the perception of foreground and background as derived from structural information theory

Acta Psychologica 55 (1984) 249-272

North-Holland

249

THE PERCEPTION OF FOREGROUND AND BACKGROUND AS DERIVED FROM STRUCTURAL INFORMATION THEORY

Emanuel LEEUWENBERG and Hans BUFFART *

Unruersity of Nijmegen, The Netherlands

Accepted July 1983

Subjects were instructed to order stimuli, consisting of a white and a black part, in accordance with the perceived foreground-strength of the white (or black) part. It appeared that this task can be

carried out consistently. The order is explained on the basis of Structural Information Theory. It is

argued that this task involves central processes, and that the strength depends on the preference for

an interpretation, in which the white (black) part is a foreground on a black (white) background.

with respect to the opposed interpretation in which the white (black) part is the background and

the black (white) part is foreground.

Introduction

Most people perceive fig. 1A as a white rectangle before a black one. Fig. 1B is similarly perceived, but the foreground-impression is not as strong as in fig. 1A. Here we will discuss the question of relative foreground-strength.

As far as we know no one has yet tried to formulate a model describing how subjects decide which pattern is the foreground and which is the background. A model for the calculation of relative foreground-strengths has also not yet been developed.

The foreground and background phenomenon is related to, but not identical to that of figure-ground. As in the example presented in fig. 2 the ground is not necessarily specified by a contour.

Gestalt-psychologists formulated several cues as to what constitutes the figure. These are supposed to infer an initial interpretation on the

* Mailing address: E. Leeuwenberg, Dept. of Experimental Psychology, University of Nijmegen, P.O. Box 9104, 6500 HE Nijmegen, The Netherlands.

OOOl-6918/84/$3.00 0 1984, Elsevier Science Publishers B.V. (North-Holland)

basis of which the pattern is investigated in more detail. Some cues are:

(a) The fig~e is usually enclosed by the ~KUH~. (b) The figure is usually smaller than the ground. (c) The figure is in general regular. (d) The figure is usually continuous rather than interrupted. (e) The figure is usually brighter than the ground.

In fig. 3 examples are presented which reveal that these cues, irrespec- tive of their value in discriminatingjigure from ground, certainly cannot provide valid criteria for the distinction between foreground and back-

Fig. 2. Figure-ground ambiguity (after Rubin. adapted from Mrtzger 1975)

E. Leeuwenherg, H. Buj$r~ / Fore and background perception 251

ground. It can also be shown that all cues together do not lead to a consistent criterion for the figure and ground. The reason is that no stable preference strength can be specified for each of the cues. In other words, sometimes one cue overrules the other, sometimes the last applies more than the first.

Figural completion is another related topic. It covers the question of how subjects complete occluded parts of patterns. For instance in fig. 4A a square is seen behind the other (Gabassi and Zanuttini 1978; Kanisza 1975) while fig. 4B is interpreted as a ‘mosaic’; a cross and a square side by side (Dinnerstein and Werheimer 1957). Buffart et al. (1981) discussed several hypotheses explaining how subjects perform the completion task. They showed that local cues, like T-junctions, or Gestalt notions, like continuation, good Gestalt or familiarity are insufficient to explain the experimental findings. They argued that such cues may only guide the perceptual inference to some interpretation. These are, however, not decisive. Buffart et al. (1981) assume that several interpretations are evoked by a stimulus and that the best interpretation reflects the code with minimum structural information. This choice criterium is supported by data of their completion experiment.

One motive of the present paper is to verify the structural information approach to foreground-strength, since it is highly related to figural completion (Buffart et al. 1981). However the difference between both phenomena is more interesting: The completion perfor- mance is explained by the simplest pattern code. For unambiguous patterns this is only one code, since the completion task requires only one outcome. For the foreground-strength judgement the prediction for each pattern is based on two codes involved in a preference measure.

First a synopsis of structural information theory will be given. Thereafter experimental findings will be explained in terms of this theory. Alternative approaches, will be discussed in the last section.

Fig. 4. Despite the equal T-Junctions between the parts in A and B, the A pattern is seen as a

foreground-background, the B pattern as a mosaic.

252 E. Lmovenberg, H. Buffurt / Fore und buckground perceptron

p-i--p~~i’~~ Fig. 5. Relation between structural codes and stimuli.

