Excerpt from
L.Kleine-Horst: Empiristic theory of visual gestalt perception. Hierarchy and interactions of visual functions (ETVG), Part 2, I

The bipolarity of figure quality

4. Line and field

I asked myself: if the double perception "(lateral) line" and "(lateral) field" is a polarized perception, which I suspected because of the polar relation between inhomogeneity and homogeneity, then the gestalt stimulus for the one gestalt quality and the gestalt stimulus for the other, must be in opposition-relation to each other. It was thus necessary to find a formulation for the gestalt stimulus Ll that would express this opposition. I sought a ratio whose increasing would result in the perception of a line, and whose decreasing would result in the perception of a field, or vice versa. I found the following definition for the gestalt stimuli Ll+ and Ll-:

Given a set of perceptual entities:

- the larger the sum of the location differences between any one perceptual entity and every other perceptual entity,
i.e. the more a row of perceptual entities results,
   the more one perceives (or tends to perceive) a "line" (Ll+);


- the smaller the sum of the location differences between any one perceptual entity and every other perceptual entity,
i.e. the more a cluster of perceptual entities results,
   the more one perceives (or tends to perceive) a "field" (Ll-).

As a demonstration, sketch seven circles of equal size in such a way that the sum of the location differences from the center of each circle to the center of every other circle ("sum of Dls") was maximized.  Add the condition that, as perceptual entities, circles do not overlap, and that the circles were required to remain touching each other. Using the same conditions, sketch seven circles of equal size in such a way that the sum of the location differences from the center of each circle to the center of every other circle  is minimized.

Figure 2-6. Demonstration of different "sums of Dl"

The solutions are to be found in  Fig. 2-6. At the most (Case A), the "sum of Dls" amounts to 56 diameters. A larger sum can only arise by a (forbidden) increase in the number of circles, or by the (forbidden) introduction of spaces between the circles. At the least (Case C), the sum of Dls amounts to 28 diameters. A reduction of this sum can only be reached through a (forbidden) reduction in the number of circles, or by a (forbidden) overlapping of circles. The definition of the gestalt stimulus Ll+ yields a row, and illuminates that in a holistic percept a row appears as a "line". The definition of the gestalt stimulus Ll- yields a cluster, and illuminates that in a holistic percept a cluster appears as a "field". Figure 2-6B shows an example in which the sum is between the maximum and the minimum.

The polarity of the gestalt qualities "line" and "field" is proved by these definitions of oppositional relations between perceptual entities as row-relation and as cluster-relation. It is thus assumed that the gestalt factor "Ll" is actualized to two different degrees, and that the different magnitudes of this actualization stem from adjacent regions.  Thus neither Ll+ nor Ll- is actualized in isolation. Instead, both Ll+ and Ll- are always actualized together, and specifically, in the spatial order:

                                          Ll-      Ll+     Ll-

                                        field    line    field

This polarity of field and borderline is seen in that it is impossible to perceive one and the same stimulus as both field and borderline simultaneously. It is only possible to perceive it either as a field, or as a borderline. The stimulus pattern in Fig. 2-7 provides an example for this conclusion.

Figure 2-7. "String" or "hill"?

Either I experience this configuration as the border of an object, of a small hill or bump, or I experience it as an independent object in itself, something like a piece of ribbon or string. This narrow black ribbon-infield is bordered off from its outfield on all sides by its own sharp border contour. In the case of the hill- silhouette, the object represented here "is" a border, but in itself does not "have" a border. Thus one either experiences it as a field (a half-closed figure) or as a border between fields, but one cannot see it  as both field and border simultaneously.

