing a scene, we perceive both the quality of the illumination (including direction) and the albedo of surfaces. Both of these qualities are constructed by the visual system, which must resolve the reflectance/illumination ambiguity. There is no default assumption as to either the reflectance of a particular patch nor the quality of the illumination. Both are inferred on the basis of structural constraints.

For example, in the case of the Ramachandran bumps demonstration, the fundamental choice is between seeing concave or convex circles with a homogeneous reflectance, or seeing part moon shapes of varying reflectances (some dark, some light, some in-between). In the Chen/Tyler stimuli, structural assumptions as to the "best" shape consistent with the stimulus produce a percept consistent with a homogeneously coloured surface under diffuse illumination. If the diffuse illumination assumption came first, we could not explain why we see the corrugations in the obviously flat picture, and we could not explain why we often perceive illumination to be directional. In addition, we can create cartoonish versions of corrugations, in which the deeper dark region is not signalled by a gradient, and still produce a similar impression of dark is deep. If structural assumptions don't favour it, however, dark will not be deep, it will just be dark.

In order to defend an a priori diffuse illumination assumption, the authors would need to explain why the assumption is made only sometimes (i.e. only when structural constraints demand it. )

I would add that their stimuli are not really consistent with diffuse illumination conditions, in the sense that both the upper and lower edges are straight, and thus we must be seeing the corrugated surfaces through a rectangular aperture. The concave sections of the surface would be at some distance from the edge of this aperture and I assume the luminance profile would indicate this in some way, with shadowing, or black holes in the gaps, something.

When it comes to 3D perception, shading follows shape, not vice versa.

On 2015 Nov 27, Lydia Maniatis commented:

In his comment above, CCC says that “The issue of diffuse illumination is a rather minor aspect of the paper...” However, based on the abstract, confirming the “diffuse illumination assumption" is presented as central goal: “These results validate the idea that human observers can use the diffuse illumination assumption to perceived depth from luminance gradients alone without making an assumption of light direction.”

In the authors' stimuli, light does, in fact, have an implied direction – the light source is fronto-parallel to the (apparent) corrugations, such that its intensity is attenuated with distance in the direction along the normal.

As a general fact, the greater weighting of what we could call pictorial cues over binocular disparity in the perception of depth did not require more corroboration. It is evident in the fact that very convincing pictorial depth effects are easy to achieve, despite the zero disparity. Also, with regard to the presence of positive (rather than zero) disparity cues, a relevant reference that was not included is Pizlo, Zygmunt, Yunfeng Li, and Robert M. Steinman. "Binocular disparity only comes into play when everything else fails; a finding with broader implications than one might suppose." Spatial Vision 21.6 (2008): 495-508. (Update 12/2: I apologise, the authors do cite this paper).

In their abstract Langer and Buelthoff (2000) conclude that “overall performance in the depth-discrimination task was superior to that predicted by a dark-means-deep model. This implies that humans use a more accurate model than dark-means-deep to perceive shape-from-shading under diffuse lighting.”

On 2015 Nov 27, Lydia Maniatis commented:

I just want to expand a little on my previous comment, with regard to the direction of the light source. As I said, the implied direction of the light is front-parallel to the corrugations, but my suggestion that the shadowing is consistent with attenuation due to distance along the normal seems inadequate. I want to add that the putative peaks of the corrugations would tend to reflect light from all directions, not only light coming along the normal, and that the troughs would receive less light because, from some directions, it would be blocked by the protruding sections. (I realise now that this is the point the author was trying to make with the north-south wall example. He is correct but again, that does not mean that the light is not directional, only that it comes from a number of directions. I think that my assumption of fronto-parallel lighting may be more consistent with the patterns than his assumption that the directions form the surface of a half-sphere (the sky), but they might be equivalent.)

On 2016 Mar 31, Lydia Maniatis commented:

Todd, Egan & Kallie (2015) provide more demonstrations of violations of the "darker-is-deeper" rule. They note that the rule is already falsified by literature: "the evidence is overwhelming that observers' judgments of 3D shape from shading do not conform to the predictions of [the rule]" (Of course - the possible falsifying cases are infinite in number).

They also note that the rule was falsified by Langer and Bulthoff (2000), who concluded from their observations that "the perception of shape from shading must be based on a process that is more sophisticated that a simple darker-is-deeper heuristic." (Todd et al, 2015).

I wondered whether Chen and Tyler (2015) had cited Langer & Bulthoff (2000) in this paper. Indeed, they do, but the implication is the opposite of the description cited above:

"Langer & Bülthoff (2000) showed that the observer can indeed discriminate between “hills” and “valleys” on a surface with this “dark-is-deep” rule" (Chen and Tyler, 2015). This description conveys a very different and misleading (I would prefer to describe it as dishonest) impression of the results of the cited reference, papering over complications and contradictions to smooth the way to a preferred but non-viable argument.