Structural information theory

Leeuwenberg (1969, 1971) proposed a grammar for the description of pattern interpretations. This grammar specifies the sorts of identities which subjects can perceive in stimuli. These identities are expressed by three syntactic production rules or operators and are discussed exten- sively in Buffart and Leeuwenberg (1983). Here we summarize their properties for series of symbols.

It will be shown later how these series are related to visual patterns. This relation is covered by the so-called semantic system. As depicted in fig. 5 structural information theory does not deal with the transfor- mation from stimulus to a code, called the “encoding” process. The latter is about the discovery of identities in patterns. The theory deals solely with the description of patterns.

The following operators are the components of the syntax: _ The serial patterns (la) and (lb) are identical apart from a reversal

of the order. This can be expressed by the reuerml operator, #[ 1, as shown in (1~).

abc

cba (lb)

#[abc]=cba 04

- Series (2a) and (2b) are iterations of identical elements or series. This can be expressed by the iteration operator, *, as can be seen in formulas (2~) and (2d).

aaa (24

ababab W-4

E. Leeuwenberg, H. Buffart / Fore- and buckground perceptmn 253

3*a=aaa (2C)

3*(ab)=ababab (2d)

_ A third operator, \, called concatenation, allows for concatenation of series (3a, 3b).

a\b=ab (3a)

abc\#[abc]=abccba (3b)

The iteration and the concatenation have the so-called distributiue property which implies that the identity of non-adjacent structures can be perceived. The series (4a-d) show four examples.

(2)*(abc) =2 *a2*b2*c=aabbcc (4a)

(2)*(((ab))c)=2*(ab)2*c=ababcc (4b)

(a b c)\(d e) = a\d b\e c/d a\e b\d c\e

=adbecdaebdce (4c)

((ab))\(cd)=ab\cab\d=abcabd (4d)

A distributive operator has two arguments, both between brackets “( )“. Their elements are cyclically distributed over several expressions until the result is produced again, i.e. until both elements are taken at the same time. Note that elements are indicated by brackets “( )“, which may be omitted if this does not give rise to confusion. A comparison of the examples in series (5) and (6) show the function of the brackets.

(2)*(((abc))) =2*(abc)=abcabc (5a>

(2) *((a b) c) = 2 *ab2*c=aabcc (5b)

((4 (b) (c)> \W (4 = a\d b\e c\d a\e b\d c \e =adbecdaebdce (5c)

254 E. ~eeuwther~, H. Buffart / Fore und background perwpt,on

(u h)\((c d)) = u\c d h\c d

=acdhcci (5d)

Every code can be an argument of an operator. Functions can be newly defined by composing operators. Series (6) shows two symmetry functions.

SYM[ah] =ub #[uh]=ubba (6a)

SYMM[

Sets

As previc

abc]=abc #[crb]=abcbu (6’4

~sly mentioned, structural information theory deals only with identities. This implies, for instance, that the series u u h h has the same structure as the series s s I I. The first two and the last two elements are equal. In this sense structure has some abstract meaning. However, there are patterns which cannot be described by one code, made up by the operators of the syntax. A demonstration follows:

pattern : ahahu

code : 2*(ub)a abstract code : 2 * ( p q) r

set : P4P4r

(74

(7b)

(7c) (74

The code (7b) of pattern (7a) only reveals that a b is repeated. The last element is not identified. In order to clarify the actual meaning of code (7b) each element is replaced by a different parameter (7~) (Collard and Buffart 1982). However this code represents many patterns (7d). It includes (7a) but also, for instance, b c b c t. Thus code (7b) does not specify the structure of (7a) sufficiently since the middle and last elements are not necessarily equal in (7d). Another code is at hand which reveals the identity of the middle and last element, just as in (7a):

code : a2*(ba) abstract code : p 2 *(q r)

set : P4’4r

(7e) Vf)

(7g)

E. Leeuwenberg, H. Buffart / Fore- and background perceptim 255

Code (7e) is also incomplete, but in combination with (7b) it will guarantee the structure of pattern (7a). If both codes apply to this pattern, only the intersection of set (7d) and set (7g) sufficiently constrains the structure of the patterns, characterized by p q p q p. Such pairs (7c, f) are called complementary codes or interpretations. It should be noted that the connection between a pattern with a set, mediated by operators, was already made by Garner (1966). The difference is that he used operators, acting on the stimulus, whilst here operators are components of the description of the pattern itself. What they have in common is that pattern “goodness” is inversely related to set-size.

