Wednesday, 6 October 2010

Runeson, the Ames Room and the Irrelevance of Equivalent Configurations

Recently we’ve been discussing several topics with Ken Aizawa at his blog, The Bounds of Cognition; there are several posts brewing from the two of us on this, but some travelling (plus, for me, a broken wrist) has slowed things a little.

I want to spend some time talking about some recent discussions on aperture vision and the Ames Room. This post will go over two papers on the Ames Room; the next few will discuss some of the more interesting points about the ecological approach that came out of the discussion with Ken. This is a really rich topic, and there’s a lot of ground. First, though, we need the set up.

The discussion began with a question from Ken: why not study what Gibson disparagingly referred to in this quote as ‘aperture vision’?
The eye is easily deceived, and our faith in the reality of what we see is therefore precarious. For two millenniums we have been told so.
     The purveyors of this doctrine disregard certain facts. The deception is possible only for a single eye at a fixed point of observation with a constricted field of view, for what I called aperture vision. This not genuine vision, not as conceived in this book. Only the eye considered as a fixed camera can be deceived. The actual binocular visual system cannot. (Gibson, 1979, p. 281)
But given that you can pull these kinds of tricks on the eye (via visual illusions), why not study it, in order to be complete?

The clearest example of such an illusion is probably the Ames Room, a room that is actually a trapezoid but which contains motion-independent information designed to make the room appear to be square from one specific viewing location (see image, plus the Wikipedia page has a video). Person A is actually further away than Person B but the static structure makes them appear to be at the same distance: Person A looks very small, Person B appears large, and if they swap they appear to grow and shrink very inappropriately. 

The geometry of the Ames Room
The trapezoidal room and the square room are equivalent configurations, layouts which project to the same optical circumstances and thus cannot be distinguished on the basis of the visual information. Non-ecological accounts of perception point to this as an example of the ambiguity of perception (the true, trapezoidal shape isn’t specified, as evidenced by your inability to see it) and that visual perception requires supplementary assumptions (about, for instance, the proper/customary shape of rooms) to resolve this ambiguity in favour of the square interpretation. The Ames Room is taken as an example of the existence of such configurations and ambiguity, which, if true, clearly undermines the ecological approach.

I have to admit, my instinct is to simply not worry about things like the Ames Room. The effect, while compelling from the right viewing point, breaks as soon as the viewing restrictions are lifted, and this fragility makes 'seeing the square interpretation' fairly uninteresting to me. Gibson’s point was that we don’t actually have an aperture vision system; the basis of vision is not the ‘simpler’ aperture, so why get overly excited about these fake, impoverished tasks? However, an empirical paper by Gehringer & Engel (1986) that claimed to test Gibson’s claims about the Ames Room sparked an excellent ecological rebuttal and analysis by Sverker Runeson, an ecologically minded psychophysicist (he of the polar planimeter). Addressing the task rigorously does end up making many valuable points that are worth spending some time on, so I’ll swallow my pride and talk about illusions again.

Gehringer & Engel (1986) tested the magnitude of the illusion under standard vs. more ecological viewing conditions (head fixed vs. free to move, monocular vs. binocular, + a condition where they could walk around as much as they wanted). The task was size matching; they were shown a 30mm diameter disc in one corner as a standard and asked to select another disc in the other corner that looked the same size (the method to find the ‘point of subjective equality’). The far corner was twice the distance of the near one, so a disc at A should be actually 60mm diameter to look like the 30mm disc at B. The magnitude of the illusion was the difference in size between the standard and matched disc, with 30mm equal to a 100% effect.

