Information theory and figure perception: The metaphor that failed
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INFORFVIATION THEORY AND FIGURE: PERCEPTS
THE IvlETAPH8R T FAlLED
IR. T. GREEN AND M. C. CCKJRlliIS Wnivemity College, London, Englmd
When, in its omnivorous way, information theory got its teeth into the probEem of figure: perception it looked as if the struggle was all over bar the shouting and, of course, a bit of data collection to round out the pictme. ATTSEAVE (1954j made an exciting contribution along these lines, and later developments, ATTNEAVE (1955, 1957), ATTNEAVE and ARNQULT (195&j., did not seem to run counter to the signposts first planted. Related contributions were being made at :ibout the same time by WOCHBERG and MCALTSTER (l953), and WEINSTEIN and F~TTS ( 1954).
More recently, ho-Never, tLrere have been indications that all is not well, and that this type of approach, although interesting methodologi- cally, has its limitations. The basic premises undfxpinning the appli- cation of information theory to figure perception, and the specific predictions made by the theory are both now receiving closer attention.
obliquely so far as CR~NBACH (1995), It has been pointed be brought to bear met. Among these
The basic position has been undermined, albeit figure perception is concerned, by GRANT (1954), TOIM (W56) and C%ENRY (I!?57 a, b) in particukr. out that before infornlation theory can legitimately on any problem certain requirements have to be requirements are:
(1) There is an agreed alphabet of signs with known and constant prob3bihtiles of occuaence,
(21 These probabihties are objective. (E.g. the probability of occx- renc~: of a given lets:r in written English can be established by standard
ng procedures to arrive at an estimate that is in principle ndent of the person conducting the operation).
Both requirements are readily fulfililed in the original context in which information theory was developed by WIENER (1948J and SHANNQN and WEW~~~ (1949), w ich arose from the problems connected with
pacities of comm ication channels. ement, however., 1s manife?t?y not fulfilled in the eption unless the ._ y :yerimenter intervenes. To meet ent the experimeii-a- is obliged to impose certain
conditions upon the task presented to the subject. Firstly, he must Deane the alphabet; that is, brea,k the figure up into a mosaic of elements and specify the possible attributes of those elements. In ~T~N~A~E~s (1954) ca these elements are small squares, each of which may take tine of ree colourq. Then, he must impose a temporal sequence on the prcse~tation of these elements to the subject. This procedure leaves Attneave open to two kinds of criticism: (a) the task as presented to the subject no longer has anything to do with figure perception, Ib) the conditions imposed are entirely arbitrary, producing artifacts pertaining onIy to those conditions, rather than leading to the formulation of general principles.
As for the second rsquirement, this is flagrantly violated. It is tacitly assumed that subjective PiJbabilities mirror objective probabilities. That subjective probabilities are related t,o objective probabilities is demonstrable; that there are systematic discrtzpancies between objective and subjective probabilities is just as firmly established by a wealth of experimental material. Ironically enough, ATTNEAVE (1953) has done his share in this direction.
Before analysing these arguments in greater detail there is something to be said for testing several of the more direct assertions made by Attneave. If in fact his approach makes the right predictions, and can be shown to be independent of the arbitrary conditions imposed by the experimenter, then there is less need to cavil at the desecration of information theory.
One of the assertions made by ATTNEAW (1954, p. 184) is !!r;lt the information contained in a figure is concentrated along its contours, par:icularly at those points where the contlour changes direction mo:;t sharply. The first part of this assertion is little more than the rephrasing of the common sense statement that a homogeneous area has, by defi-
14 8. T. GREEN AND P/I. C. COURT.IS
nition, no shape. Only the edges of a lomcgeneot7s area can tell us anythkag about the shape of that area. This would appear to be a truism -incontestable, but not very illuminating. aradolically, as we shall see, it also happens to fall some way short of the tmth.,
The second part of the assertion is highly questionable. Information is here. meant to be selecti.ve information and corresponds to the predictability of a given state of affairs. For corners to have a high information content they must have a low probability o be d&cult to predict from other parts of the figure. not so. On the contrary, corners become highly predictable once infor- mation is available about other parts of the contour.