Information loud

The intersection of the two sets specifies the structure completely and more accurately than each of the two sets. The intersection set has also fewer different parameters than the two sets. Thus, the lower the number of parameters the more accurate the description. In the codes (7c, 7f) the number 2 has also to be conceived as a parameter, although it is removed from consideration in the sets (7d, g). The complete number of different parameters of the codes (7c, f) equals 4. This number is called the structural Information load (I).

Newly defined functions may contribute to the load of a code. Their contribution can be calculated from their abstract definition. It equals the difference between the load of the right-hand side and the load of the left-hand side. So the load of SYM and SYMM in (6a, 6b) equals 1, since from their abstract definition it follows that I(SYM) = 2 - 1 and I(SYMM) = 3 - 2.

SYM[x] =x\#[x]

SYMM[x (Y)l = X\Y\#bl

(84

Semantics

A square can be described as four times a 90 degree angle (outer angle) each followed by a length 1. This can be coded as in (9a). Equally a triangle is coded in (9b), and a regular hexagon in (SC).

4*(90 1) (9a)

3*(120 /) (9b)

6*(60 1) (94

Although the codes have three descriptive elements the patterns have only two degrees of freedom, since the number of iterations and the angles are coupled. Therefore the number of iterations is implicitly given. In those cases the number is replaced by the symbol @ and not counted as a unit of information. So (9d) represents an arbitrary regular polygon.

e*W> (9d)

As an operator, @ continues its argument until an earlier element is met in the construction of the pattern from the code. Therefore it is considered as a semantic operator, only applicable to visual patterns. In table 1 this operator is added in the survey of code operators.

Leeuwenberg (1971) introduced the “grain” as a special semantic element. This grain is denoted by &. It stands for a minimal length of line. Any length of line 1 can be expressed by the grain: I= n * &. Both I and n carry each one unit of information. Therefore the grain carries no information.

The last property has the following implication: suppose there are two squares of different size (lying in one plane). The first is described by (lOa), the second by (lob).

@*(an*&)

@*(W?*&‘)

FBI F k’l

I=2

/=l

(IOa)

(lob)

WC) (IOd)

Table 1

Summary of operators and functions

Operator or function

Iteration

Concatenation

Symmetry

Continuation

Primitive code Code Load

aahh ((2))*<(a)(h)) 3

uhah 2*(oh) 3

ahch ((cJ)(c))\((h)) 3

uhhu SYM[Ub] 3

ahcha SYMM[a h(c)] 4

0(10... @*(u) 1

E. Leeuwenberg, H. Buff&-t / Fore and background perception 257

The code (lOa) can be specified as a function of the grain (10~). Use can be made of this expression for the representation of the second square (10d). The last code carries only one unit of information due to F. Thus for two squares in one plane I= 3 holds. The first requires I = 2, the second I = l,due to the “reference” function. The last function is basic to structural information theory.

Preference

The mutual dependency of complementary interpretations in describing the structure of a stimulus raises the question of which interpretation a subject actually uses. The answer is both, but they are not “seen” at the same time (fig. 2) and are not always equally preferred. Without denying the role of the peripheral aspects like, for instance orientation, and local cues during inference (Buffart and Leeuwenberg 1983) we can hypothesize that the preference for an interpretation is mainly determined by its relative accuracy. That is to say, that the preference for an interpretation increases with its accuracy at the cost of the preference for other one(s).

Since the accuracy of complementary descriptions can only be com- pared in terms of their structural Information loads, the theoretical preference for an interpretation is expressed as a decreasing function of its load and an increasing function of the load of the complementary interpretation. Formula (11) shows the theoretical preference expressing the preference of interpretation A with respect to its complementary interpretation B as a quotient of their loads. It is the simplest function if only two complementary interpretations are involved (Leeuwenberg 1978).