The worst case was the restricted, monocular viewing (error = 21.61mm); however, the effect decreased in size as viewing restrictions were relaxed until it was 7mm in the binocular free head movement case, and merely 2.6mm when the observer could walk around. The authors, however, concluded that Gibson was wrong because this final residual effect was still statistically significant, and thus illusions and assumptions are indeed real contributors to perceptual experience even under ideal viewing conditions:
If Gibson's claim were merely that illusions, such as the DRI, diminish with increased environmental contact on the part of the perceiver, the evidence of this study would provide unequivocal support for Gibson's theory.… However, Gibson's claim was not simply that illusions will be modified in a veridical direction as one adds further information, but rather that if access is allowed, the actual spatial layout will be picked up. This latter concept leaves no room for any perceived rectangularity in viewing a trapezoidal three-dimensional configuration. Nevertheless, the results suggest that the illusion is present, to some degree, even under the optimum conditions of observation. Therefore, in this instance of a three-dimensional spatial layout, perceptual organization cannot be said to be wholly determined by the environmental-optical structure….To us, however, the results suggest that factors other than the simple pickup of information in the ambient optic array are involved in the perception of the distorted room. (Gehringer & Engel, 1986, p. 185)
Way harsh, dudes, given that the residual effect in a judgment task was 2.6mm – statistically reliable but not exactly damning in its magnitude (and I wonder if anyone’s done a reaching task in an Ames Room setup?) But the last sentence is effectively Ken’s question, and given I didn’t want to break a sweat on ‘mere aperture vision’ I had a quick Google Scholar search which led me to Runeson (1988), who had decided to rise to the challenge.

Runeson’s reply
Runeson’s first point is to say ‘way harsh, dudes’, also highlighting some clear limitations of the judgment methodology (for more on the action vs. judgment measure issue, see Bingham & Pagano, 1998 and perhaps a future post). Apparently this is what the ecological approach is up against: you break a huge illusion like the Ames Room down to a 2.6mm error and it’s still not good enough!

Runeson’s second point was to remind everyone what Gibson actually said on the Ames Room; that if you get to explore it becomes immediately obvious that the room is skewed - qualitatively not a rectangle. Gehringer & Engel’s claim that Gibson predicted a perfect, quantitative perception is incorrect:
Given their experimental technique, Gehringer and Engel's argument would furthermore require that the ecological approach proposed perfect isomorphism even at the level of elementary Euclidean size measures and for arbitrary, small, and detached objects at that. There is no support for this in the Gibsonian position. In fact, Gibson discouraged such a view and proposed that special metrics be developed to fit the requirements for perception and action in organisms, as exemplified by the concepts of layout and affordance (Gibson, 1966, 1979, chap. 8). (Runeson, 1988, p.296)
(Ken worried (e.g. here and here) that this somehow implied Gibson banished the concepts of physics and geometry from psychology, making Runeson’s use of both later on a contradiction. This isn’t true, and I’ll return to this point in a later post.)

Third, Runeson points out that there are multiple potential sources of information about the shape of the room to which participants had varying levels of access in this study (binocular, motion based, motion-independent monocular). In the world, these generally agree due to the lawful nature of the projection of world properties into perceptual variables. In the Ames Room, however,
…motion-independent monocular information has been meticulously manipulated to specify the wrong room shape. When the perceiver is deprived of the other types of information, he or she is at the mercy of what the static view is specifying, and thus illusion results. When, as in the experiment, motion based and binocular information is also made available, conflicting information results because the motion-independent information remains present (Runeson, 1988, p. 297)
Gibson makes two points about this circumstance; first, in cases where information is conflicting, it’s not ever clear a priori which information a perceiver will use (and when the various information sources calibrate each other, the potential uses multiply). Second, perception is skilled performance; different perceivers will have access to different information with varying levels of skill. The exact usage that emerges must be empirically determined. What you could safely predict, however, is exactly what Gehringer & Engel found, namely a decrease in the magnitude of the illusion as other sources of information were made available.

