August 1970
A Terminology for Describing the Layout of Opaque Surfaces
and the Occluding of One Surface by Another
J. J. Gibson
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 References to these essays must cite them explicitly as unpublished manuscripts.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.
A surface is defined as the interface between an opaque reflecting substance and the medium (air) in which points of observation exists and in which animals can move about.
1. The concave corner. The apex of the dihedral angle formed by plane surfaces when the substance is on the side of the obtuse angle and the medium is on the side of the acute angle.
2. The convex corner or edge. The apex of the dihedral angle of two surfaces when the substance is on the side of the acute angle. As the angle becomes more acute the edge may be said to become “sharper.”
3. The curved concavity. A curved surface area when the medium is inside the curve and the substance is outside.
4. The curved convexity protuberance. A curved surface area when the substance is inside the curve.
Occlusion is defined in ecological optics as the non-projection of a surface to a point of observation in the medium. It is caused by a convex corner or by a curved convexity; a concave corner and a concavity do not occlude. Concealment and hiding are synonymous terms for occlusion.
5. The occluding edge. The borderline between the projected and the unprojected surfaces (faces) of the dihedral angle forming a convex corner, i.e., the apex of the angle. The projected surface is said to “face” the point of observation and the unprojected surface not to do so; the former sometimes is called the “front” and the latter the “back.” The edge also occludes that portion of any other surface that lies behind it, commonly called the “background.”
6. The occluding convexity. The borderline between the projected and the unprojected portions of the curved surface at a given point of observation (the locus of a set of tangents to the surface). It also occludes the portion of any other surface that lies beyond the protuberance.
A precise meaning can now be given to what we most commonly call an object in the environment: it is a composition of convex and concave corners and of convexities and concavities as defined above. (Apolyhedral object is composed of the first two and a curved object of the second two, but all combinations are possible.) This description is superior to one in terms of analytic geometry for the purpose of visual perception. It enables us to speak of an object–any object whatever.
We can now distinguish between an object and the outline or closed contour of an object in an optic array, and we can observe that the latter corresponds only to the occluding edges (and occluding convexities) of the object. The figure ground phenomenon in perception (as usually described) results when the optical information normally available for the perception of an object is limited to an outline or silhouette, that is, to the information for the perception of its occluding edges (or occluding convexities). The figure-ground phenomenon is therefore a case of reduced perception rather than a prototype of perception, or the basis of perception.
In most displays of optical information the outline or silhouette is frozen in time, that is, change of the occlusion is eliminated, and the phenomenal object tends to become depthless except for the separation of the “figure” from the “background.” Also when the closure of lines or contours is experimentally manipulated, ambiguous or equivocal perceptions arise of the concavity and convexity, and of occlusion. Thus the dihedral angles in the staircase figure will appear to reverse between concave and convex; or the direction of occlusion will reverse so as to convert a goblet into two facial profiles.
The new hypothesis is that the perceiving of corners, edges, convexities, and concavities (the first four definitions above) together with the perceiving of occlusion (the next two definitions) is based on the pickup of “formless invariants” in the structure of the optic array. This pickup is more basic than form perception; it develops in animals and children before the perceiving of “forms” develops. It is assumed that the back of an opaque object and the background behind an object are not unseen (contrary to the usual assumption) unless a special attitude is adopted enabling one to experience the world as if it were a flat patchwork of colors. Only when the patchwork is taken to be the basis of perception, developmentally and logically, does it theoretically necessary to interpret the figure-ground phenomenon as evidence for a process of sensory organization. Otherwise it can be interpreted in the way suggested above, as a by product of the perception of occlusion.
Mathematical note. Ordinary three-dimensional geometry includes some of the concepts and terms employed above but not others. Dihedral angle, apex, plane vs. curved, acute vs. obtuse, inside vs. outside of a curve, tangent to a curve, line-closure and perhaps projection are ordinary geometrical terms. But the concept of opaque substance vs. medium (along with interface and reflecting surface) is foreign to abstract geometry, since geometrical space is “everywhere perfectly transparent” (Nicod). The point of observation with its ambient optic array does not exist in such a space. The convexity-concavity concept only arises when a point of observation is recognized as being in the medium. So does the notion of the facing of a surface and the notion of front and back (or in front and behind). And the occlusion of one surface by another is wholly relative to a given point of observation. The notion of changing occlusion with movement of the point of observation is foreign to abstract geometry, although the latter admits motion relative to a coordinate system.
The question is whether or not the kind of space defined by these concepts, a space that takes account of the features of layout and the fact of occlusion, is a “geometrical” space, and if so what kind it is.
Acknowledgment. This memo owes much to discussions and collaboration with John M. Kennedy. He is developing, however, a descriptive system of his own, in his doctoral thesis, which may differ from this one in some respects.