P(A > B) = I(B) : I(A)

Foreground-strength

For the specification of the foreground-strength two interpretations are relevant. Taking, for example, fig. lA, according to one interpretation, white is foreground; in which case the pattern is presumably composed by two rectangles. In the other interpretation black is foreground. In that case the composition is as depicted in fig. 6A. These two opposed interpretations are not only relevant for the foreground strength specifi-

Fig. 6. Complementary interpretations of fig. IA and IB which fix the relative poutions of the

rectangles.

cation, but also complementary with respect to each other. It means that, for instance, fig. 1A is the only pattern which is comprised by two rectangles and also composed by the parts of fig. 6A. For these reasons it is assumed that the code-loads of these two opposed interpretations are involved in a preference measure (formula 11). specifying foreground-strength. If the first interpretation. comprising two rectangles, is the target of this preference measure, the outcome is assumed to stand for the foreground-strength of the white part in fig. IA. The target interpretation is called “the foreground interpretation”. denoted by E The opposed interpretation is called “the complementary interpretation”, denoted by C.

Without any calculation it is clear that fig. 6A is more complex than fig. 6B. So the preference for white as foreground is higher in fig. 1A than in fig. 1B. Along the same line of reasoning the patterns of fig. 7 are predicted to have a decreasing foreground-strength from left to right.

As already stated both F and C codes are assumed to be complementary. This characteristic has a few technical code implications. First, the specification of the relative position of the two rectangles of fig. 1A as well as the relative position of the parts in.fig. 6A can be omitted in the F and C codes, since even without this specification fig. 1A is fixed by the F and C codes. In general the black and white parts, which stay in different planes, can be described independently within the F and C codes. As a consequence the code of the black part embodies no reference to the code of the white part or the reverse. Second, it is

UOtBrn A B c D

Fig. 7. Four identical interpretations with decreasing foreground-str~llgth.

E. Leeuwenberg, H. Buffart / Fore and background perception 259

completely arbitrary to conceive one of the codes as the intended target (F) code: Both F and C are equal candidates. Therefore it may be considered reasonable to have Fand C codes in the preference measure, whose summated information load is minimal.

In the following part the consequences of the statements given for the concrete patterns used in the experiment, will be discussed.

Application to foreground-background

A code of a square is shown in (12). The angle is indicated by the symbol a and the length by the symbol 1. A small circle in a drawing (see fig. 8A) indicates the point where a code starts and an arrow indicates the starting direction. In general, every point and every

direction may be chosen freely as starting point and starting direction. The load of the code determines whether it is a good choice or not.

a?*0 4

z=2 02)

The load of (12) equals 2. It is a minimal code. Notice that the continuation stops when, during the construction of the pattern, the starting point is reached.

The minimal code of fig. 8B is shown in 13a. Codes 13b, 13c and 13d follow from the evaluation of the operators indicated.

minimal code : ((2) *cm W)\W 034 z=5

distribution : (2*m2*12*k)\(a) (13b) iteration : (mmllkk)\(a) (13c) concatenation : mamalalakaka (134

I”. I=? B I=5

Fig. 8. Examples to be coded.

Any other starting would lead to a code with a load greater than 5. The orientation, after finishing the construction, differs by 180 degrees from the starting direction, but this does not matter since the code construction agrees with the pattern.

In fig. 9 the components of two complementary interpretations are depicted below the pattern. If we conceive of the two squares as the components of the intended target code (F). implying white as foreground, the load of both interpretations can then be derived from the load of formula (12) and (13). The load of interpretation F. consisting of two squares in different planes, equals I(F) = 2 + 2. The load of the complementary interpretation equa!s I(C) = 2 + 5. Using the preference-formula (11) the theoretical foreground-strength of the white pattern in fig. 9 equals. P( F > C) = l(C): I(F) = 7:4 = 1.75.

Figs. 10 and 11 show two stimuli used in the experiment which have the same white-foreground interpretation (F), but where the complementary interpretations (C) differ. In fig. 10 it is a mosaic-interpretation and in fig. 11 the complementary interpretation comprises: black triangles and a white square. The calculated loads are indicated in the

I=.’ I = i I = .? I = .’

Fig. 9. An examplt: of a stimulus and Its task-dependent interpretations

Fig. 10. Stimulus whose foreground-background interpretation is the same as in fig. 11. Its

complementary one is a mosaic interpretation.

,=1 1=5 I = ? I=&

Fig. 11. Stimulus whose foreground-background interpretation is the same as in fig. 10. Its

complementary one is a foreground-background interpretation.

262 E. Leeuwenherg, II. BuJjb-r / Fore ond buckground perception

figs. The theoretical foreground-strengths for both figs. are

Fig. 10: P(F> C) = I(C) Z(F)= (4 + 5):(4+ 2) = 1.50 and

Fig. 11: P(F>C)=/(C):/(F)=(2+5):(4+2)=1.17

respectively. Indeed, our subjects judged the foreground-strength in fig.

