6.3.3.1 Stimuli
Circles are very easy to display using the Psychophysics toolbox in MATLAB® so we altered the formula for the smooth edged object (see Equations 6.1 and 6.2) to generate a smooth curricular object using plain polar coordinates. Unfortunately, when integrated the circular smooth stimulus is only dependent on 𝜎−1 not 𝜎−2 (due to only one 𝑓(𝑟, 𝑝) term in Eq. 6.2),
so we expect a smaller decrease in perceived peak depth than for the square-based
stimulus. Therefore, in order to trial the circular objects, we initially piloted the experiment with two sharp edged objects to test if naïve participants could complete the task given circular objects and circular luminance windows. If pilot participants could do the task with circular stimuli, then we would explore the effect of smooth circular objects to see if there was a measurable decrease in perceived peak depth in these stimuli.
𝑓(𝑟, 𝑝) =1 2[tanh ( 1 𝜎(𝑟 − 𝑤 − 𝑝 2 )) − tanh ( 1 𝜎(𝑟 − 𝑤 + 𝑝 2 ))] Eq. 6.1 𝛿(𝑟, 𝜃) = 𝛿𝑝𝑓(𝑟, 𝑝) Eq. 6.2
118
Both sharp edged disparity defined objects were of identical size (radius 96arcmin, black outlined cylinders in Figure 6.9). The test object has a luminance window with a radius of either 74arcmin (0.8 times the size of the disparity defined object, as shown in in the anaglyph in Figure 6.10), or 111.6arcmin (1.2 times the radius of the disparity defined object), as shown diagrammatically as the dark grey region on the lower cylinder in Figure 6.9. The
comparison object has a luminance window of radius identical to the disparity defined object (96arcmin), as represented by the dark grey circle on the top cylinder in Figure 6.9.
In order to reduce the curtain effect, we added disparity to the luminance window that was consistent with the disparity of the dots at the edge of the window. The window with a fractional size of 1.2 has zero disparity, while 0.8 has the disparity of the peak of the test object. The disparity of the window with fractional size of 0.8 and the peak depth of the test object were stepped between seven values equally spaced between 5.8 and 8.4 arcmin. The luminance window on the comparison object and the peak depth of the comparison object had a disparity of 5.8arcmin.
Pilots were able to complete this experiment with extractable PSEs without reporting a perception of the curtain effect. Therefore, we ran this experiment on naive participants. Our main objective is for the
experiment to be able to be completed by the majority of participants as we expect the disparity edge of the sharp object to be too well defined for the luminance edge to strongly influence segregation. However, it would be interesting to confirm this hypothesis, if the experiment was doable by naïve participants. If the experiment was successful, we would have then moved onto smooth circular stimuli.
Figure 6.9: Diagram of the displayed depth of the luminance windows for the circular
object.
Figure 6.10: Anaglyph of circular stimulus in Experiment 5. Comparison object (top) and test object with luminance window of 1.2 times object size (bottom).
Note that the region with no dots is only due to the exaggerated disparity used in
this screenshot. Comparison Object Uniform Background Test object Luminance window
119
6.3.3.2 Results – circular stimuli
Figure 6.11 shows the results for circular stimuli, where the background was black (<0.01 cd/m2) with a mid-grey (18.67cd/m2) luminance window and white (37.06cd/m2) dots. Out of eight participants only seven were able to complete the demo stage. Out of these, two had PSEs for both luminance window sizes outside of the measured range of disparities, and therefore was rejected. From the remaining five participants, only one, Participant D had extractable PSEs for both the 0.8 and 1.2 luminance windows. The remaining three were capable of completing the experiment with the smaller 0.8 luminance window (Participants E, F, G and H see Figure 6.11). Out of these, all but Participant F had PSEs far outside of the displayed disparity range for a window 1.2 times the diameter of the stimulus. Note that normally participant F’s data point at 1.2 should be excluded, but as it is only just outside of the range it is included for interest. Additionally, several participants self-reported the circular luminance window as appearing as a separate object to the disparity defined object.
Figure 6.11: The PSEs for five participants. No PSEs were extractable for participants E, G and H for the 1.2 luminance window, and the 1.2 for F is extrapolated, not interpolated and
therefore likely has additional errors over the calculated standard error bars.
As the data is in the majority of cases completely flat, we cannot extract meaningful thresholds (typically these were on the order of infinity).
6.3.4 Discussion
By using a circular window with white dots and a mid-grey luminance window on a black background, we appear to have made the task easier than in Experiment 4 as some naïve
5.5 6 6.5 7 7.5 8 0.7 0.8 0.9 1 1.1 1.2 1.3 PS E (ar cmin )
Fractional size of luminance window Par D
Par E Par F Par G Par H
120
participants can complete the experiment with meaningful results. However, we still have a low success rate for a psychophysical task – only one of eight participants were able to complete the entire experiment with usable results. Four had good performance on only the smaller luminance window.
Interestingly three participants consistently chose the comparison stimulus almost all the time for the larger luminance window. One interpretation is that they are viewing the stimulus with the larger window as very much flatter; however, given the poor past performance at the luminance window experiments it is probable that these participants were ignoring the dots, comparing the disparities of the luminance windows. The disparity of the 1.2 luminance window was 0 arcmin, and the disparity of the 0.8 luminance window was identical to the peak depth of the test object. If participants were comparing the disparity of the luminance window to the comparison object, then we would expect participants to always select the comparison object as having a greater peak depth when the test object was displayed with a luminance window of 1.2. When the test object was displayed with a luminance window of 0.8, then we would expect the participants to act as unbiased observers. This is approximately what these three participants did, although it does not explain the minor flattening effect observed in the 0.8 radius stimulus. Given the number of participants that could not complete the experiments at all, the only solid
conclusion we can take is that these participants were unable to correctly complete the task as requested, and were each following a different strategy.
The circular objects provide multiple more problems: the continued reporting of the curtain effect when viewing a smooth edged circular object; the expectation of a decreased
flattening effect when compared to square objects; and being much more complex to model. We will therefore return to the square based stimuli in future experiments. However, this experiment and its pilots seem to indicate from the increased performance (and self-reporting from pilots) that the use of white dots on a black background is easier to perceive than the mid-grey background with white and black dots. We will therefore
continue using this regime in future to increase clarity of the disparity defined object. Potentially the most likely avenue to produce a usable result without the curtain effect is to revert to displaying the luminance edges using the dots themselves. As the dots make up the disparity defined objects, then it should be clear that the luminance boundary is a property of disparity defined object, and not a second object which is individually defined in depth. A similar technique to this failed in Section 6.2, but the change in dots to all being white and the increased overall luminance may alleviate the problems found there – we discuss this in detail in the next Section.
121