Apparent Depth Threshold for the Benussi Effect
Using the single staircase psychophysical method, the apparent depth threshold for the Benussi effect was determined for 5 observers. The threshold occurred at an eccentricity of 2r/3, where r equals the radius of the larger circle expressed in millimeters.
Is the Benussi Effect a Kinetic Depth Effect?
Rapid, successive presentations of an eccentric circle pattern and its mirror-image elicited apparent depth and, as has been previously demonstrated for the Benussi effect, there was an increase in apparent depth with an increase in circle eccentricity. Taken together, these data were interpreted as contravening Wallach, Adams, and Weisz's account of the Benussi effect as an instance of the kinetic depth effect.
Rigidity and Misperceived Motion
Dynamic patterns that have a rigid interpretation (ie could be produced by the changing projection of a rigid object in motion) are not always perceived by human observers as representing rigid objects. The pattern studied by Braunstein and Andersen (1984) provides one example of this phenomenon. Similar examples have been described in the past. They include the Mach illusion (Eden 1962; Lindsay and Norman 1972; Ullman 1979), some instances of the Ames window (Ames 1951), the distorting Necker cube (Sperling et al 1983), the spiral illusion (Kolers 1966), the misperception of rotating planar figures (Wallach et al 1956), and the perceived distortions of rotating 3-D objects (Wallach and O'Connell 1953). In discussing the role of rigidity in the interpretation of structure from motion (Ullman 1979), I have described two conditions under which rigid structure may not be perceived even though the changing image is compatible with the projection of a rigid object in motion. The first condition has to do with the availability of static three-dimensional (3-D) cues. If information regarding the 3-D shape of the object is available in the static projections, the perceived 3-D shape and its changes over time may be affected by the static cues, and not only by a structure-from-motion process. Under such conditions, as the image changes, the perceived shape may distort rather than move rigidly. Examples of this situation include the Mach illusion, the distorting Necker cube, and the nonrigid motions described elsewhere (Ullman 1979, chapter 5). The second condition arises from misperceptions of the motion pattern in the changing image. For a variety of stimuli (eg the barberpole illusion, the rotating spiral illusion), the perceived motion differs from the physically correct motion. Such misperceptions are associated primarily with smooth contours that lack identifiable, traceable features. (See Ullman 1979 page 171; Ullman and Hildreth 1983; Hildreth 1984 for further discussions of this problem.) It is not surprising that when the motion pattern is perceived incorrectly, rigid motion may be perceived as nonrigid. The use of rigidity in the interpretation of structure from motion means that a rigid interpretation is sought for the perceived 2-D transformations. If the perceived 2-D transformations are different from the correct motion, distortions are likely to occur. In examining the role of the rigidity assumption, care must be taken therefore to ensure that two requirements are met: first, that no 3-D structure is perceived in the static projections; second, that the motion is not misperceived. The second requirement seems to be relevant to the experiment of Braunstein and Andersen. As they have noted, the figure used in their experiment was composed of spiral arcs. As illustrated by the standard spiral illusion, the rotation of such patterns is often misperceived: a motion roughly perpendicular to the contour is perceived instead of the true rotation. It seems therefore that the stimulus described by Braunstein and Andersen is simply an example in which a misperceived motion