.,-:. Itr

q - ----~ .:’

:. 2 t _’

.,: ,._ A+5 ,.--I __

ii

2ti

Fig. 12. Stimuli, figural representations of the C and F interpretations and their preferences

E. Leeuwenherg, H. Buffurr / Fore- and background perceprion 263

Let us consider especially the complementary interpretations Cl C2 of the experimental patterns, presented in the first column of fig. 12. In these the white part is depicted as a dotted surface. Each of the patterns is surrounded by gray as in fig. 10 and 11. The complementary interpretations consist of a white background (Cl) and black fore-

.)

.,,‘. :::. 0 1. ..’

:

c3 ._ : : ._ : .,: % 1..

.‘; :

m

. . 0 :.. ._

@ ‘..

-77 ..’

v

ICFI) + I(F2)

,+5

yY-2

L + 3

2+?

I + 7

2+3

I + 5

7-Z

I + 5

2 + 2

I +6

5.r 2

2 + 6

,+‘a

2+3

3+5

Fig. 12 (continued)

_I + 2 + _)

2+5+2

---

2+5

:+i+.’

ground (C2). If the white is supposed to lie in a plane between the gray and the black part the white background is always a surface with a specific contour, otherwise it would extend across the gray surrounding. In principle the white background may have any shape, as long as it

E. Leeuw~enherg H. Buffart / Fore - and background perceprion 265

satisfies the following two requirements: first the summated information load of the C and F components is minimal. (See the part on foreground-strength.) Second the stimulus is uniquely specified by these C and F components. For instance C2 of stimulus 1A in fig. 12 is described as a square with a circular hole in it. However, the position of this circular hole is specified by Cl, if this is a pentagon. This is the unique regular polygon (I = 2) which can be constructed inside the black part of C2, so that its corners touch the outer sides of this square and its sides touch the contour of the circular hole of C2. In this way the circular hole of C2 stands necessarily in the middle of the square. If, for instance, Cl was a square, the hole did not necessarily stay in the middle. If the pentagon were larger, it would extend across the gray surrounding. If the pentagon were smaller the gray would be visible within the circular hole of stimulus 1A.

For pattern 12A the Cl is a diamond, I = 3, otherwise the hole in C2 cannot be fixed. For pattern 2B the Cl is T-shaped, otherwise the stimulus is not uniquely described.

There are complementary codes in which the position of the hole in the black part is not fixed by the white background shape, but by the C2 or F codes. Such complementary codes are the simplest for the patterns: 4A, B, 5A, 6A, B, 7A, B, 12B in fig. 12. In these cases a white surface with an undefined contour is assumed. However, this surface lies not only behind the black but also behind the gray part, otherwise the white would cover the gray part. For this color difference one unit of information is assigned. In fig. 12 such undefined white surfaces are depicted in Column Cl, as an area of dots without contour.

Experiment

Method

Material

We used 48 stimuli consisting of black and white shapes on sheets of 10 X 10 cm gray paper. The stimuli were divided into two equal groups of 24. The second group were black white reversals of the first group. One group of 24 stimuli is shown in the first column of fig. 12. These 24 patterns consist of 12 pairs, A and B, fulfilling the following two theoretical requirements.

(I) The foreground-background interpretations as well as the complementary interpretations of both stimuli have at least one subpattern in common.

266 E. Lreuwmberg, H. Buffart / Fore- and background perception

(2) The foreground-strength of the white shape in A is greater than that of the white shape in B, except for the IIA-B pair where both are equal.

Subjects

Two groups of 15 undergraduate students at the University of Nijmegen served as Ss. They were naive with respect to the foreground-background problem and were not familiar with structural information theory. One group were shown the stimuli as in table 2. The other one judged the black-white reversed stimuli.

Procedure

Each S was individually instructed to rank order, without ties, a randomized set of the 24 patterns according to the perceived foreground-strength. The foreground in the stimuli shown in fig. 12 was defined as the white shape, and in the other stimuli as the black shape. There was no time-limit and SS were free to correct their answers as much as necessary.

