The concepts of invariants in ecological optics

The concepts of invariants in Ecological optics. The ecological approach to visual perception Appendix 2 중에서:

The theory of the concurrent awareness of persistence and change requires the assumption of invariants that underlie change of the optic array. Four kinds of invariants have been postulated: those that underlie change of illumination, those that underlie change of the point of observation, those that underlie overlapping samples, and those that underlie a local disturbance of structure.

It would simplify matters if all these kinds of change in the optic array could be understood as transformations in the sense of mappings, borrowing the term from projective geometry and topology. The invariants under transformation have been worked out. Moreover it is easy to visualize a form being transposed, inverted, reversed, enlarged, reduced, or foreshortened by slant, and we can imagine it being deformed in various ways. But, unhappily, some of these changes cannot be understood as one-to-one mappings, either projective or topological (Chapter 6). Consider the four kinds.

1. Invariants of optical structure under changing illumination. Sunlight, moonlight, and lamplight can fluctuate in intensity, alter the direction from which they come to the layout, and differ in color. Hence the illumination can change in amount, in direction, and in spectral composition. Some features of any optic array in the medium will change accordingly. There must be invariants for perceiving the surfaces, their relative layout, and their relative reflectances. They are not yet known, but they almost certainly involve ratios of intensity and color among parts of the array (Chapter 5).
2. Invariants of optical structure under change of the point of observation. Note that a different point of observation is occupied by one eye of the human observer relative to the other, but that the invariants over this so-called disparity are the same as those under a change caused by a displacement of the head. A change and a difference are closely related. Some of the changes in the optic array are transformations of its nested forms, but the major changes are gain and loss of form, that is, increments and decrements of structure, as surfaces undergo occlusion. Proportions and crossratios underlie the transformations, however, and extrapolations, interpolations, gradients, and horizon-ratios underlie the increments and decrements. In short, the flow of the array does not destroy the structure beneath the flow (Chapters 5 and 13).
3. Invariants across the sampling of the ambient optic array. What I called looking around involves the reversible sweeping of the field of view over the whole array, back and forth, with continuous successive overlap. There is presumably a common structure in the sliding sample, and this may be thought of as invariant (Chapters 7 and 12).
4. Local invariants of the ambient array under local disturbances of its structure. Besides the motions of the sun, the observer, and the observer’s head, there are local events. These include not only displacements and rotations of rigid detached objects, but also deformations of rubbery surfaces—in fact all sorts of events from a rolling ball to rippling water, and from a growing infant to a smiling face. Each produces a specific disturbance of optical structure. But the surface, the ball, the water, and the face are seen to be continuations of themselves by virtue of certain non-disturbances of optical structure (Chapter 6).

These four kinds of invariants are optical. There are also surely invariants in the flow of acoustic, mechanical, and perhaps chemical stimulation, and they may prove to be closely related to the optical, but I leave them for the reader’s speculation. The study of invariants is just beginning.

The theory of the extracting of invariants by a visual system takes the place of theories of “constancy” in perception, that is, explanations of how an observer might perceive the true color, size, shape, motion, and direction-from-here of objects despite the wildly fluctuating sensory impressions on which the perceptions are based. With invariants there is no need for theories of constancy.

The reader, however, may consult a recent survey (Epstein, 1977) for the view that invariance-detection is only one more theory of perceptual constancy. These terms and concepts are subject to revision as the ecological approach to perception becomes clear. May they never shackle thought as the old terms and concepts have!