A model of visual processing of this class of stimuli responses will need to account for changes in the direction of apparent motion. When elements are isolated, the apparent direction of motion follows that of the envelopes; when multiple elements are placed in proximity, the direction of apparent motion changes to agree with that of the carrier. I will proceed to quantify this reversal effect in subsequent sections. In order to do so I asked naïve observers to make binary classifications of their impressions of the overall direction of motion (clockwise or counterclockwise.) However, binary responses collapse together a number of perceptual qualities, so that these simple direction judgments do not fully capture the appearance of these stimuli.
Below are three demonstrations that place the fixation point in the center of the screen and the moving elements on a circle of constant eccentricity. The motion of the individual elements is the same in each demo; only the spacing and number of elements changes. These movies are arranged to loop, however the psychophysics I will discuss in subsequent sections is based on brief ( 500ms) presentations of motion.
Figure 2.1 shows six elements, so the spacing between elements is 1.04e measured circumferentially. In this demonstration the carrier motion is clockwise and the envelope motion is counterclockwise. For all observers I have shown this stimulus to, the perceived direction of motion is counterclockwise, in agreement with the envelope motion. This illustrates that higher order motion can be clearly seen in the periphery, and that at these wide element spacings the envelope motion dominates the perception. Compared to other stimuli it is relatively difficult to tell the direction of motion of the carrier, so we could say that the envelope motion “captures” the carrier motion (Hedges et al., 2011). For the largest values of carrier strength, (for these demonstrations, the carrier strength C as defined in General Methodsł::bel sec:methods is 100%,) the carrier motion might appear as a “wind” which overlays the moving envelopes, somewhat similar to the appearance of a low-contrast moving grating superposed on a stationary pedestal grating (Lu and Sperling, 2001). Incidentally, when carrier motions are directed opposite to envelope motion, as can be seen in Figure 1.1, the elements appear to have more flicker, and the perceived motion, while agreeing in direction with the envelope, seems less smooth.
As the number of elements in the display increases and the spacing between elements decreases, the appearance of the motion changes. The demonstration in Figure 2.2 increases the number of elements to 16; the spacing between elements is 0.39e, which seems close to the “critical spacing” for many observers. Generally the carrier motion becomes more visible and observers begin to equivocate in their reports of perceived motion direction. The perception is a mixture of both carrier and envelope motions, but the form of this mixture can take on several different appearances. Observers viewing stimuli near the critical spacing described a number of different qualitative impressions of the stimulus:
The subjective speed of the motion can change as spacing is brought near critical; if carrier motion opposes envelope motion, the perceived speed of the stimulus reaches a minimum at a certain spacing, being faster in the direction of envelope motion when spacing is larger and faster in the direction of carrier motion when spacing is smaller.
Some observers saw motion directions in agreement with the carrier immediately after stimulus onset which then changes to be more in agreements with the envelope motion. For this reason I asked observers in Experiment 1 to respond within a restricted time window. Observers often reported the sensation of giving a mistaken response (i.e. they gave a response but their perception of motion changed after they had committed to the response.)
One perceptual phenomenon that did not seem to occur is bistability. Both the carrier and envelope motions are individually consistent with a global rotation of the display around the fixation point, so that we might have anticipated perceptions exclusively consistent one rigid movement or the other (Anstis and Kim, 2011). However, the appearances of critically spaced stimuli tended to reflect a mixture of two motions rather than one overriding motion, and there was never the spontaneous all-at-once switch that occurs for perceptually bistable stimuli.
The third demonstration in Figure 2.3 has 22 elements spaced at 0.29e. For most observers it becomes difficult to see the envelope motion at this density especially at short viewing durations. When elements are this closely spaced the overall impression is of motion in the direction of the carrier. There is not as much of the appearance of two separate motions. However, the amount of subjective flicker does appear to increase when carrier motion is incongruent with envelope motion.
While I did not describe the stimulus construction in detail to naïve observers, all observers after having practiced at the task employed in Experiment 1 commented spontaneously on the two forms of motion being employed. More than one observer when commenting on the stimuli called the envelope morion “real” and the carrier motion “fake.” However the two motions are not equally salient or distinguishable in all conditions; the carrier motion appears less salient when spacing is wide, with few elements on screen, and envelope motion is more difficult to discern in the contrary situation. Motion after-effects appear to always be directed opposite the carrier motion regardless the spacing or the envelope motion.
There seems to be some individual variation as to how relatively strong carrier and envelope motions are. For some observers I was able to find a configuration of carrier strength, envelope motion, and spacing which I would perceive as clearly being clockwise but the observer would perceive as counterclockwise. While appearance was affected by carrier motion, it was not always affected in the direction of carrier motion; I sometimes found that adding carrier motion in one direction to a stimulus prompted a report that the stimulus was now moving in the opposite direction to the change. Sometimes I could even find a stimulus whose carrier and envelope motion were clockwise but whose appearance was counterclockwise to a particular observer. An effort at modeling the processes underlying this behavior will therefore have to capture this individual variation and the apparent nonlinearity in carrier motion perception.
There are too many stimulus parameters to explore the entire configuration space exhaustively, but I can report some impressions as to the robustness of the appearance of the stimulus. In particular I wondered whether the density-driven reversal of apparent motion was robust to changes in stimulus properties such as element size and eccentricity. A scaling of critical spacing with eccentricity and robustness of critical spacing against changes in target size target size have been proposed as two diagnostic tests of visual crowding (Pelli, 2008).
Adjusting the spacing from wide to narrow by adding more elements revealed a point at which the appearance of motion changed from envelope-dominated to carrier-dominated. I noted the spacing (or equivalently the number of elements) at which the appearance seemed to change, while varying other stimulus parameters. I found that I could vary the eccentricity, size, and velocity of the envelopes by a factor of 2 in either direction, while the critical spacing required to induce a change in motion appearance remained roughly the same. Similarly I could vary the spatial frequency and temporal frequency of the carrier by a factor of 2 in either direction without much affecting the critical spacing. At the extremes of the configuration space, the change in character of the motion was present among other percepts of motion, and could become hard to distinguish. The largest effect seemed to be for spatial frequency and element size, for which a change of a factor of four (going from 0.67 to 2.67 cycles per degree at 10 degrees eccentricity, the element size scaling inversely) only modestly increased the number of elements required for reversal, from 13 to 18. Scaling all spatial parameters (element size, eccentricity, envelope velocity, spatial frequency) at once did not affect the spacing at reversal; the critical spacing scaled with eccentricity.
The demonstrations shown in Figure 1.1 and in this section suggest that multiple motion elements placed in proximity in peripheral vision interact in such a way that the carrier motion becomes more perceptually salient and the envelope motion less so. When envelope and carrier motion are put into conflict, the inter-element spacing (depending on retinal eccentricity) appears to be the most reliable determinant of which component wins. In the following sections I report psychophysical experiments designed to capture and model the determining factors explaining perceived motion direction.