Table 2

Rank of stimuli due to foreground-strength: predictions and results

Pattern P(F> C) 30 subjects

(all)

Score Rank

10 A 1.75 646 24.0

2A 1.75 626 23.0

8A 1.60 519 19.5

6A 1.60 474 18

2B 1.57 579 22.0

3A 1.50 519 19.5

IA 1 so 418 13.0

5A 1.50 522 21

7A 1.50 468 16.5

11 A 1.29 468 16.5

11 B 1.29 454 15.0

5B 1.25 452 14.0

6B 1.20 343 11.0

12 A 1.20 337 10.0

38 1.17 381 12.0

10 B 1.17 325 8.0

7B 1.00 326 9

9A 0.89 198 6.0

1B 0.89 184 5.0

4A 0.87 227 7

12 B 0.69 163 3

9B 0.67 170 4.0

8B 0.63 111 2.0

4B 0.50 90 1.0

15 subjects

(white)

SCOX Rank

323 23

316 23

274 21

221 15

297 22

251 19

213 13

265 20

239 1x

220 14

234 16

236 17

159 10

158 9

203 12

151 8

170 11

92 6

87 4

118 7

88 5

77 3

49 1

59 2

15 subjects

(black)

Score Rank

323 24

310 23

245 17

253 19

282 22

268 21

205 13

257 20

229 16

248 18

220 15

216 14

184 12

179 11

178 10

174 9

156 8

106 6

97 5

109 7

75 3

93 4

62 2

31 1

E. Leeuwenberg, H. Buffart / Fore - and background perception 26-l

Table 3

Statistical analysis: the reliability of the data and their correlation with the predictions

White Black Total

Spearman correlation r = 0.94 r = 0.96 r = 0.96

With predictions P < 0.01 P < 0.01 P < 0.01

Kendall coefficient for w = 0.89

concordance between subjects p < 0.01

Mann-Witney-test on A > B

Pair 11 p > 0.10

Pairs 2 and 5 p < 0.02

All other pairs p -C 0.01

Prediction

In the second to the fifth columns of fig. 12 the subpatterns of the theoretical interpretations [l] are drawn. Columns 4 and 5 show the foreground-background interpretations and column 2 and 3 the complementary interpretations. The theoretical foreground-strengths are presented in column 5. The order of the stimuli following these strengths is shown in the first column of table 2. Their theoretical strengths are given in column 2.

Results

For each pattern the rank orders are summed. For the white foreground stimuli these sums are presented in column 5 of table 2. In column 6 the ranks of these sums are given.

In column 7 and 8 the same is presented for the black foreground stimuli. In column 3 and 4 the same is given for both white and black foreground stimuli together.

In table 3 the results are summarized. It shows that the obtained rank orders agree roughly with the preference values. For every A-B pair the A stimulus is judged to have a higher foreground-strength. The pair of stimuli 11A and B have equal foreground- strength, which is reflected by the slight difference of the summated rank orders.

Discussion

The predictions are very sensitive for a change of only one unit of the load. Nevertheless predictions, based on a slightly different notion

[l] The codes themselves are not presented in this paper, but are available on request from the

authors.

agree equally well with these results. Thereby complementary codes are allowed which reflect mosaic interpretations for patterns (4AB, 6AB, 7AB, 12B) which, in this paper, are handled as patterns with holes. On the one hand a mosaic code can be slightly more simple. because use can be made of the reference function. On the other hand it can be slightly more complex, because the positional relation between the black and white part has to be comprised in the codes. To this alternative as well as to the approach presented in this paper, the complementarity and the minimum principle apply. The analysis presented in this paper might be preferable while it handles the complementary code as well as the target code as a foreground-background code.

In the present approach three stimuli are analyzed as objects in three different “planes”; the F-interpretation of 1B and 10B and the C-interpretations of 11A and 11B. In these cases we deviated from the earlier formulated theoretical principle that both interpretations in a pair have to be strictly complementary with respect to the stimulus. We left the relative position of the subpattern in the lowest “plane” with respect to the other subpatterns out of consideration and restricted ourselves to these “two level” complementary aspects for two reasons. First, with respect to the task this relative position is not important since the codes guarantee that the object in the third “plane” is the background for all other subpatterns. Second, in a pilot study on the three stimuli subjects scarcely made any distinction between the foreground-strengths when the object in the third level is shifted or rotated, or even replaced by another regular polygon.

