I. Empiristic Association Hypothesis

In Parts 1 to 7, the ETVG hierarchy theory, which explains "veridical" visual perception, was presented. The Interaction Theory introduced in this Part 8 accounts for a great part of the deviations from "veridical" perception, which have been observed in over one hundred years of perceptual psychological laboratory work: deviations from that percept that one would expect to arise, based on the effects of the sensory stimuli alone. Both what is to be understood by "deviation" and by "gestalt perception" was defined in Part 1.

In the Interaction Theory, the second Part of my 1961 "Theory of Optical Gestalt Perception" is expanded. It concerns the 17 factors of the lowest five psychic hierarchy levels. "Attention" can be included as the eighteenth factor, although it is not in itself a gestalt factor in the same sense as defined above. Each of these factors influences every other factor and itself. These factors are located at several different levels; this does not present a fundamental barrier to their interaction, although it may indeed play a role. Neither the four physical factors nor the quantity, orientation and form factors are included in the system of interactions presented here. (Although there are interactions of the factors at Levels 6 to10, both between themselves, and also with the factors at Levels 1 to 5). We are then dealing with 18 x 18 (324) different processes of influence. As they give rise to "gestalt perception" as well, they are termed "gestalt laws"; each law will be assigned a symbolic expression.

There are also at least two important "polarity laws"; without knowledge of these laws and their proper application, every attempt at explanation is bound to be a hazardous undertaking. This is because there are only two possible directions when influencing a variable: an effect either increases or decreases the variable. Every interpretation, regardless of the approach, thus has a 50% chance of being correct. The reader will become convinced of the fruitfulness of the theory only by critically interpreting the facts within the framework of ETVG, and noting how often these interpretations are actually correct. For this reason, this Part 8 has two aims: first, to describe the interaction theory, and second, to demonstrate the procedure by which phenomena may be accounted for, by using this theory. It does not, however, aim to "prove" anything.

The claim that all 17 figure factors interact with each other and with the factor "attention" is quite simple to substantiate. In Part 4, it was shown in some detail that the figure factors are implicitly acquired memory contents that have developed from the stimulus relationships inside the retinal image. Since these memory contents are derived from one and the same general structure of the stimulus, specifically from the retinal image "object in its surroundings", they are strongly associated with one another. This is the central Empiristic Association Hypothesis of the Empiristic Interaction Theory of Visual Figure Factors. Thus, if an association between A and B exists, the actualization of A alone is sufficient to cause the actualization of B, and likewise the actualization of B alone is sufficient to cause the actualization of A. Functional entities - i.e. gestalt factors - that are associated with one another in this way have dependent phenomenal correlates: the gestalt qualities. Since the latter constitute the percept "figure in its outfield", representing the "object in its surroundings", we can "see" from this "object in its surroundings", just which associations exist between the gestalt factors.

Let us recall those relationships that are commited to memory by newborns, and that thus subsequently become gestalt factors (Parts 1,2,4): The stimulus pattern "figure in its outfield", which is extremely interesting for the infant, and which is the form that each "object in its surroundings" takes when projected on the retina, is a system of abstract relationships and interrelationships among single proximal stimuli, that is memorized in great detail during infancy. A strong actualization of a gestalt factor will be henceforth indicated by "+" and a weak actualization by "-". The infant becomes familiar with the world as follows: "something very bright" (Pml+) and "something not so bright" (Pml-) exist that are spread out (Ll-) and bordered off against everything else bright (and colored) by a line (Ll+). This line encloses (Fl+) an "infield", so that this field (Ll-) is closed off (Fl+) from the open (Fl-) urrounding field. For its part, this surrounding field, the "outfield", encloses the unity of infield and enclosing contour, i.e. the "figure". Moreover, the infield is small (Dl-) and the outfield is large (Dl+). The borderline (Ll+) is a row of inhomo- geneities (Gml+), and the two fields (Ll-) bounded by this borderline are clusters of homogeneities (Gml-). An inhomogeneity is characterized by a large difference in brightness (Dm+) extending across a very small difference in location (Dl-). In contrast to this is the case of homogeneity: this is a very small or non-existent brightness difference (Dm-) extending across a large location difference (Dl+). The brightnesses or locations, which are same or different are Pml aspects. The Pml factor, which is necessary for producing the Pml quality "here is something bright", is a memory content itself; it has been developed from a combination of Z-functions. With help of this implicit (functional) learning process, the infant is capable of detecting an "object in its surroundings" as a static, two-dimensional "figure in its outfield". For the sake of simplicity, in this description of the functional learning process, the implicit memorization of the relationships and interrelationships among the specific outputs of only the twelve (+/-) functions of six factors with m and l aspects, has been taken into consideration, excluding the functions with depth (d) and time (t) aspects, which are discussed in Part 7.

