Motion Parallax and Motion Perspective in Visual Perception
J. J. Gibson, Cornell University
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1. Parallax = the “difference in direction of a body caused by difference in position of the observer” (Astronomy). (Note that all astronomical motions of the observer are rotary not linear).
2. Motion parallax = apparent angular velocity of objects, which is inversely proportional to real distance and consequently permits a “safe conclusion” about distance. (Helmholtz)
3. The differential apparent velocity of the elements of a plane surface (motion perspective).
1. A plane surface and an eye (the terrestrial situation, not the astronomical situation).
2. That the surface has “elements“, of equal size.
3. That the surface is very large (like the terrain).
4. That the eye moves (is displaced) with a unit velocity.
5. That the eye is fixated in the direction of its displacement.
6. That the eye receives a hemispherical sheaf of rays from the elements of the surface.
How to describe the differential velocities across the hemispherical sheaf of rays, with reference to the “information” this contains as regards the distance of the nearest point of the surface, the relative distance of all points of the surface, and the direction of displacement (locomotion) with reference to the surface? What variables (or features) of the ray-sheaf can be specified which reflect (or co-vary with) these tridimensional facts? The pattern of differential velocities will vary with the angle of the surface to the level of displacement. Hence there is the general case of a surface at any angle to the line of displacement, and two special cases (a) the surface parallel to the line of displacement (which yields a sheaf filling only half of the hemisphere) and (b) the surface perpendicular to the line of displacement (which yields a full hemispherical sheaf).