Other explanations

A third analysis has been made of the patterns which predicts the data worse (Y = 0.85). Hereby also a target code and an alternative code are used, both reflecting a foreground-background interpretation. However the alternative codes refer straightforwardly to the simplest white background shapes and the black foreground just as the C components of stimulus 2A, 3AB, 8AB, 9Ab, 10A in fig. 12. The target codes do not differ from the codes presented in this paper. In other words the complementarity principle is not strictly applied in these codes. This means that not all stimuli are uniquely specified by the combination of the target and alternative codes.

E. Leeuwenberg H. Buff&-r / Fore and background perception 269

One could also suppose that subjects ordered the patterns according to the simplicity or goodness of their Gestalt. In a pilot study all five subjects judged 3B to be simpler than 4A. Indeed the foreground- strength of 3B appeared to be higher than the strength of 4A. However, the perceived strength of 5B is lower than that of 3A although 5B is also judged to be simpler than 3A. Similarly 5B and 6B are judged to be simpler than 5A and 6A respectively, while the perceived foreground- strength of 5B and 6B is lower than that of 5A and 6A. Thus the straightforward simplicity hypothesis seems to be rejected.

Another assumption, which is also rejected is that the simplicity of the foreground-background interpretation mainly determines its own strength. These interpretations are pairwise equal in the case of 3A and 3B, 5A and 5B, 6A and 6B, and 11A and llB, but only the results of the llA-B pair may be interpreted to, show an equal foreground- strength. Similar arguments falsify the assumption that it is merely the simplicity of the foreground or of the background which determines the strength.

The falsification of the simplicity-assumptions may be ascribed to a special influence of the relative position of foreground and background. It looks as if the foreground-strength is lower when the relative position is simpler. This conforms with other findings: For instance, a distinction between Figure and Ground becomes easier when their relative positions show more asymmetry with respect to their shapes (Metzger, 1975). However, the structural specification of the relative position in codes leads to predictions which are not in agreement with the data. Neither the Load of the relative position, or the Load of the foreground-background interpretation or the load of the stimulus-code, nor their differences or quotients show any relevance. Several other criteria determining the simplicity or goodness of patterns have been proposed such as the number of lines and angles (Hochberg and McAlister 1953; Hochberg and Brooks 1960), the measure of regularity, symmetry or homogeneity (Bahnsen, 1928; Koffka 1962; Wertheimer 1923) and the selective information (Attneave 1959; Garner 1962). These criteria have been found to be unsatisfactory (Buffart et al. 1981; Hochberg 1978, Kanizsa 1975).

From the point of view of Structural Information Theory one may understand why models which explicitly try to correct the influence of the relative position will fail. The theory states that judgements about perceptual aspects are only due to interpretations.

270 E. Leeuwenberg, H. Buffart / Fore- and background perception

The results of experiments on brightness-illusions seem to challenge the latter assertion which, in accordance with Gregory (1972, 1974) explains the Ehrenstein-illusion in fig. 13A (Ehrenstein 1941; Coren 1972) on the basis of the idea that one interprets it as a star of black lines with a bright disk superimposed rather than as twelve terminating lines. However, this explanation would also hold for figs, 13B and 13C, where the illusion is less strong or almost not observed. Artificial intelligence programs on early stages of vision (Davis and Rosenfield 1981; Marr 1976) stress this point showing that several cooperative local cues can evoke a percept, even when a single cue does not.

On the other hand van Tuijl and de Weert (1979) showed for a special type of brigthness-illusion, the so-called neon-illusion, (van Tuijl, 1979) that not only sensory conditions determine the occurrence of the illusion but that structural aspects also play a role. Rock (1977) discussing perceptual inference with respect to perceptual constancies and brigthness-illusions, argued that a percept is a hypothesis, and that the perceptual process is inferring and testing hypotheses rather than straightforward encoding. Cooperative mechanisms take part in the inference, but not in the perceptual decision. They are mainly con- cerned with the first stages - retina and areas 17 through 19 - of the visual system (Buffart 1978, 1981; Ginsburg 1975). The output of these first stages is the input, the “stimulus”, of the central or cognitive system, where the structural aspects are processed. The output of the latter system produces perceptual behaviour (Hochberg 1974) which influences the input of the visual system thereby stabilizing or destabi- lizing the output of the first stages and the percept itself. Thus even the “automatic” processing during the first stages may be influenced by cognitive aspects.

Fig. 13. The Ehrenstein-illusion depends on the proximity of the end-points of the black-lines.

E. Lmuwenberg, H. Buffart / Fore and background perception 271

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