1. Viewpoint-independence and compensation

Richard Wollheim (1980) coined the term ‘seeing-in’ for the special perceptual state associated with seeing pictures. Though few agree with Wollheim’s account of depiction, everyone seems to agree that ‘seeing-in’ is a perfect name for the perceptual state evoked by pictures. When we look at pictures we can see what they are about in them. Seeing-in is a special perceptual state because it is twofold. We see the picture surface, and are aware of it as a colored two-dimensional plane, but we are simultaneously aware of the picture’s content. (Wollheim 1980, 1987, 1998)

Many agree that pictorial experience is sometimes twofold in this manner, but Wollheim was controversial because he insisted that pictorial experience is essentially twofold. One motivation for this view is that it provides a ready explanation of an interesting phenomenon. Wollheim (1980) points out that even though what we see in a picture—from a postman to a piazza—is always depicted from a point of view, we are able to see it in the picture almost independently of the viewpoint we take toward the picture itself. Being aware of the picture surface itself allows us to notice that the picture is oblique to our line of sight. We then compensate for this off center viewing angle, which allows us to see the picture’s content in it, regardless of the poor angle from which we have of the picture.

It is not obvious why twofold experience is needed to compensate for oblique viewpoints, however. Dominic Lopes (1996) responds that “the required information may be processed along with a wealth of other visual information at a ‘sub-personal’ level.” (1996, 48-49) The person-level experience of seeing a picture need not be twofold if sub-personal compensation mechanisms correct for oblique viewing angles. Psychologists like Maurice Pirenne (1970) and Michael Kubovy (1986) side with Lopes. “When the shape and the position of the picture surface can be seen, an unconscious psychological process of compensation takes place, which restores the correct view when the picture is viewed from the wrong position.” (Pirenne 1970, 99) Kubovy, who also cites the Pirenne passage, says “Indeed, the robustness of perspective suggests that the visual system infers the correct location of the center of projection.” (1986, 86) Information about orientation need not be part of the experience of seeing the picture, since it could be used by our perceptual systems without our awareness. What these two approaches have in common is that they insist on some kind of compensation that corrects for odd viewing angles. They differ only concerning the nature of compensation required. A third view, which I defend here, is that no compensation is necessary. Pictorial content is the kind of thing we can access without correcting for oblique views of the picture. This proposal requires recognizing a complexity to pictorial content that many have failed to notice. The next section adumbrates this complexity. Section three points out a special feature of pictures that section four uses to argue against compensation, and section five considers some empirical results that bear on the issue. The weight of evidence is against compensation, though the data are far from conclusive at this point.

2. Bare bones content

It is a commonplace in discussions of pictorial representation that many different scenes can result in the same picture. Ernst Gombrich’s (1961, 249) discussion of the Ames chair demonstrations is perhaps the most famous example of this. Both a chair and a disjoint collection of line segments can result in the same picture. Those pictures in one’s family album certainly represent relatives on different occasions and at different locations, but there is a sense in which they could just as well represent cleverly designed mannequins on cleverly designed sets. These alternative possibilities—chairs and jumbles, relatives and mannequins—have something in common, of course. Pictures in linear perspective, for example, pick out some information about color and illumination and spatial features that are invariant under projective transformations. This is no more and no less than what all of the different interpretations of a given linear perspective picture have in common. Thought of in this way, there is a sense in which pictures represent quite indeterminate states of affairs. If one takes this to its extreme, as John Haugeland does, “...all the photos ‘strictly’ represent is certain variations of incident light with respect to direction....” (1991, 189) Haugeland calls this minimal kind of content the “bare bones” content of a picture.

Bare bones content is a far cry from the “fleshed out” content that we usually ascribe to pictures: relatives, chairs, and so on. In fact, we rarely if ever ascribe bare bones content to pictures. For Haugeland, “The point is…to distinguish, within the undeniable contents of everyday representations, a substructure that is skeletal…” (1991, 189) Bare bones content and fleshed out content are not just two contents that pictures have. The former, though usually unnoticed, constrains the latter: all fleshed out contents must be consistent with a picture’s bare bones content. And though one can flesh out a picture’s content in a myriad of fashions, each picture has only one bare bones content. This skeletal substructure can help resolve the debate over compensation.