In his origina! demonstration Attneavr: used a figure and a scanning sesluence that lent credence to his assertions. The figure used represented * a bottle of ink (black) on a table (brown), laid out in a 50 ?( 80 matrix. (See fig. 1). Starting at the tom left hand corner the subject was required to gues: the colour each square in turn (black, white or brown), proceeding from left to right in ascending rows until he reached the top right hand corner. This procedure r*nakes the prediction of the corner of the table practically impossible. Any corner on the left hand side of the figure is just as impossible to predict, although, due to symm&ry, corners on the right hand side become highly predictable.
Attneave was not entirely unaware of the dangers inherent in this particular scanning sequence. e states (1954, p. 184): Our scanning procedure introduces a certain artifact here, in that a particular subjec::
1. Illustration of redundant visual stimulation (after Attneave 1954).
lNFORMATION T EORY AND FIGURE PERCEPTION 15
make errors a linear contour only the first few times he crosses t is fairly ob he starting point of the sequence and the
direction of scan randomly over a large number of sub- jects, su ated errors would e distributed evenly along suieh a
oes not, however. draw the further conclusion that the unpre- e table is largely an arzifact of this same
Ai172. o show that the distribution of errors made in building up a re is dependent on t e guessing sequence used, and in particular
that errors do not necessarily accumulate at points where the contour of the figure changes direction most sharply.
Appuram. A wooden board, with a surface divided into a matrix of 400 half inch squares (20 X 2Cj. Each subject was provided with half inch wooden blocks and half inch per;pex blocks which were to fo the figure and ground of the pattern rSzspectively.
Subjecrs. Eight men and eight women fr a college populntion. PPoceQure. Two kinds of guessing seque were compared. Group L. Linear scanning. A guessing sequence very similar ~3
Attneaves in which successive guesses were adjacent and in whiL!k the subject started guessing at the bottom right hand corner of the board and guessed from right to left along each row until he arrived at the top left hand corner.
Group R. Randomised scanning. A guessing sequence in which * tccessive guesses were dispersed over the whole :Irea of th.c boa!,d in a random manner.
The pattern which the subjects were required to build up by guess- work was chosen for its lack of symmetry and its straight line contours
The naure of the task was explained to the subject, who guessed whether each square was part of the figure or ground as it was presented to him, trying to make as few errors as possible, After each guess; the appropriate block was put in place.
Results. The distribution of errors for the two groups are given ifl figs. 3a and 3b. As may be selen, group L produces errors in hne with
- / -
Fig. 2. A less redundant pattern.
-I- \ r .- [ -
-- :--- ---
1 . ..^
-1. I .~--
g. 3. Ia) Distribution of errors, group E.
~wever. reveal9 an tircly diflcrent picture. sequence pro-
racteristic: that rrors to occur
e contour rather than the areas.
ake significanrly more errors at corners than
onstration makes it clear that: (a) errors do not necessarily collect at the corners of a figure, (b) the number and location
errors is a function of the scanning procedure, so that general state-
18 R. T. GREEN ANTI M. C. COURT.IS
men,ts about the location of information cannot be derived from an experimental technique of this sort.
Attneave (1954) supported his assertion about information being concentrated at points of maximum curvature with another kind of argument. He displayed irregular closed line figures and required his 80 subjects (1954, p. 185) . . . . to draw, for each of sixteen outlined sl~pcs, a partern of ten dots which would resemble the shape as closely as possible, and then to indicate on the original outline the exact places which th: dots represente,d. There was a definite tendency for dots to be placed corresponding to points of maximum curvature.
This technique, too, may readily be shown to be a vehicle for artifacts. By choosing suitable figures and numbers of dots it is possible to con- firm or refute Attneaves assertion. Show your subject a square and allow him four dots and he will place them at the four corners, precisely according to ahe principle. Give him eight dots and he nearly always places the other four smack in the middle of each side, precisely opposing the same prlncipte. Display an ellipse and his behaviour is slightly more variable. Four dots are usually placed as in fig. 4a, thereby confirmitlg aJud refuting the principle. Out of 57 subjects, 49 gave this responsti_ Occasionally, they are placed as in fig. 4b, which is a kind GF compromise between the principle and its converse. Six subjects did this. The remainiug two subjects gave schizoid responses, their dots bearing no obvious relation to the figure. When allowed eight dots the most common response is to place them at roughly equal intervals round the perimeter. In thr. example given by Attneave the fi.gure has certain characteristics that may help to account for his results. It is irregular, has no straight linet, nor smooth curves. Again, it would seem, the results are task specific and do not lead unequivocally to the formulation of a general principle of the type asserted.
