Excerpts from
L.Kleine-Horst: "Empiristic theory of visual gestalt perception. Hierarchy and interactions of visual functions" (ETVG). Köln
2001, Part 1. III 5

Lateral brightness gradient (Gml)

Is it possible to describe the perception of "moon in the sky" with the gestalt qualities of the factors Pml, Dm, and Dl alone? No, one cannot. The bright blob is bordered off completely against the dark field, and this by a sharp line. But "line", "border off", "sharp", and "complete" are qualities which cannot be described or explained by the gestalt factors previously discussed. One has to assume the existence of further gestalt factors whose actualization creates these classes of qualities.

Let's look at the "border-conditions" between "brightness" and "darkness" (= small brightness) in Fig. 1-10A more closely: within the bright blob "moon", brightness  sensations  of  equal  magnitude  are triggered at all locations. Brightness sensations of equal magnitude are triggered at all locations also of the dark part "sky", but the degree of brightness in the sky area is much lower than which in the moon area. There are also certain other locations where brightness and darkness meet: pairs of larger and smaller brightnesses exist at such locations; the elements of a pair lie close together. Each locus at the edge of the moon is characterized by this ratio of a large brightness difference to a small location difference across which the brightness difference extends.

 

Figure 1-10. Receptive retinal area for the perception of "inhomogeneity" (Gml)

  In Figure 1-10B, a small cloud is in front of the moon. At the place where the moon shines through the cloud, the conditions on the border are different: there is a brightness difference which is just as great as between the brightness of the moon at (c) and the darkness of the night-sky at (a), but the transition from one degree of brightness to the other is not as abrupt as in 10A. The distance (location difference Dl) across which the total brightness difference (Dm) extends is greater in the case of the edge of the moon, "blurred" by the cloud in 10B, than in the case of the "sharp" edge of the moon in 10A. If the ratio of Dm to Dl is large, we are dealing with an "inhomogeneity", with a "brightness-jump", an "abrupt" local change in brightness, a "steep" brightness decrease or increase.  In the case of a small ratio, a gradual transition from one brightness to the other can be perceived; the border between greater and lower brightness is "softer", the clouded edge of the moon is "blurred".

In order to perceive this degree of sharpness of the change in brightness, which is to say the degree of steepness or the magnitude of the brightness gradient, a separate gestalt factor is needed. The ratio of Dm to Dl cannot be detected by the factors Dm and Dl alone. The factor Dm creates a relationship only between brightnesses (to be more exact: a relationship between Pmls with respect to their brightnesses), and Dl establishes a relationship only between locations (to be more exact: a relationship between Pmls with respect to their locations). Neither of these two factors establishes a relationship to the other factor. In order to establish such a relation- ship, a quantitative relation, for example, between the brightness difference Dm and the location difference Dl between Pmls, the visual system needs a separate gestalt factor. I call this factor, whose existence I have to assume, the "lateral (l) brightness (m) gradient (G)" ("lateral" means "in frontal plane"). It does not matter what a factor is called, but it would be useful to agree on a name that could be part of an international scientific language. I thus propose the term "Gml".

The hierarchical relationships between Gml and the previously discussed gestalt factors are certain: Gml may be actualized, based on a certain measure ("actualization threshold") of the ratio of a brightness difference to a location difference, across that the brightness difference extends. This brightness difference and this location difference are required for them to have been perceived, i.e. the gestalt factors Dm and Dl need to have been actualized beforehand. On the other hand, Dm and Dl can be experienced independently from the quantitative relationship Gml, that exists between them. Thus, Gml is to be found above Dm and Dl in the visual functional hierarchy.  

6. Lateral line (Ll) 

Pml, Dm, Dl, and Gml enable us to detect the brightness gradient of a stimulus source. Especially "conspicuous" are the large brightness gradients at the edge of the moon. They appear as intense "inhomogeneities". At the edge of the moon, many such inhomogeneities are lined-up. Of course, this spatial arrangement of the inhomogeneities cannot be "recognized", "discovered", or "detected" by the factor Gml, because this factor can detect only inhomogeneities. Now a human being is apparently able to perceive the lined-up inhomogeneities as a "row" or "line". In order to be able to explain this perception we have to postulate a "lateral line factor". I assign it the symbol "Ll". Since we do not deal with "depth line" (Ld) and "temporal line" (Lt) in the Parts 1-6, we can abbreviate "lateral line" as "line" in what follows. I assume a row of inhomogeneities to be the gestalt stimulus of factor Ll. If inhomogeneities lie next to each other, in the form of a row, the gestalt factor Ll is actualized and its specific gestalt quality, "line", will be introduced into the percept. With the aid of this factor, one may perceive the row as a "line". The row itself, as long as it is not perceived as a line, is not taken in at all - it does not exist phenomenally. Before the actualization of gestalt factor Ll, only the inhomogeneities exist phenomenally. The row does, however, exist functionally, i.e. the loci of the inhomogeneities functionally form a row; this functional row-arrangement is the gestalt stimulus actualizing the line factor. Ll detects the row-relationship between the inhomogeneities. The inhomogeneities will then be perceived as having this relationship, as a "line".

 This only happens, however, if the gestalt stimulus Ll is strong enough to actualize the gestalt factor Ll, so creating the gestalt quality Ll ("line"). If the gestalt stimulus Ll is not strong enough, it only "activates" the factor Ll without actualizing it, and the quality Ll does not emerge.

The small retinal areas, via which  the gestalt factors Pml, Dm, Dl, and Gml are actualized, are illustrated in Fig. 1-11. By the additional actualization of factor Ll, each part of the edge of the moon may be detected as a "line".  

Figure 1-11. Receptive retinal area for the perception of "line" (Ll)

                                                                

7. Lateral closedness (Fl) 

One relationship of a few lines to each other applies to all figure contours: the closedness of the line(s). A (relatively) closed line borders off a part of the total visual field from the rest of it. The enclosing contour along with the contour-enclosed field forms the "figure" lying in its "outfield". All the small (functional) "lines of the moon-edge" together produce the single (phenomenal) enclosing border-contour of the moon.

The closedness of a line is a new gestalt quality. When one "adds" the gestalt quality "closedness" (Fl), the previously existing gestalt quality "line" (Ll) becomes "closed line" (Ll, Fl). In order to be able to perceive "closedness", one has to already be able to perceive "line", for it is this very line that is closed. We may therefore once again claim that the gestalt factor that enables us to perceive "closedness" must be located above the "line" factor in the visual function hierarchy. I call it "closedness". (I also call it "figuredness" or "figure factor", for reasons that will later become understandable.) The name used is not so important. What is important is to know what effects it has, and under which conditions these effects come about. Also important is an abbreviation by which it may be immediately identified, independent of all informal terms. Its abbreviation, in an international formalized language, shall be "Fl". In Fig. 1-12 you see a number of lines in a "closedness-relationship". Fig. 1-4 depicts the partial hierarchy of the visual system that enables us to detect the figure contour that we have been discussing.

Figur 1-12. Receptive retinal area for the perception of "closedness" (Fl)

"Expanded model of of gestalt perception"

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