3. A special feature of pictures

Once we take on board the distinction between bare bones and fleshed out content, we are in a position to notice an important feature of pictorial representations. In the late 70s, Sherry Levine produced a controversial series of photographs. She made photos of some Walker Evans photographs that were basically indistinguishable from Evans’ originals. This was controversial because she displayed her photos as her own work. In a sense, they are her own work: she made photos of Evans’ photographs while Evans made photos of life in the rural United States. In another sense, their similarity to Evans’ originals makes them seem like mere copies. Controversy aside, this sheds light on an interesting feature of pictures. Many different scenes, like a chair and a jumble of line segments, can result in the same kind of photograph or linear perspective picture from any given point of view. Levine’s photos show that one potential subject for any given picture is a plane that has shapes and colors indistinguishable from the picture itself. So, in a sense, the rural US, a well-designed Hollywood set, or simply a photo like Evans’ could result in a photo like Levine’s. Elsewhere (2003, forthcoming) I relate this to what I call the transparency of pictures. (I thank Aaron Meskin for pointing out Levine’s work to me.)

The bare bones content of a picture tells us that certain colors and rather abstract spatial properties, like being a conic section, being straight, and so on, are instantiated at certain relative locations. Bare-bones content captures what all of the diverse possible sources of a picture have in common and thus that upon which any precisification of the content to something more fleshed out must build. Pictures instantiate the very properties specified by their bare bones contents. Linear perspective, for example, is a way of making pictures based on projections that preserve some feature of what they are created from. The so-called perspective invariants are those abstract spatial properties that the picture itself shares with whatever results in the projection. The Evans photo and a scene from rural life share these invariants as well as some properties like relative brightness. By contrast, if there is some kind of bare bones content to descriptions, there is no reason to think that the descriptions themselves instantiate it. Descriptions generally do not describe themselves, so acquaintance with a description is not generally acquaintance with an instance of its content. This is part of why we seem to have such immediate and intimate access to picture’s contents, as opposed to those of descriptions.

4. Viewpoint-independence without compensation

With this special feature of pictures on the table, we are in a position to address viewpoint independence. First, most instances of pictures’ bare bones contents are three-dimensional, like scenes from one’s family history. One thing about three-dimensional scenes, however, is that they are not instances of the bare bones content of a picture simpliciter. They are only instances of that content from a point of view, which is why we take fleshed out contents to be viewpoint-relative. Three-dimensional scenes generally only satisfy the bare bones of a picture from a certain point in space. Calling this a point of view may suggest that there is something particularly subjective about it, but that is misleading. The point of view of a picture, given a fleshed out content, is just that point in space from which the three dimensional scene in question satisfies the picture’s bare bones content. We can often put ourselves, subjects that we are, at those points, but that does not make the point itself subjective.

Now, pictures are very special instances of their own bare bones contents because they satisfy their own bare bones contents irrespective of viewpoint. The picture is a two-dimensional surface, so every portion of it is visible from any point in space not in the picture plane itself. Whether some object or state of affairs is an instance of a picture’s bare bones content from a given point depends on whether it exhibits the perspective invariants constitutive of that content from that point. A picture exhibits its perspective invariants from any and all points that are not in the picture plane. That is, no matter what perspective one takes on the picture, it has the same perspective invariants. So pictures are instances of their bare bones content from any point of view. Margaret Hagen (1986, 104) points out that “the invariants captured in such pictures [in linear perspective] are exactly those that remain invariant across subjective movements of the observer...” (italics Hagen’s). Again, there is nothing particularly subjective about the points in question, but the picture has its perspective invariants from any of the points from which a subject can view the picture. This is not to say merely that pictures have their bare bones contents irrespective of viewpoint: they do, of course, but so does any other kind of representation. Rather, unlike most instances of the bare bones content of a picture, a picture is an instance that is not relative to some other point in space, such as the points of view characteristic of the other fleshed out instances of a picture’s content.

What does this interesting fact about pictures and their bare bones content have to do with the viewpoint independence of fleshed out content? Since the picture manifests all of its perspective invariants independently of the view we take of the picture, oblique views are just as good as direct views for getting at those invariants. So the viewpoint does not matter as far as bare bones content is concerned. In contrast to Pirenne, Kubovy, Wollheim, and Lopes, we do not need to compensate for oblique views if pictures make their bare bones contents available to us independently of viewpoint. Now, recall that fleshed out content is consistent with bare bones content, so the way we flesh out a picture’s content depends on its bare bones content. If we have viewpoint-independent access to bare bones content, it is reasonable to make two predictions about picture’s fleshed out contents. First, we flesh out pictures’ contents consistently across viewpoints since they afford the same bare bones content (and do not require compensation to do so). Second, if we fail to flesh out a picture’s content consistently between two viewpoints, then the distinct fleshed out contents should both be consistent with the picture’s bare bones content. In this case, one needs an explanation for why the fleshed out content changes, but that is independent of the compensation hypothesis. Both of these questions are empirical and the next section focuses on the first, since it relates directly to compensation. The data suggest that my proposal about there being no need for compensation has decent but inconclusive empirical support.

