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

Functional antagonism

1. The functional structure of the figure perception system

Fig. 2-14 illustrates the hierarchy of those gestalt functions that constitute the static, two-dimensional figure/outfield perception. Looking at the moon causes certain gestalt stimuli to arise, i.e. specific relationships and interrelationships between functions, ultimately triggered by sensory stimuli. The gestalt stimuli Pml+ and Pml- actualize the gestalt functions Pml+ and Pml-. The perceiver then "sees", i.e. he detects either "here is something bright" or "here is something dark".

Figure 2-14. System of the antagonistically actualized gestalt functions
of the static, two-dimensional figure/outfield perception

The actual functional brightness differences between the "Pmls" (with Pml alone, however, not capable of being experienced) and the actual functional location differences between the "Pmls" (likewise not capable of being perceived at this point) are the gestalt stimuli for the actualization of the gestalt factors Dm and Dl, in their positive and negative functions. Here Dm+ indicates the larger of the two brightness differences, Dm- the smaller. The latter has a minimum value of zero, in which case it signifies "no brightness difference", or "brightness sameness". These terms are to be understood in all cases as being "relative". Correspondingly, this holds also for "large location difference" and "small location difference". The former means "somewhat farther apart from one another", the latter "somewhat closer to one another".

Gestalt factors of each hierarchy level refer to relationships between the activation of the gestalt factor(s) of the next-lowest level; consequently, Gml refers to the relationships between the activation of Dm and Dl. Since Gml+ can be best represented as a ratio of a large brightness difference to a small location difference, in Figure 2-14 lines denoting the direction of actualization have been drawn from Dm+ and Dl- to Gml+, and likewise, corresponding lines from Dm- and Dl+ to Gml-. A line (Ll+) is a relationship between inhomogeneities (Gml+), a field is a relationship between homo- geneities (Gml-), as the corresponding lines drawn on the diagram illustrate. The twofold reference of the positive function of the gestalt factor Fl to a borderline ("closed line"), as well as to a field ("closed field"), is illustrated by the lines leading from Ll+ and Ll- to Fl+.  Fl-, on the other hand, has no reference to Ll+, but only to Ll-, to a field. This is because the outfield is in fact a borderless field. For this reason, no line has been drawn leading from Ll+ to Fl-, but only from Ll- to Fl-. It now also becomes clear what the question marks in Fig. 2-2 stand for: for Ll- ("field"), whereby "line" and "closedness" are labelled respectively Ll+ and Fl+.

     2. The receptive retinal areas of the gestalt factors

The retina is the location where light stimuli impinge upon the photoreceptors. According to the three-sphere theory of visual perception, these sensory (material) entities ("photoreceptors and absorbed light energy") have corresponding functional entities. Certain relationships between the (functional) outputs of the (material) photoreceptors constitute the gestalt stimulus Pml+ for the gestalt function Pml+, which in turn creates the (phenomenal) gestalt quality Pml+ "here is something bright". It creates also the gestalt stimulus Pml- for the function Pml- that creates quality Pml-, "here is something dark".

Now during "normal" perception, every perceptual quality is to be found in many varying degrees and at many different locations. In order to prove the polar character of perceptual experience, one must consequently specify that perceptual qualities, among the total of all perceptual qualities, form the two poles of the quality, and this in such a way that when one pole appears, the other also appears, when one pole disappears, the other also disappears, and finally, so that when one pole increases in magnitude (becomes more intense), the other does so as well.  

It is to be assumed that the "receptive retinal Pml areas" are very small. In  Fig. 2-15A, several of these small "receptive Pml areas" are represented as small disks. By means of these areas the gestalt function Pml+ ("bright") is actualized, by means of other adjacent areas, the gestalt function Pml- ("dark"). For the moon and the sky, Fig. 2-15B illustrates a rough schematic distribution of the receptive Pml areas via which "moon-brightness" (+) and "sky-darkness" (-) can be assumed to be actualized (see, however, Part 3 - "filling-in").