Fourth (and I’ll come back to this point in more detail later), Runeson makes an argument that perceptual systems need not know how to cope with all the technically possible geometric configurations that can give rise to a given static optic array (i.e. equivalent configurations). First, ecological vision (as conceived of by Gibson) tends to solve the problem entirely by providing the necessary disambiguating information. Second, even if vision was derived from static arrays, the number of actually possible configurations which can produce the same static array is tiny compared to the number of technically possible configurations – ‘prevailing physical and ecological constraints’ such as gravity, etc all act to make it so. The Ames Room, while technically possible, is the result of careful reverse engineering from a static optic array specifying a square room to the one trapezoidal room that matches that static array; it is not an ecologically actual possibility. The net result is that the odds of an organism regularly encountering (and thus having to deal with) equivalent configurations requiring additional disambiguation is staggering low, if not zero. The ‘smart’ solution is therefore to build a system that doesn’t include any unnecessary assumptions about what might happen, but rather is attuned to the environment in which it actually evolved. In fact, it’s not even clear how mere possibility could even get into the evolutionary equation to affect the development of a perceptual system:
Here it becomes even more obvious that the argument from equivalent configurations is mistaken. Optical patterns can be deliberately generated in many ways: carpentry, model building, painting, photography, shadow casting, electronic displays, and so forth. Undoubtedly, new types of equivalent configurations will be contrived as analytic and technological tools improve. If each dimension on which equivalent configurations can be generated is taken to prove the existence of an ambiguity that requires perceivers to hold a corresponding antidotal assumption, then one would be forced to the absurd conclusion that perceivers have already acquired assumptions to cover each of the ambiguities that will become realizable in the future. Hence, the equivalent configurations figuring in perceptual theorizing are more appropriately understood as hypothetical, occasionally material, artifacts than as discoveries about nature. (Runeson, 1988, p.303)
The Ames Room illusion depends on there being two different physical configurations that lead to the same static optic array; this many-to-one ambiguity was long assumed to be the basic problem of perception until Gibson rejected this assumption of ‘necessary proximal ambiguity’ (an assumption which Turvey, in his trademark style, has apparently given the magnificently overpowered name, the ‘doctrine of intractable nonspecificity’). Runeson explains how, for the specific case of the Ames Room, that even though it was technically possible to build this equivalent configuration, it wasn't ecologically likely enough to have influenced the development of a smart perceptual mechanism attuned to the ecological constraints of its environment; in fact equivalent configurations are so ecologically implausible that it’s not even clear how a perceptual system could begin to acquire the necessary assumptions the cognitive approach claims it requires to cope).

Following on from this, I’ll talk in more detail about this odd concern that Gibson banned physics from psychology, and more on the equivalent configurations issue, because these were two key issues that emerged in discussions with Ken that I think really deserve some attention.

Bingham, G.P. & Pagano, C.C. (1998). The necessity of a perception/action approach to definite distance perception: Monocular distance perception to guide reaching. Journal of Experimental Psychology: Human Perception and Performance, 24 , 145-168. Download

Gehringer, W., & Engel, E. (1986). Effect of ecological viewing conditions on the Ames' distorted room illusion. Journal of Experimental Psychology: Human Perception and Performance, 12 (2), 181-185 DOI: 10.1037//0096-1523.12.2.181 (Download)

Runeson, S. (1988). The distorted room illusion, equivalent configurations, and the specificity of static optic arrays. Journal of Experimental Psychology: Human Perception and Performance, 14 (2), 295-304 DOI: 10.1037//0096-1523.14.2.295 (Download)


  1. Excellent post. I don't really have anything to add since I agree with everything you say. I'm looking forward to the rest of the posts in this series!

  2. Ok. But, this still does not address the issue of robustness of Runeson's solution. The "all of the equivalent configurations but one are so implausible that evolution ignores them" reply seems to be a pretty broad generalization from the apparent success in *one* case. And, indeed, that's the point of my drawing attention to the case of amodal completion in this post:

  3. You're right, at one level; but Runeson (and Gibson) repeatedly make the argument that identifying what a perceiving organism has learned to use is an empirical question, because of the richness of options. The full research programme on any question requires analysis of the information available that might do the trick, and empirical testing to see which ones are actually used (for example see this paper by me & Geoff which I aim to post about in the coordination series.

    So you're right, it is a bit of a generalisation at one level. But actually it's a statement of theoretical principle that is empirically testable; 'smartness' like this has numerous advantages over 'rote-ness' and when possible you'd expect to see it - figure out the smart, task specific solutions for each task and go look see. Framed this way, it's less over-generalisation and more testable hypothesis that will either work or not work.

    The amodal completion task is still on my mind, but I may not get to it right away while I think out loud some more about these issue to clarify my thinking.

  4. Speaking of equivalent configurations: shadow art is another example of how fragile and viewpoint-dependant these are, plus they reflect the idea of having to have been meticulously reverse-engineered.

  5. The shadow art examples are fascinating.

    But, one can get a sense of what folks like Richard Gregory where talking about in "massive ambiguity" if you think about people not perceiving a table with a hole in it covered by a book or whole objects instead of fronts of objects. This is something that Alva Noe tries to handle from a kind of Gibsonian perspective. (Runeson mentions the table case in his Ames room paper.)