As in the case of inhomogeneity/homogeneity, in the case of line/field we are able to find a dynamic polarization: the sum of the location differences between each and every perceptual entity and every other perceptual entity is, in the case of the row of points shown in Fig. 2-8C, larger than that in the case shown in Fig 2-8B (simply because there are more points within a line of equal length in 8C). Consequently, the gestalt stimulus for L+ is larger in C than in B, and the row of points in C is perceived as "more of a line" than in B. And, although the fields in B and C are, as stimuli, completely equal, the fields in C are perceived to a larger degree as "fields", and in fact, as  fields independent from each other. The extreme case of "field" perception on both sides of the line is shown in Fig. 2-8D because here the borderline runs continuously through the diagram. An extreme lack of the two field experience is illustrated in Fig.2-8A. Because where there is no borderline, there are no independent fields, there is only a single undivided field.

Figure 2-8. Relatioinship between line and field


5. Closedness and openness; figure and outfield

The gestalt factor "closedness" or "closedness/openness" (Fl), has a twofold, or even threefold, referent. Insofar as a line is closed, it encloses a field; this field is confined by the borderline. "Closedness" thus refers, on one hand, to "line"; it is "closedness of the line". On the other hand, it refers also to "field"; it is "closedness of the field". A field that is more or less confined by a borderline is a finite field. A "closed line" and a "closed field" (enclosed by the line) constitute  a single  percept:  a  "figure".  A figure is consequently a confined part of the total perceptual field, a part that stands out from the remaining infinite field, in principle, by its borderline ("contour").

Insofar as it is a figure, a figure consists of an "infield" and a "figure contour". The "rest of the world" constitutes the "outfield" of this figure. Insofar, the relationship between "figure" (Fl+) and "outfield" (Fl-) is the third referent of the gestalt factor Fl. The infield is closed with respect to the enclosing contour; the outfield is open with respect to the contour, enclosing the infield. Here we have to distinguish between two polarities: the first being "closedness/ openness" that corresponds to the twofold actualization of the gestalt factor Fl. The second polarity does not refer to the factor Fl alone, but to the entire hierarchy of the factors Pml to Fl; it is the "figure/outfield" polarity (see  Fig. 1-3H).  The figure is one of the poles of a visual percept, polarized up to and including the Fl factor, and the outfield is the other. Every figure has "its" outfield, every outfield "its" figure. Frequently, the outfield of a figure is in turn confined, creating a second figure, whose infield consists of the first figure and its outfield. In this case we have a two-layer infield-contour-outfield (ico-) relation- ship, a second-order ico-system. This will be discussed in greater detail in Part 6.

Now we shall try to find out the definition for the gestalt stimulus of Fl:

The more a line encloses a field,
a) the larger the "closedness of the line" is, and the more the line is the "contour" (c) of the field;
b) the larger the "closedness of the field" is, and the more the enclosed field is an "infield" (i);
c) the more the enclosing line and the enclosed field form a "figure" (ic); and
d) the more the non-enclosed field beyond the enclosing line is the figure's outfield" (o).

The less a line encloses a field,
a) the larger the "openness of the line" is, and the less the enclosing line is the "contour" (c) of the field;
b) the larger the "openness of the field" is, and the less the enclosed field is an "infield" (i);
c) the less the enclosing line and the enclosed field form a "figure" (Fl+); and
d) the less the non-enclosed field beyond the enclosing line is the figure's "outfield" (Fl-)

Thus, the gestalt stimulus for Fl+ is the degree of "enclosing" ("closedness", Fl+), i.e. the ratio of the length of the field-enclosing line to the whole circumference of the field, and the gestalt stimulus for Fl- is the degree of "openness" (Fl-), i.e. the ratio of the not line-enclosed part of the circumference to the whole circumference. The definitions of the gestalt stimuli for Fl (as well as for Ll and Gml, mentioned before) were found intuitively; it is likely that the "real" gestalt stimuli will need to be defined somewhat differently.

