Excerpts from
L.Kleine-Horst: "Empiristic theory of visual gestalt perception. Hierarchy and interactions of visual functions" (ETVG). Köln
2001, Part 1, III 3

 Brightness difference (Dm) and location difference (Dl)

Since we went to such lengths to see that we may experience brightnesses but not brightness differences with factor Pml, it has to be our next concern to find a separate factor with which we may experience brightness differences. This factor shall be designated by the symbol "Dm". "D" stands for "difference", "m" for "modal". Factor Dm distinguishes Pml percepts with respect to their modality. There are  small  and  large  differences of brightness. The stronger the gestalt factor Dm is actualized,  the  larger  the  perceived brightness difference. Besides brightness, also color is an aspect of modality. In this book, however, will color seldomly be taken into specific consideration.

 

Figure 1-7. Two Pml areas form one Dm area

 As in Fig.1-6, small fields have been drawn in Fig.1-7. Each circular field represents a retinal area receiving sensory stimuli, which then actualize the factor Pml. In order to experience brightness difference, a larger retinal area is needed because at least two "Pml areas" are necessary to compare the degrees of brightness that they transmit, in order to give rise to the perception of "brightness difference". The perception of a brightness difference is possible only in the case of (bb'); in the other two cases, in which brightnesses of the same intensity are transmitted by the retinal areas, "no brightness difference" is detected.

We are not only able to perceive brightness differences, but also location differences. There has to be a gestalt factor that enables us to make this distinction, which I assign the symbol Dl, since index "l" stands for "location". Thus Dl means the difference (D) between the Pml percepts with respect to the locations (l), at which the stimulus sources are perceived, or with respect to the retinal locations of the stimulated receptors.

The functional location difference (corresponding to the distance of the stimuli on the retina) is the gestalt stimulus that actualizes the gestalt factor Dl. If one assumes that the visual system is able to grasp stimuli as far apart as (a') and (b) in Fig.1-7, then their "objective" location difference would actualize the factor Dl strongly, and "large location difference" or "far apart" would be experienced. The Pml stimuli pair (cc'), as well as the pair (bb'), and (aa'), would actualize factor Dl only slightly; the two objects would be perceived as "lying close together". It is of little importance how one chooses to informally designate the spatial interval between retinal loci, or between perceived figures, the symbol "Dl" serves as an unequivocal formal designation.

If you asked me how I know all of what I claim here, I would have to confess: I do not really know it, I simply worked it out. Maybe you would tell me then that you do not believe me that all this is true, I do not expect you to believe it to be true. I only expect you to do what I do: to make the assumption that it is true. These are only hypothe- ses. These hypotheses, however, are not coincidently stated side by side but are connected with each other in such a way as to form a theory of convincing logic. Perhaps a few scientists will exclaim: "How could we have been so blind as not to have seen this!" It is the blindness of those caught up in their dogmas. But now they will receive their "enlightenment".

4. The hierarchical relationships between Pml, Dm, and Dl

The relationship between Pml and Dm is a hierarchical one. This can be shown easily by the following consideration: we can experience brightness without experiencing brightness differences, for example, when we perceive only a single brightness (Pml). But we are not able to perceive brightness differences without perceiving more than one brightness simultaneously. This relationship may be understood as a hierarchical one, where Dm is located one level above Pml.

Figure 1- 8. Possibility and impossibility of actualizing Pml and Dm

There are three steps of actualization of the gestalt factors Dm and Pml: first, it is possible that the stimulus is so weak that not even Pml is actualized (Case 1-8A). Second, it is possible that Pml is actualized, but not Dm because the stimulus is too weak for the actualization of the latter (Case 1-8B). Third, it is possible that both Pml and Dm are actualized (Case 1-8C). It is, however, not possible for a higher-level gestalt factor to be actualized without the actualization of all the lower-level gestalt factors above which it is ordered (Case 1-8D).

What is true for Dm with respect to Pml is also true for Dl with respect to Pml. We may perceive a location without perceiving a location difference, but we cannot perceive location difference without perceiving the locations whose differences we perceive. Therefore we also need to assume which Dl is located at least one hierarchy level above Pml, for with Pml we perceive not only the brightness but also the location of a stimulus.

This consideration, however, does not enable us to tell whether Dl can be found at the next higher hierarchy level above Pml or at any other higher level. It is only certain which Dl is above Pml (the same is true for Dm). The hierarchical relationships set for Pml, Dm, and Dl so far could therefore be as those shown in Fig. 1-9. Dm and Dl are in each of these cases above Pml. The question is: which of these cases is true? The question begs for clarification of the hierarchical relationship of Dm and Dl to each other. Having considered the relationships of all the gestalt factors to one another, I assume that Case 1-9C is true.

 Figure 1-9. Logically possible hierarchical relationships between Pml, Dm, and Dl

"Lateral brightness gradient (Gml)"

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