Fig. 4. (a) USUZI~ location cpf dots. (b) Common alternzitive.
INFORMATION THEORY AND FIGURE PERCEPTION 19
. . . *
* . . . . . .
. * 6
Fig. 5. (a) Drawing made by abstracting 38 points of maximum curvature from the contours or a sleeping cat, and connecting these points appropriately with a straightedge (after Attneave 1954). Cb1 Broken contour, corners omitted. (cl Broken contour, corners included. (d) Points of maximum curvature.
Attneaves final argument draws upon the fact that (1954, p. 185): Common objects may be represented with great economy, and fairly striking fidelity, by copying the pointc at which their contours change direction maximally, and then connectiag these points appropriately with a straight edge. This was ihustrated, as in fig. 5a, by a sleeping cat. This same, drawing can be treated rather differently by leaving out the points and retaining the centre portions of the lines, as in fig. Sb. The linkeness to a cat is no longer so orvious as in the original, but is probably little worse than that obtained by omitting the other half of the lines and keeping the corners, as in tjg. 5c. The 38 dots representing points of maximum curvature, fig. Sd, Seem to convey little on their own. A reasonable conclusion to draw from this exercise is that points of maximum curvature carry little information per se. Only when directbn is indicated does the $gure take shape, and this function may be per- formed by various parts of the comour, not necessarily those parts
20 R. T. GREEN AND nc c. COURTIS
encompassing comers. shape and of a on a head is least as drawing in the lower as it be if half enclosing corner were
pursue this of thought may turn the practices professional cartoonists. are three styles in use. The of these the line of heavy with little
to introduce quality. Peunctts, and Donald are f&z in this Then, in more sophisticated comes the drawing with often delicate, to form pattern of and shade in line a photographic
The Rip Carol Day Gun Law are familiar of this of treatment. sophisticated of and
relatively is a patchwork style which shape con- veyed cunningly contrived and patches, being indicated than drawn. Hodson is outstanding exponent
is technique. (See figs, 6a-h.) A comparison of these three styles may throw some light on figure
perception in its natural habitat. The task confronting a cartoonist is to represent in black and white some more or less familiar part of our visual world in a re~ognis;tble form. A photograph does the job exactly, an41 the chiarascuro style is an approximation to this. For this reason it i; the least interesting of the three techniques in the present context. Ht is when the cartoonist aims for a more economical style that we begin to see how complexity may be reduced without loss of vital features- how an impression may be conveyed without supplying all the material. In simple fine drawings subtleties of Bight and shade are ignored or only crudely indicztcd. A set of conventions is adopted whereby a heavy comour, pha several special features, is used to facilitate recognition ,Jf the figure represented. A face, for instance, is conventionalised in terms of eyes, nose, mouth and ears placed within a clear cut boundary. Expressions are conveyed by eye-brows, shape of eyes aud mouth, and an occional line around the mouth, nose or forehead to indicate the ringing into play of particular muscle groups. With this simple equip-
ment a skiLled cartoonist may convey a vast range of facial expressions, remarkably subtle in their overtones.
These simple line drawings seem to support Attneaves contentions
INFORMATIO;J THEORY AND FIGURE PERCEPTION
Fig. 6. (a) Prelate. (b) Outdoor type exercising at bar. (c) On parade.
(d) Businessman. (e) Woman on floor. (f) Woman reclining. (g) Woman walking. (h) Office boy.
22 R. T. GREEN AND M. C. COURTIS
about the location. of information, but even at this stage there is more going on than mleets the eye. There is a selection process involved whereby certain contours are pressed into service, while others, just as clear on a photograph, are dispensed with. Attneaves cat would be drawn by a competent cartoonist using far less of the contour to convey an impression quite as realistic.
Even the contours that are used do not consistently obey the Attneave formula. Points of rapid curvature such as the end of a chin, nose, finger, knuckle, angle of jaw or dome of the forehead are often left out, although perceptually they ar...