5. Evidence for and against compensation

Some data seem strongly in favor of compensation. Pirenne (1970) was interested in why certain pictures seem to retain their content through massive changes in viewpoint while others, in particular ceiling frescoes, often look lopsided unless viewed from just the right point. In a letter to Pirenne, Albert Einstein sketched a proposal that Pirenne developed. The claim is familiar by now: when looking at a picture, we have perceptual access to the orientation of the picture plane. This allows us to compensate for the oblique view and thus read the picture correctly. Ceiling frescoes do not give us access to the orientation of their surfaces, compromising compensation and resulting in large distortions. Moreover, conflicting cues for orientation affect picture interpretation. Pirenne illustrates this point with a picture of Nixon standing before one of his campaign posters. The poster is at a rather oblique vertical and horizontal angle to the picture plane. While Nixon looks just fine in the photo, the poster of Nixon looks distorted, and the distortion endures arbitrary changes of viewpoint. Pirenne’s view is that we compensate for the orientation of the picture of Nixon, which forces us to see the campaign poster behind im as askew, regardless of the point from which we view the picture of Nixon. We cannot compensate for the odd view of the Nixon poster by reorienting the picture, so it always looks distorted. By contrast, if we were viewing the Nixon poster itself from an odd angle, it would not look distorted because we could mobilize or compensation resources.

Three predictions follow from the compensation proposal. First in the absence of information about the orientation of the picture, our interpretations should be distorted—as with the ceiling—when the picture is viewed obliquely. Second, if information about orientation is available, then interpretations should not distort even given changes in viewpoint. And third, in the presence of conflicting information—as with the Nixon poster—interpretations should be distorted.

Busey, et al. (1990) tested something like the first proposal on photographs of faces. Subjects viewed the photos at varying orientations, though the cues that would indicate the orientation of the picture plane were removed. Even under these conditions, subjects experienced no so-called “distortions” for pictures rotated vertically by up to 22 degrees. Perceived distortions appeared for horizontal rotations smaller than 22 degrees. Given the lack of access to the picture’s orientation, the undistorted interpretations cannot be due to compensation via adjusting for the angle of the perceived picture. In general, these data are inconclusive because they involve faces. For a long time psychologists have known that people are specially equipped to perceive faces accurately and rapidly under all sorts of conditions, so this may account for at least part of the lack of perceived distortion. Both of Pirenne’s examples involve faces, but they also involve fairly large angles—closer to 45 degrees than to 22—with fairly large horizontal components. Cutting (1987) noticed that though moviegoers noticed no distortion at 22.5 degrees, distortions were evident at 45. (I owe the preceding reference to Sheena Rogers’ (1995) excellent review of literature on picture perception.) Cutting (1988) comes out in favor of compensation for still pictures, following up on results by Goldstein (1979, 1987). In cinema, which was the focus of Cutting (1987), the picture is viewed from a relatively great distance, and information about its orientation is difficult to discern. It would be interesting to know to what extent the distortion of the Nixon poster is reduced when the photograph is viewed under Busey’s conditions, removing information about the picture’s orientation. To my knowledge, this has never been investigated.

Halloran (1989) tested the second hypothesis, to the effect that in the presence of information about surface orientation, there should be no distortions. He found that this is true for small angles, but false for large ones. His study follows up on one by Rosinski et al. (1980) that argued in favor of compensation. Rosinski found no distortions when surface information was available, but Halloran showed that increasing the angles at which the picture was viewed, among other things, produced distortions. Halloran’s data fit well those of Cutting and Busey, who suggest that there is no compensation mechanism at all. There are no distortions for small angles even without knowing the picture plane’s orientation, but distortions appear for large angles. It is likely, then, that we just do not notice any distortion for these small rotations and that large angles are sufficient to alter our interpretations. Rogers (1995, 151) suggests that the data, though in conflict, are overall against compensation. Topper (2000) suggests that compensation is “an experimentally confirmed fact” (119). He leans almost exclusively on Rosinski’s work, however. Though he mentions Halloran, Rogers, Cutting, Busey in the footnotes, he does not point out that these papers call compensation into question.