Figure 2-9. From "openness" toward "closedness"

Fig.2-9 shows three solid lines of equal length that, from A to C, increasingly enclose one of the two fields, and where the degree of closedness ranges from 50% - 100%, and the degree of openness ranges from 50% - 0%. In Fig. 2-9A it is immaterial which field is interpreted as being the "enclosed" field, since neither field is more enclosed than the other. This means, that each of the two fields is either closed or open to the same degree, and thus this pattern has no Fl-functions at all; the line here is a pure fourth-level Ll-line, bordering off two equivalent fields. In the case of Fig. 2-9B, the closedness is approx. 70%, the openness accordingly approx. 30%; the percentages in Case C are 100% and 0 %, respectively.

As just mentioned, at the Ll-level, the contour separates two equivalent fields; the field on one side has the same "weight" as the field on the other. Neither of the two takes precedence over the other. The situation is different at the Fl-level, since here the borderline runs partially, or entirely, around one of the two fields. This more or less enclosed field is, with respect to the enclosing field, of particular importance: it forms, along with the enclosing contour, a unified percept: the "figure" that stands out from the enclosing "outfield". If the "weight" of two fields, however, is approximately the same, so that each field is equally easy to be experienced as a "figure", a "reversal figure" is created. Such a dynamic polarity relation existing between figure and outfield will now be demonstrated. As in the cases of inhomogeneity/homogeneity and line/field, the polarity of figure/outfield is characterized by the impossibility of perceiving both poles at the same location simultaneously: one perceives a particular stimulus pattern as either figure or outfield. To do both at once is mostly impossible. This is proved by the "reversal figures" or "ambiguous figures": stimulus patterns that may be experienced for some time in one way, are then suddenly experienced in a completely different way. One of the most familiar of these is the pattern consisting of two "faces" and a "vase" (Fig.2-10). Either one sees the black vase as a figure, in which case the white field is its formless outfield, or one sees two white profiles, in which case the black field is no longer a vase, but an amorphous outfield between the faces. One cannot see both the faces and the vase simultaneously, as then one would be seeing three figures at once without an outfield, which is impossible. When the percept "switches", the infield-outfield relation is reversed.

This reversal is essentially based on a functional change in the border contour, which you can observe particularly clearly, albeit with some effort, in the "Necker cube" (Fig. 2-11). In the literature, one usually reads of a "reversal of perspective" taking place here, but it is not this change of perspective that is essential. If you carefully analyse and compare both phenomena, before and after the reversal, you will observe that the infield remains the infield even after the reversal: it is the interior of a hollow body. And the outfield is still the outfield; specifically, it is the exterior of the hollow body. But the six walls of the (hollow) cube have changed their border function. These walls form the "borders" of the (three-dimensional) body. Thus every "wall" of the cube consists of two sides: one directed inwards and one directed outwards. The sides that were turned outwards before the reversal are directed inwards after the reversal; the sides of the cube wall that were previously directed inwards, are turned outwards after the reversal, like a sock worn inside out.  If you wish to follow this reversal of the sides from "outside" to "inside" for yourself, I recommend that you first draw several Necker cubes and then fill in the phenomenally square sides of the walls with red one at a time, so that you can observe the change in the border function of the two sides of each  cube wall when the reversal occurs.


    In the patterns we have dealt with so far, there is only an either-or interpretation: either a figure or an outfield is perceived (or either an inward or an outward view occurs), there is no gradual transition from the former interpretation to the latter. One cannot even say that the stimulus that one has just perceived as a figure is "more" a figure than an outfield, as one could say of a color that it is more red than yellow. When dealing with such a reversible figure, one can at best state that it exhibits the tendency to spontaneously appear more frequently as a figure than as an outfield (or vice versa). Certain interpretations tend also to "stay" longer than their polar opposites. One can, however, devise series of stimulus patterns in which the ease (i.e.probability), with which one interprets an element of the series as a "figure", increases or decreases.

In the series shown in  Fig. 2-12, the figure-character of the small square decreases from A to C as the character of its outfield as an "outfield" decreases. A "good" outfield is, among other things, a field that completely encloses its figure. This means, that a "good" figure is a figure that possesses its enclosing contour as a contour of its own. Here, however, the small square figure exclusively possesses its own contour only in Case A; in B, it shares a quarter of its contour with the large square, and in C half. In the definition of the gestalt stimulus for Fl, we have to take into consideration this property of the figure-contour.

