Invariants in the Changing Optic Array and What They Specify for an Observer in an Environment

June 1971

Invariants in the Changing Optic Array and
What They Specify for an Observer in an Environment

J. J. Gibson, Cornell University

The World Wide Web distribution of James Gibson’s “Purple Perils” is for scholarly use with the understanding that Gibson did not intend them for publication. References to these essays must cite them explicitly as unpublished manuscripts. Copies may be circulated if this statement is included on each copy.


The following hypotheses are based on the general assumption of ecological optics that the ambient optic array normally undergoes changes, and that a “frozen” array is a limiting case—the case of a motionless observer in an eventless world. The information about the layout of the world is more or less ambiguous in this limiting case because many of the invariants-under-change are not then isolated. Since a picture represents a sample of such a frozen ambient array, the pictorial “cues for depth” are insufficient to explain normal perception; hence they are omitted from consideration here (cf. Kennedy, 1970; Gibson, 1971). References to the experiments tending to show that these invariants can actually be picked up by an observer, from the Cornell laboratory and elsewhere, are listed along with the hypotheses. They are not always conclusive because they were not performed with these explicit hypotheses in mind, although they often anticipate the present formulation.

It is here assumed that the environment is normally “cluttered,” i.e., that some of its component surfaces are hidden or occluded at any fixed point of observation (unprojected in a given ambient array) and that a wholly “open” terrain and an unfurnished windowless room constitute a limiting case. Hence the formula reducing environmental layout to the slants of surfaces and their changes of slant (Gibson, 1950) is insufficient, along with the theory of optical gradients as a substitute for the depth-cues. The implications of the horizon of the open terrain, and the vanishing limits of texture-density and textural change in the ambient array will not be followed up here, although a supplementary set of hypotheses could be limited for this problem. Neither will the implications of the dual optic array at two binocular points of observation. In the left-hand column are listed what may be called invariants or regularities in the topological structure of the array (optical stimulus-information as contrasted with optical stimulation) and in the right-hand column are listed what they specify or “mean.”

I. A persisting texture in the ambient optic array, elements of which map themselves over time. A solid substance in the environment, with a surface facing the point of observation (Gibson and Waddell, 1952).
Ia Scintillation of the texture of the ambient optic array with no elements that persist for long, and no mapping to themselves over time (i.e. no invariants). A chaos, i.e., a nonexistence of solid substances and an absence of persisting layout.


II. A region of the ambient optic array without texture or structure (a non-array). Air, sky, or interspace in the environment with no background behind it.
III. A contrast-contour in the optic array (border). Highly ambiguous: not only an edge in the environment but also many other things.
IIIa. A closed contour in the optic array: a form or silhouette. Ambiguous: may be either a detached object in the environment or a window (hole). But also a patch of pigment on a surface, or a cast shadow.
IIIb. The size-transformation of a closed contour or form in the optic array, i.e., an expansion or contraction of the contour as such. Somewhat ambiguous: expansion specifies approach and contraction specifies recession but the former may be either approach of something or approach to something, and the latter may be either recession of or recession from something (Gibson, 1957; Gibson and Gibson, 1957).
IV. A contour in the array on one side of which the optical texture persists in time (i.e., the one-to-one successive mapping of elements is perceived on that side of the contour). The occluding edge of a surface (or an object) in the environment (Gibson, Kaplan, Reynolds, and Wheeler, 1969. Also the film).


IVa. The progressive deletion of texture elements on the other side of such a contour or its inverse, the progressive accretion of elements. A surface in the environment being concealed behind an occluding edge or the opposite event, a surface being revealed at an occluding edge (film on optical transitions).
V. A closed contour in the array with persistence of texture elements inside the contour and deletion or accretion of elementsoutside the contour. A detached solid object with occluding edges in front of a background in the environment (film on optical transitions).
Va. The reverse: A closed contour in the array with persistence of texture elements outside the contour and deletion or accretioninside. A hole or window in front of a background in the environment (film on optical transitions.)
Vb. A closed contour in the array with persisting texture inside (V) and with both deletion and accretion outside, the one being equal to the other.

— Equality of deletion and accretion.


— Axis of deletion to accretion.


A solid object moving in front of a stationary background with a “leading” edge (covering it) and a “trailing” edge (uncovering it).

Parallel motion of the object to the surface of the background.

— Direction of motion

Vc. A rectilinear contour at which a disruption of adjacent elements of the optical texture occurs without deletion or accretion of elements on either side of the contour (a limiting case). The linear motion along itself of a straight occluding edge of an object in front of a stationary background. (In the limiting case this might be confused with a shearing motion of a surface relative to an adjacent surface at a crack in the substance.) (Gibson, Gibson, Smith, and Flock, 1959).
VI. A persisting “frozen” texture of the ambient optic array, not only mapping to itself over time (I) but also unchanging in pattern and form. A permanent environment with a stationary observer (ego) but with a more-or-less indeterminate layout (Gibson, 1958).
VIa. Motion perspective of the texture of the ambient optic array (centrifugal and centripetal flow to opposite poles, i.e., magnification and minification). Locomotion of the observer relative to a permanent environment with a fixed layout (Gibson, Olum, and Rosenblatt, 1955).
VIb. Centrifugal flow of the texture in an ambient optic array (magnification) or its inverse, centripetal flow (minification). Locomotor approach to a surface in the environment or its opposite, recession from a surface (going away from.) (Gibson, Olum, and Rosenblatt, 1955).
VII. Size-transformation of a closed contour (IIIb) with persistence of texture-mapping inside the contour but not outside (V) and a frozen texture outside (VI). Approach of a detached solid object to a stationary observer in a permanent environment (Schiff, 1965).
VIIa. Same as above but with magnification (centrifugal flow) of the texture outside the contour. Approach of the observer to a stationary detached object in the environment (Gibson, 1958).
VIII. The pole of the centrifugal flow of the texture of an array (the center of magnification in the ambient array). The direction of the path of approach of the observer to the permanent environment (the object at which locomotion is aimed) (Gibson, 1955).
VIIIa. A symmetricalmagnification of a closed contour and its enclosed texture (the center of the figure and the center of expansion coincide.) Approach of a solid object on a collision course toward the observer (Schiff, 1965).
VIIIb. Asymmetrical magnification of a closed contour and its enclosed texture (the center of magnification is outside the closed contour.) Approach of a solid object on a non-collision or “passing” course (Schiff, 1965).


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