Some of Jan Koenderink’s, et al. (2004) results test the third prediction, that interpretations should be distorted in the presence of conflicting information. They found little evidence for compensation even when the conflicting information involves 45 degree vertical obliques. In this study, subjects observed a computer monitor on which was depicted a picture in an obvious frame on a brick wall. Subjects viewed the monitor head-on and at a 45 degree angle and were always aware of the monitor’s orientation. The image on the monitor was presented either head-on, in a plane parallel to the monitor’s surface, or at a 45 degree vertical oblique. In the latter case, the picture on the monitor is a picture of the wall, picture frame, and picture as seen from a 45 degree angle. (There were other conditions as well, but they are less relevant to the case at hand.) There was no significant difference in subjects’ interpretations of the oblique presentation while viewing the monitor head-on and the head-on presentation viewing the monitor obliquely. In both cases, the figure was seen as somewhat slenderer than the head-on presentation viewed with the monitor head-on, and the oblique presentation viewed obliquely was, unsurprisingly, the most compressed of all. Though slightly compressed, it did not seem distorted, which suggests that conflicting orientation information does not thwart our interpretations of the picture, contrary to Pirenne’s hypothesis.

The fact remains that Pirenne’s (1970) Nixon example seems skewed irrespective of the view one takes of it. Koenderink’s experiment does not make use of pictures viewed at horizontal obliques or angles with both vertical and horizontal components. The experiment is therefore far from conclusive. The foregoing has also ignored a wealth of data about how interpretations change as one’s distance from the picture plane changes. Those data conflict much as those for oblique angles do. Yang and Kubovy (1999) retreat from Kubovy’s (1986) strongest claims favoring compensation because of data concerning interpretations at different distances from the picture plane. Also, I am unaware of any studies of how interpretations change with distance when pictures are viewed obliquely. There is clearly much more work to be done figuring out how we perceive pictures. For now, the important point is that though there is some support for the compensation hypothesis, it is far from obvious that we compensate. In fact, data strongly suggest we do not, and this fits with the current proposal.

On my account, we flesh out pictures’ contents consistently across relatively small oblique angles because we have viewpoint-independent access to their bare bones contents. No compensation is necessary. This is a way of unpacking Cutting’s (1987) and Busey’s, et al. (1990) suggestion that at these small angles there is no need for compensation. When the angles are large enough to affect the interpretations of pictures, these alternative fleshed out contents seem to be consistent with the picture’s bare bones content anyway. At these angles, depicted objects seem to be compressed, or thinned out. Rogers (1995, 138) points out an apt claim from Gombrich’s Art and Illusion: “if trees appear taller and narrower, and even persons somewhat slimmer, well there are such trees and such persons” (1961, 144). When seen obliquely, the picture occupies a smaller horizontal visual angle. This compression results in a slimmer fleshed out content. A question that has rarely been asked is whether the distinct interpretations of a picture when viewed from varying viewpoints are consistent with its bare bones content. Those who have written on this topic in the past seem to assume that the fleshed out content we assign to a picture when we view it head-on in ideal conditions is the only fleshed out content of the picture, the others being “distortions” of it. This is the wrong way to think of pictorial content and it obscures what the viewpoint-independent access to pictorial content consists in. We have viewpoint-independent access to pictures’ bare bones contents, and this results in consistent fleshing out of those contents across many viewpoints. For now, the main goals of the paper have been met: offer an alternative to the compensation hypothesis and show that is has some empirical support.

To close, here is one case that might make trouble for my account and the compensation hypothesis. We interpret anamorphic pictures quite differently depending on the point form which we view them. In the end, I think that the distinct interpretations of anamorphic pictures are consistent with their bare bones contents, but I cannot argue for that here and it is far from obvious. In any case, anamorphosis is not a friend of the compensation hypothesis. Compensation would suggest that the unintelligibility of anamorphic pictures when seen head on should carry over to when they are seen obliquely, since when seen obliquely we compensate for the odd viewing angle. Alternatively, when we seen an anamorphic picture head on, we should compensate so that we get the content from it that we get when we view it obliquely. Neither option seems to be what happens.

References

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