When it is stated that a gestalt factor interacts also with itself, what is meant is that the specific gestalt stimulus of a gestalt factor actualizes the gestalt factor in such a way that both the positive and the negative function are increased, resulting in a greater "Prägnanz" of the phenomenal perceptual organization. This mutual amplification of the positive and negative functions of a gestalt factor is what was called "active antagonism" in Part 2.

The eighteenth factor included in the web of mutual influences is the (likewise polarized) factor "attention"; the newborn watches the "object" very attentively (A+), but the surrounding environment is less interesting and consequently receives little or no attention (A-). When one takes the twofold positive/negative antagonistic actualization into account for every factor, there are then 36 x 36 = 1296 cases where the gestalt laws are applied. As each of these cases appears in two logically identical forms, there are a total of 2592 application forms of gestalt laws. In addition, there are 2592 "similar" symbolic expressions, for which, however, there are no corresponding gestalt laws, i.e. they are "empty" terms. Handling these approx. 5200 genuine or empty symbolic expressions does not present a significant problem; one must simply strictly formalize the gestalt laws.


 II. Formalizing the gestalt laws

The first formalization of the gestalt laws has already been introduced by assigning a symbol to each gestalt factor. The symbol of a gestalt factor consists of a main letter, usually uppercase, to which one or more lowercase letters can be added as indices. The form of a gestalt law is determined as follows:

1. Syntax

a)The symbols of two interacting gestalt factors are written alongside each other. Example: Fl Dl

b) The factor on the left represents the independent variable, the factor on the right the dependent variable. In other words, the factor on the left influences the factor on the right. If, for example, Fl is actualized by means of its specific gestalt stimulus, then Dl, too, can be actualized (at least activated to below its threshold) not by the specific gestalt stimulus Fl, and not by the specific gestalt stimulus Dl, but  by the unspecific output of the actualized gestalt factor Fl. This output is an unspecific input (i.e. an unspecific gestalt stimulus) for all those gestalt factors with which Fl interacts, and thus for the factor Dl (see Figure 1-13).

c) An increase in the degree of actualization of a gestalt factor is indicated by "capitalizing a symbol", i.e. writing the main letter uppercase, a decrease by writing the main letter lowercase. Thus "fl Dl" means that a decrease in the actualization of the factor "closedness" leads to an increase in the actualization of the factor "location difference". One can express this relationship also as "the less Fl, the more Dl." Thus a gestalt law does not have the form "if X then Y", but rather, depending on the individual case,

                "The more X, the more (less) Y", or
                "The less X, the more (less) Y".

The plus/minus sign is, as mentioned previously, reserved for the indication of the opposing ends ("poles") of a dimension; the actual effect of a gestalt factor, however, extends across the entire dimension of a gestalt factor. Thus, the form "the..., the...." (as expressed above) is more suited for characterizing this effect. The gestalt laws are neither purely qualitative nor purely quantitative laws, but rather a combination of both - according to both, the qualitative-informative and the quantitative- informative effect of every figure factor (Part 2). A gestalt law does not provide a mathematical description of the relationship between an independent and a dependent variable, but it does decribe the relationship between the direction of change of the one variable and the direction of change of the other.

2. "Gestalt locations"