  Figure 2-15. Receptive Pml+ and Pml- areas (A) and their distribution (B)

 Functional relationships between Pml percepts, the gestalt stimuli Dm and Dl, actualize both the gestalt functions "brightness difference" and "brightness sameness" (or large brightness difference and small brightness difference, respectively) as well as the gestalt functions  "location difference"  and "location sameness" (or large and small location difference). Since every receptive retinal area of Dm comprises a relationship between more than one receptive area of Pml, it follows that the area of Dm is larger than the area of Pml.

Figure 2-16. Receptive Dm+ and Dm- areas (A) and their distribution (B)

 Fig. 2-16A illustrates several receptive Pml areas near the edge of the moon (more exactly, of course; near the optical projection of the edge of the moon). Dm areas are represented by encircled pairs of Pml areas. One can see on the diagram that Pml areas must be brought together so that a polar Dm perception arises: a Pml+ area and a Pml- area form a Dm+ area, via which "large brightness difference" is actualized. Two Pml+ areas or two  Pml- areas,  on the other hand,form a Dm- area, via  which "small brightness difference" (or "brightness sameness") is actualized. The Dm+ and Dm- areas overlap somewhat, and are therefore adjacent: a Pml+ area which, along with a Pml- area, forms a Dm+  area, forms also a Dm- area with another Pml+ area. Likewise, a Pml- area along with another Pml- area also forms a Dm- area. Fig. 2-16B shows the distribution of Dm+ and Dm- areas; the Dm+ areas are all located on the moon-edge region (figure contour), and the activated Dm- areas are found in both the moon-region (infield) and the sky-region (outfield).

There are no Dl-areas independent from Dm-areas. The factors Dm and Dl are located at the same hierarchy level, and thus form a common percept. For this reason, somewhat lesser attention has been paid to the more complex interrelationships at the D-level. Fig. 2-17 illustrates that a Dm-area can be larger or smaller, depending on whether the brightness difference is combined with a larger or smaller location difference, respectively (but I am not sure).

Figure 2-17. Equal brightness difference with unequal location difference

As shown in Fig.2-18A, a yet larger receptive retinal area is necessary for the reception of those sensory stimuli, whose relations and interrelations give rise to the gestalt stimulus Gml.  The edge of the object provides the Gml+ gestalt stimulus: a large ratio of brightness difference to a small location difference across which the brightness difference extends. The gestalt stimulus for homogeneity (Gml-), that is immediately adjacent to the gestalt stimulus Gml+, is derived from light stimuli reflected by the surface of the moon and by the sky, and consists in a ratio of a small (even non-existent) brightness difference to a large location difference across which the brightness difference extends. Here "large location difference" means that brightness sameness is relayed via a number of retinal Dm- areas.  The distribution of the activated Gml- /Gml+/Gml- areas is depicted in Fig.2-18B; the "large location differences", across which the Gml- gestalt stimuli extend, are depicted by drawn-out negative signs. In  Fig. 2-18A one can see that, as in the case of Dm, the positive and negative areas partially overlap also in the case of Gml.

Figure 2-18. Receptive Gml+ and Gml- areas (A) and their distribution (B)


Figure 2-19. The transition from Gml areas (A) to Ll area (B)

 As shown in Fig. 2-19A and B, a number of Gml+ areas "in a row" compose an Ll+ area; a number of Gml-  areas "in a cluster" compose an Ll- area. As seen in Fig. 2-20, in "closing" several lines (Ll+), we enclose a field (Ll- ) to form a uniform closed borderline (Ll+, Fl+). This field is closed, finite, and confined (infield, Ll-,Fl+); the other field is open, infinite, and unbounded (outfield, Ll-,Fl-). The reader will have recognized that the "essential" difference between figure and outfield exists solely at the Fl level.

Figure 2-20. Receptive area of  the figure/outfield perception

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