Figure 2-12. The more a figure possesses its contour as a contour of its own,
the more it is detectable as a figure

There is another, and I assume, until now not yet recognized, relationship between figure and outfield: their size relations. We can formulate a "size-relation law" that is relevant in the cases, when the one field that bounds the other field, is itself bounded by a contour:

"The smaller field is the infield, the larger field is the outfield".

This is true even in the case, that the smaller field is the enclosing field, and thus is to be expected to be the outfield. This is depicted quite clearly in the series A - C in  Fig. 2-13. In  Fig. 2-13X, the relevant contours and fields have been assigned letters. In A the small square (pc) within the larger square (qd) is easily perceived as a figure whose (finite) outfield is the larger square (see also the Delboef illusion in Part 8). The large square is a figure, too, with respect to its own outfield (r). In B the small square (pc) is still not too difficult to perceive as a figure; but in C the previous outfield (q), because of its smallness in relation to the previous infield (p), tends to become an infield itself. As such, it represents a "thing" - something like a picture frame. As an infield, (q) is completely enclosed by contours, specifically by the contours (c) and (d). In this process the previous outfield (r) of the large square, as well as the previous infield (p) of the small square, form together the outfield of the "picture frame". Section (p) of the outfield (pr) then has the appearance of a "hole". The contour (c) of the small square has changed its border function: the inner side of contour (c), previously directed  toward   the  infield (p),  becomes  an  outer  side, directed toward the partial outfield (p); the outer side of (c), previously directed toward the outfield (q), becomes an inner side directed toward the infield (q). One can see that the fields can change their functions as well: the infield becomes an outfield, the outfield becomes an infield.

Figure 2-13. The smaller the surrounding field, the more it is experienced as an infield

When one looks through the center in Fig.2-13C, one sees the outfield extending "behind" the object, stratified in the dimension of depth. One can often perceive a figure as lying in front of the outfield. For this reason, one hardly speaks of an "outfield" in traditional psychology, but uses "ground" and "figure/ground relationship" instead. Size relationships between figure and outfield play an important role in many so-called "geometric-optical illusions", as well as in many other visual-psychological laboratory findings (see the laws of interaction in Part 8).

6. The polarities of Pml, Dm, and Dl

The polarity relationship between two gestalt qualities of different intensities in adjacent areas, and originating due to gestalt stimuli of different magnitude actualizing the same gestalt factor, applies not only to the gestalt factors Gml, Ll, and Fl, but also to the gestalt factors Dm, Dl, and Pml.

Since there are many reasons for the complexity of the conditions at these levels, they will not be dealt with in detail in this book.  At present it suffices to contribute a rough sketch, using polar perceptual terms like those we have already dealt with. One often speaks of "low-contrast" and "high-contrast" figures. What is meant here are small - or large, as the case may be - brightness and color differences; the former are represented by Dm-, the latter by Dm+.

In the case of the gestalt factor Dl, perceptual entities that are "close to one another", and have small location differences (as well as those with a small degree of length), are indicated by Dl-, while perceptual entities of a large length, as well as those that are "far from one another", or that have large location differences, are indicated by Dl+.

There are also polar perceptual terms such as "bright" and "dark", "here" and "there", for the polarities at the P-level. In this way, "here is something bright" finds its twofold polar opposite in "there is something dark". There is a special condition, however, which would seem to contradict the polarity of Pml phenomena, as has already been mentioned: at the P-level, one cannot make distinctions at all, including distinctions of "bright" and "dark", "here" and "there". Now we have a problem: on one hand, one cannot perceive "bright" and "dark" at the same time, on the other hand, the expected polarity of the Pml perception necessarily requires the simultaneous experience of both poles, "bright" and "dark" (also valid for the l-aspect of Pml). The solution of the problem will be presented in Part 3.

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