February 1966

Note on the Perception of Slant

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 References to these essays must cite them explicitly as unpublished manuscripts.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 set of problems centering around what has been called visual space perception, or sometimes depth perception, has been extremely difficult to solve because of the conceptual difficulties in defining just what the problems are, that is, in reformulating them coherently. In 1950, I tried to break away from the traditional statement of the problem in terms of the "third dimension" (Berkeley, 1709; Helmboltz, 1865) by restating it in terms of surface and slant. The problem is to explain the perception of the slant of a surface, I argued, not the distance of its points. But when it came to defining the slant of a surface, for purposes of experiment, I could not fully escape from the traditional way of thinking. I defined it as the degree of departure from the frontal plane (the plane perpendicular to the line of regard). This was called "optical" slant as distinguished from "geographical" slant (Gibson and Cornsweet, 1952). The latter could be defined with reference to the plane of the terrestrial horizontal and planes perpendicular to it. Optical slant varies as the eyes move from point to point over a plane surface; geographical slant does not.

What we are mostly aware of, as the eyes explore the environment, is not the optical slant of each surface at the momentary point of fixation but the geographical slant of each face of a whole layout of surfaces constituting the environment. The information for perception of a layout of surfaces is in the array of ambient light surrounding an observer (Senses, ch. 10) but this is quite distinct from the local information for the impression of optical slant at each fixation point. The "gradient of density of optical texture" at the fovea of the retina is information for optical slant but this does not explain the perception of environmental layout. As one looks upward from one's feet to the horizon, the optical slant of the earth's surface varies from zero to its upper limit but the geographical slant of the surface does not vary at all.

How does an observer, animal or human, perceive the constant geographical slant of a wall, or the earth, despite the ever-varying retinal impressions of optical slant on the retina? Formerly, I could only imagine that the registration of varying eye-posture must somehow compensate for the variation of the retinal gradient (Gibson and Cornsweet, 1952), It was taken for granted that momentary sense-impressions were entailed in space perception and sensations had to be "integrated" over time. Now, with the concept of the ambient optic array and its primary earth-sky contrast coordinate with the concept of the visual system as distinguished from the retina, we can entertain a new hypothesis. The invariants of the optic array (of instead of physiological optics) and the geometrical (not retinal) gradients of this array can be considered stimulus-information for the system. Observers with panoramic eyes (horses) can register these invariants directly, and observers with frontal foveated eyes (men) can register them over a series of fixations each overlapping the previous one. The ever-varying impressions of optical slant, then, are not the necessary basis for the detection of geographical slant. They are simply the consequence of how frontal foveated eyes have to work (Senses, ch. 9).

The concept of gradients as information for the perception of slant (Gibson, 1950a) did not make clear the radical difference between gradients of the retina and gradients in the ambient light. A rate of change of texture relative to a retina that moves about conveys no information; a rate of change of texture relative to the external array explored by a mobile retina carries much information. The reason for the failure to clarify this radical difference was that the experiments were performed with a pictorial display (Gibson, 1950b; Gibson and Cornsweet, 1952) which is a confusing compromise between the two cases since the picture can easily be thought equivalent to a stationary retinal image. Subsequent experiments on the perception of surface-slant (Flock, 1964, and references) have also used pictorial displays and have therefore not faced up to the basic problem (and in the end the simplest problem) which is the perception of geographical slant. The problem of the physiological interaction between eye-movements and the changing patterns of physiological excitation that go with them (the retinal sensations of traditional theorizing) is an entirely different problem.


G. Berkeley, Essay towards a new theory of vision, 1709.

H. Helmboltz, Physiological optics (vol. 3), 1865.

J. Gibson, Perception of the visual world, 1950.

J. Gibson, The perception of visual surfaces. Amer. J. Exp. Psych., 1950, 63, 367-384.

J. Gibson and Janet Cornsweet, The perceived slant of visual surfaces-optical and geographical. J. Exp. Psych., 1952, 44, 11-15.

H. Flock, A possible optical basis for monocular slant perception. Psychol. Rev., 1964, 71, 380-391 (with references there given).