Every interpretation is concerned with the relationship betwen stimulus and perceptual experience. We wish to be able to explain both why, given a certain stimulus configuration, a certain perceptual experience results and why, given a certain change of a stimulus, a certain change of the perceptual experience results. For each interpretation concerning interactions it is thus necessary to specify which stimulus changes have taken place, as well as the resulting phenomenal changes. Moreover, this must be expressed both in terms of the influenced gestalt factor that is affected by the stimulus change, and in terms of the gestalt factor that immediately conditions the phenomenal change. It should be noted that these changes can take place at completely different locations. A location of the retina, defined as the Zl-location of the oculomotor coordinate system, is not what is meant by "location" in this context; indeed, gestalt processes can take place at all possible Zl-locations (and subsequently appear at the corresponding locations in the perceptual field). Such physical (material-functional) locations, are not what is meant here, but psychic (functional-phenomenal) locations and thereby locations that arise through the operation of the gestalt factors themselves: these are locations of fields and contours (borderlines), and they are locations in fields and contours. A location in a (phenomenal) infield is completely different to a location in its (phenomenal) outfield. Since, in reference to a pattern of sensory stimuli, one may analogously speak of a "material infield" (corresponding to the projection of the object's surface onto the retina) and a "material outfield" (corresponding to the retinal projection of the object's surrounding), individual receptors possess, independent of their physical (Yl-/Zl-) locations, also a completely different "psychic" location. A receptor's psychic location is determined by whether it receives light from the object's surface, or from its surroundings. More precisely: it is neither the material location (Yl), nor the physio-functional location (Zl) of a receptor that is relevant to a gestalt factor. It is rather the psycho-functional locations of the gestalt factors P to F that are relevant, by "superimposing" upon the physio-functional locations. In practice, this means that we have to "convert" the (material) retinal locations of the sensory stimuli into the (functional) locations of the gestalt factors involved in information processing. It is by way of the agonistic-antagonistic actualization of these gestalt factors that the bipolar gestalt qualities appear at certain (phenomenal) locations. In the context of ETVG and the integrated theory of interaction, the physical retinal locations and cortical areas in which information processing takes place, are - I'm sorry to say! - completely irrelevant. Only those functional locations which we term also "gestalt locations", or "ico-locations", are relevant. It is likewise irrelevant which "physiological mechanisms" or "single neuron" activities happen to underlie the gestalt functions. The theory is thus largely independent of empirical physical findings. Because the gestalt functions themselves, however, are none other than combinations of neuronal (Y) excitations (Z), the greatest confirmation of the theory can be expected from neurophysiological and neuroanatomical findings.

One cannot recognize an evolutionary hierarchical structure by means of a "bottom-up" thought process, but only by means of a "top-down" thought process, or at least by means of a combination of the two processes. This means that one cannot derive higher levels of a hierarchy from lower levels, but it is to some degree possible to recognize, given the structure of a higher level, which elements of this structure stem from lower levels. This epistomological method has played a key role in the development of ETVG. Now that the functional hierarchy that produces percepts is known, we can recognize the future task of confronting the hierarchy with the important findings of neurobiology (begun in Part 3) and psychophysics.

The locations of material, functional, and phenomenal events need to be precisely indicated in respect to the above mentioned gestalt locations. The most important gestalt locations are infield (i), enclosing contour (c), and outfield (o). The letters in parentheses are the indices that must be added to the gestalt factor symbols in order to indicate the gestalt location at the Fl level. We refer to the Fl level because, in the vast majority of cases, the perceptual entities that we are dealing with are figure/outfield systems (Level 5). Unfortunately, one cannot neglect that the gestalt factors are located at various hierarchy levels, so that polarities arise also at the lower Levels 1 to 4 (concerning the issue of "hidden" polarity at the P level, see Part 3). Within a percept of a certain hierarchy level, the qualities of all those lower levels, upon which the highest level is constructed, are to be found. This means, for example, that in a figure/outfield system ("ico-system"), not only does the polarity "figure/outfield" from the fifth level exist, but the polarity "borderline/field" from the fourth level as well; this fourth-level polarity appears at the fifth level as contour/ infield polarity. In a percept that has been developed through the fourth level, we in turn find the third level polarity "inhomogeneity/ homogeneity". Strictly speaking, the locations of inhomogeneity are not identical to the locations of a borderline, since a line can be located also "between inhomogeneities", similar to the case of a row of points (Part 2). Likewise, the locations of homogeneity are not wholly identical to the locations of a field, because the former, at their original level, do not extend as far  away from the inhomogeneity as at the next-highest level, on which they, due to the effects of the line factor, are distributed over a wide "field" (Ll-). However, viewed less strictly, one may assign the inhomogeneities to the locations of the borderline, and the homogeneitites to the locations of the field. One can do this because, for the most part, we are dealing with percepts that consist of borderlines and fields. We may thus take the line to be the location of the inhomogeneities, and the field to be the location of the homogeneities. Thus the two important "polarity laws" mentioned above, are described. The different gestalt locations (and, as the need arises, also their relationships to one another at various different hierarchy levels) shall be indicated with indices. Although the following suggestions do not include the entire repertoire of possible gestalt locations, they suffice for practical interpretation, at least as far as static, two-dimensional ico-systems are concerned.

