The Ecological Approach to Visual Perception

By James J. Gibson | Go to book overview

APPENDIX 2
THE CONCEPT OF INVARIANTS IN ECOLOGICAL OPTICS
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.
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).
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 cross- ratios 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).

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