Marroquin J. L. (1976) Human Visual Perception of Structure. Masters degree thesis, MIT Dept. of Electrical Engineering & Computer Science

p. 6

There is ... a basic issue that is only very seldomly discuscussed: What do we mean by "visual experience"? Very often the problem of vision is oversimplified, and to "see" a scene is identified with the task of computing a verbal description of it. This problem is difficult enough, but it is important to recognize that there is much more in visual perception than assigning verbal labels to "objects".

If we pay attention to what we actually see, instead of thinking about it, we find that our visual experience is richer than any verbal description. This fact becomes evident as we observe a pictoric representation of a landscape - i.e., a non-verbal description - and compare the visual image with a literary description of the same scene or, further, with a list of the "objects" it contains. Moreover, we all recognize that certain visual patterns have qualities such as simplicity, elegance, unity, beauty, harmony, etc., but all these words denote experiences which are almost impossible to be described verbally, and which cannot be explained by a theory which considers visual perception merely as the assignment of verbal labels.

A further consequence of the "labeling" models is the belief that perception is based on the "detection" of certain features or structures that are "out there". This concept can be useful in the construction of "pattern recognition" devices, but as a model of human perception it can be very misleading because ... it is contradicted by many experimental facts.

A more realistic framework is to consider that the main function performed by the processes that underlie visual experience is to organize the input information in such a way as to construct what we call "reality", i.e. our world of surfaces, textures, structures, objects, etc. From this standpoint, perception is considered to be the result of the interaction of two systems of "forces": External forces originated by the pattern of stimulation at the retinal mosaic, ("proximal stimulus") and internal organizing forces resulting from the topological structure of the neural network.

At this point it is impossible to determine experimentally what "subjective experience" is (and maybe it will never be possible). However it seems reasonable to suppose that it arises as a correlate of physiological processes occuring in the brain. If this is the case, it follows that there must be an isomorphism between the structure of subjective experience and that of the underlying brain processes. If we adopt this point of view, then we may say that the structures we perceive in the world are constructed, rather than detected, by the brain. The subjective perception of structure is the correlate of internal organizing processes acting upon the visual input.

This does not mean, of course, that all the organizations we see are purely imaginary. Our survival demonstrates that the structures constructed by the brain are generally well correlated with the objective structures occuring in the physical world. For example, the internal construction of a region of the visual field as a segregated unit is generally correlated with the existence of a corresponding unit in the physical enviroment (i.e., an "object"). A corollary of this theory is that our perception along a "continuum" between Chaos and Order, must be restricted to a small region within it by our perceptual apparatus, in the same way as our perception of the electromagnetic waves is restricted to a small region of the spectrum. This conjecture is supported by the fact that when we observe an unstructured (chaotic) pattern, such as dynamic "noise", the brain tends to impose structure on it, thus limiting our potential perception of "disorder", and on the other hand, a pattern with too high adegree of organization tends to fragment and be perceived as a collection of lower order "substructures".

p. 34

The basic law that the perceptual organizing processes follow is a tendency to form segregated units of increasing size and complexity in a hierarchical way. This means that the most stable organization of a large field is not that in which elementary "atoms" or micro-elements are held together by a single global force, but rather, a tree-like structure in which the microelements are held together in small clusters or "molecules", which in turn, are grouped together into larger units, and so on until the whole field is organized.

We observe two forces in action as the cause of this behavior: Cohesive forces which tend to form clusters, and "surface tension" forces, which segregate these clusters as independent, complete units. As the analogy with the physical process from which I am borrowing this term suggests (the formation of soap bubbles, for example), both forces arise from a single underlying principle: the attraction forces between units. These forces, in turn, follow two important laws: the "principle of homogeneity" and the "principle of relative proximity".

p. 35

1.3.2 Principle of homogeneity:

This principle, first observed by the Gestalt Psychologists, can be stated as follows: "Homogeneity in a field generates cohesive forces and inhomogeneities generate segregating forces." This means that if a region in the retinal mosaic receives uniform stimulation, it will form a unit, while discontinuities in the stimulation (edges, lines) will segregate the unit from the rest of the field.

...

1.3.3 Principle of relative proximity:

This principle states that the attraction force between two units varies directly with their size, "strength", and with the degree of similarity between them, and inversely with the distance between their centers of gravity.

This principle is slightly recursive in the sense that the "strength" of a unit depends on the local attraction forces between the sub-units that form it, as well as on the degree of its internal organization.

p. 100

The patterns that I have used as stimuli in this work represent the interaction of two opposite principles: randomness and order (in the form of group structures). Aside from their usefulness as stimuli for psychophysical experimentation, such patterns are characterized by the great fascination they exert on the observer, and by the fact that they are "meaningful" and significant. They "make sense". In fact, group structures have always fascinated mankind, as an analysis of the artistic representations of any culture will reveal. * What is even more interesting is the fact that they have always and everywhere been used as religious and magic figures, as symbols of the most profound and incomprehensible mysteries of the human mind. Thus we find representations of groups in the pyramids of Egypt, and in the Gothic Cathedrals in Europe; in the structure of the 64 hexagrams of the ancient Book of Changes (I Ching) regarded as the basic source of Chinese philosophical thought, and in the Tibetan Mandalas on figures for meditation; in the archetypical astrological figure in the religious sculptures from ancient Mexico.

If, following Jung's interpretation ** we regard religious and magical imagery as a symbolic representation of man's and woman's inner reality, we must deduce from these facts that group structures should appear in the organization of higher mental processes.

Also supporting this conjecture is the work of Piaget (1971, 1974) on the development of intelligence. After long and careful observation and experimentation with children, Piaget concluded that the mental processes underlying intelligent behavior (not only logical and mathematical capabilities, but also the ability to recognize the conservation of weight, volume, length, etc. for example) are structured in group-like fashion.

* See Weyl (1952), and also Budden (1972), who presents examples of group structures present in musical compositions

** See Jung (1958)

Budden F. (1972) The Fascination of Groups. Cambridge University Press.

Weyl, H. (1952) Symmetry. New Jersey: Princeton University Press.