 They are:

        a,b,p,q,r,s =  examples of indices for fields and contours, to be used as needed to avoid confusion

 3. The basis row of interaction factors

In order to begin "interpreting" the 2592 "faces" (i.e. application forms) of the 324 gestalt laws, let us arrange the relevant 18 factors into two rows, the symbol expressions in the second row will be written in the "complementary notation". Furthermore, let us order them according to level, and from left to right within each level according to Fig. 7-1. This sequence is merely suggested to aid the memorizing of the 18 interaction factors. "Attention" has to be hierarchically beneath the other perceptual factors, because it (here simply in the form of direction one's gaze) performs the biological task of focusing the entire functional detection system on a certain object in its surroundings, in order to obtain more information about that object (and its surroundings). Thus, "attention", with the symbol "A", is assigned to the "zero" level. A single expression of this row (Gmlc, for example) will be called a "phrase", so that the full symbolic expression of a gestalt law consists of two phrases.

The (double) basis row of the 18 interaction factors in phrases is as follows:

Aic  Pmlic  dmic  dlic  ddic   dtic   Gmlc   Gdlc    Gmdc    Gmtc   Gdtc      Gltc     Llc     Ldc    Ltc    Flic   Fdic  Ftic
ao  pmlo   Dmio  Dlo  Ddo  Dto   gmli,o   gdli,o   gmdi,o   gmti,o  gdti,o   glti,o     lli,o    ldi,o   lti,o    flo     fdo    fto

The "standard notation" of a gestalt law is obtained by pairing the phrases from any row. The gestalt laws dealt with here are not laws in quotation marks, as was the case with the "gestalt laws" of the early Gestaltists who lacked precision; the laws displayed here are genuine, and they strictly regulate the interactions of the figure factors. Although it is true that  these laws can be  even more precisely formulated, they are presented here in a form in which they could be empirically tested. I expect them to be further developed rather than disproved under such close examination.

In the upper row, the phrases are written in the form according to which they relate, to the "figure" (ic), the infield (i), or the contour (c). In the lower row, they are written according to how they relate to the complementary respective gestalt locations. (Instead of "ic", one can also write "i", as "i" is an essential aspect of the "figure".)

The portion of this double basis row that is relevant for our actual interpretation purposes is as follows:

                        Aic   dmic   dlic    dtic   Gmlc    Llc    Flic
                        ao   Dmio   Dlo    Dto   gmli,o   lli,o   flo

To understand the notation here, we need to imagine only what we had to learn as infants, i.e. we have to get to know which memory contents have become strongly associated with the ico- locations, i.e. with infield, contour and outfield. The infant observes the "object in its surroundings" very attentively, but everything else tends to be ignored. Thus the large degree of direction of attention toward the figure (phrase Aic) is associated, first, with a strong perception of a figure (phrase Flic), second, with a lesser focusing on "everything else", i.e. the figure's outfield (ao), and third, with a weak perception of "everything else" (flo). Furthermore, as infants, with Aic, ao, Flic, and flo, we had associated a sharp (Gmlc) object edge (Llc), bordering off two fields, infield and outfield (lli,o) that are relatively homogeneous (gmli,o). Almost every object is a particular color and brightness, that are different to the brightnesses and colors found in the surroundings. Thus, both the brightness and color sameness within the infield or figure (dmic), are associated with the large brightness and color difference between infield and outfield (Dmio), and both are associated with the previously mentioned experiences. What is true of Dm, is true also of Dl: the mean of all differences between the locations belonging to the object is relatively small (dlic), but the mean of all location differences within the surroundings is relatively large (Dlo). And: the light reflected from a (small) moving object causes only a short excitation of the receptors it impinges upon (dtic), but objects fixed at their locations in the object's surrounding, cause longtime excitations of the "outfield-receptors" (Dto). In the case of Dm, sometimes the phrase Dmo can be used, if the brightness and color difference within the outfield (which contains many objects of different brightness and color) is to be compared with the brightness and color differences within the infield, for example, in the law "Dmo dmi".

4. The procedure of interpretation

The factors listed in the abbreviated double basis row, comprised of 2x7 phrases, give rise to 49 different gestalt laws. In order to be able to account for (or perhaps to recognize being not able to account for) a phenomenon using one of these laws we must proceed as follows:

1. We establish which independent and which dependent variables we are dealing with, in other words, which gestalt factor is being affected by the change of the sensory stimulus, and which gestalt factor is responsible for the phenomenal change. Once we have done so, we have determined one of the 324 classes of gestalt laws with which the stimulus-experience relation is to be accounted for; we consequently know the "left-hand" and "right-hand" symbols of the applicable gestalt law.

2. We establish whether the measured (or estimated) value of the dependent variable increases or decreases when the measured value of the independent variable increases or decreases. Having done so, we know which symbols are to be written in capitals and which in lowercase.

3. The ico-relationships must be determined, i.e. at which ico- location ("gestalt location") the stimulus change takes place, and at which ico-location the phenomenal change takes place. Having done so, we know the location indices for both the left-hand and the right-hand symbolic expressions, and we then form two phrases and the symbolic representation of the relevant law that consists of these two phrases.

4. We check whether the resulting two-phrase symbolic expression actually corresponds to a law of interaction in the Empiristic Interaction Theory of Visual Figure Factors. This validity check must proceed as follows:

a) Every combination of two phrases from the double basis row defines a valid gestalt law.

b) If, in the course of interpreting empirical findings, one comes upon a notation deviating from rule a), this deviation obtained is a variant of a valid gestalt law, provided that it can be converted into a standard notation (i.e. notation composed of the phrases appearing in the basis row) by performing the following operations  an even number (2,4,etc.) of times ("transformation rules"):

- conversion of the capital letter of a factor-symbol into a lowercase letter, or vice versa.

- conversion of a location index into its complementary index.

c) If an odd number of operations leads to the standard notation, it follows that a valid gestalt law has not been found, and that the empirical findings have been  interpreted incorrectly.

Of course, one should not conclude that the "correct" gestalt law has been found merely because an expression can be converted into the standard notation; as mentioned previously, a random guess has a 50% chance of being equivalent to the standard notation of a gestalt law. What is admittedly less relegated to chance, is selecting the gestalt law that governs the observed phenomenal change from among the 324 possible gestalt laws. It must be remembered that each of the 324 possible gestalt laws can be written in four equivalent standard notations. An example: Fig. 8-1 shows the four standard notations, all expressing the general gestalt law Fl dl.

Figure 8-1. The combinations of a left-hand phrase and a right-hand phrase
that lead to the four standard notations of the general gestalt law "Fl dl".

16 expressions with the symbol of "lateral closedness" on the left and the symbol of "location difference" on the right are arranged in Table 8-1. Eight of them are valid, eight invalid. The underlined expressions represent the four standard notations. The four logically identical forms, which may be obtained by transforming the capital/ lowercase letters and/or the location indices of the standard notation an even number of times, are included as well, and indicated by "a". The eight invalid expressions may be obtained by transforming the standard notation an odd number of times; they do not denote any valid gestalt law.

These validity check rules can be illustrated with an example: let us assume we have established that the more closed a figure is, the shorter the length of a line within  a figure appears. First, we need to express this finding symbolically: Flic dlic. Next, we compare both terms with those in the double basis row and find that the expression in the basis row matches the symbolic expression of our findings. Thus we know that we can explain our empirical findings with one of the laws of interaction (provided, of course, that we have not made a mistake somewhere).

Now it could be that we have formulated our findings somewhat differently - perhaps due to a different experimental procedure: "The less the field (a) is contour-enclosed, the larger (or less smaller) a line within the field (a) appears." The symbolic expression obtained from this example is: flac Dlac. For the case that (a)=i, we then have flic Dlic. Neither of these symbolic expressions is to be found in the basis row. But by performing the allowed transformation operations two times, we obtain, for example, the expression "Flic dlic" and note that "flac Dlac" is in fact one of the eight valid expressions of an existing gestalt law.








Flic dlic

flic dlic


flic Dlic

Flic Dlic


Flic Dlo

flic Dlo


flic dlo

Flic dlo


flo dlic

Flo dlic


Flo Dlic

flo Dlic


flo Dlo

Flo Dlo


Flo dlo

flo dlo

Table 8-1.  Eight valid and eight invalid expressions of the gestalt law "Fl dl".
The underlined expressions are standard notations

A few suggestions for further procedures: whenever a gestalt factor is simply referred to, its symbol is capitalized. In alluding to a gestalt law in general, the symbol is capitalized or written in lowercase according to the form it takes in that part of the double basis row referring to the figure (i.e. the upper row) with the omission of the location indices. We thus have, for example: A Fl, Fl dl, dm dm, dl Gml. A "class" of gestalt laws, i.e. the group of all gestalt laws with the same dependent variable, and all independent variables, shall be indicated by "XFl-laws", "Xdl-laws", and so forth. In the practice of interpretation, however, the nomination of location indices is absolutely necessary for the unambiguous indication of the correct usage of a particular gestalt law. 

The examples in the following chapter will provide a glimpse into the interpretational possibilities and procedures of the interaction theory.

Excerpt from L.Kleine-Horst: Empiristic theory of visual gestalt perception. Hierarchy and interactions of visual functions (ETVG), Part 8, I+II

III. Examples of gestalt laws
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