Stimuli were created using the Matlab Psychophysics Toolbox (Brainard, 1997; Pelli, 1997; Kleiner et al., 2007), and were presented on a 1920 x 1080 pixel resolution 25” LCD monitor with a 240 Hz refresh rate. The monitor was tied to a PC that was custom built to optimize timing and processing speed, and to minimize lags. The PC’s frame rate was 125 fps, and was benchmarked in FRAPS (frame rate benchmarking software; (Beepa, 2013)) during test runs of the experiment to verify observed frame durations matched those specified in Matlab. Participants were seated approximately 100 cm from the screen, making each pixel of the screen approximately 0.02 of visual angle. Responses were recorded via mouse movement and button clicks that corresponded to the current task.

The stimuli consisted of black annuli (each subtending 0.5 of visual angle in diameter) presented within an invisible 4x4 grid of equally-spaced possible presentation locations. The invisible grid was positioned centrally on the screen. There were 3.5 of visual angle in horizontal and vertical size and 0.5 of space between grid element locations, measured center to center.

The 16 possible stimulus locations within the grid were randomly divided into two frame presentations, split by a blank frame, each consisting of 8 positions designated to each frame. Each annulus contained a 45 gap in its ring, and the gaps were presented at either a 0, 45, 90, or 135 orientation. All stimuli were presented against a uniform gray background, set at 50 percent of the monitor’s RGB range (i.e. at Weber contrast). While the current stimuli are not common in psychophysical orientation research, work in visual acuity has found that contrast acuity for Landolt C is about double that of sinusoidal gratings and well above the limit of acuity for the eye (see Bondarko & Danilova, 1997; McAnany & Alexander, 2008), and that orientation discrimination is relatively high (Harrison & Bex, 2015), which suggests that these stimuli and arrangement should be more than optimal for use in the current study.

For the target stimulus of the segregation blocks, one randomly selected location of the 16 presentation locations was occupied by an annulus that was bisected into two halves, dividing the gap in the ring centrally; one piece of this annulus was presented in the first frame, and one half was presented in the second frame, such that overlaying the two halves would create a full annulus object. Identification of this stimulus from the distractors requires the participant to represent each frame distinctly within time, and to identify the odd element.

For the target stimulus of the integration blocks, one randomly selected position out of the remaining 15 stimulus presentation grid locations consisted of no annulus on either frame, and was therefore missing an element in the position. Identification of this missing element from the distractor stimuli requires the participant to represent an integrated percept of both frames to identify the location where no information was presented on either frame.

Of the 16 possible stimulus locations in the integration and segregation task blocks, 14 locations consisted of full annuli (each with a 45 gap in the ring), 1 location consisted of an annulus segmented across the two frames, and one location where no annulus was presented, equating to 7.5 annuli being presented per frame in these tasks.

In the orientation averaging task, all 16 locations across both frames (8 locations per frame) were occupied by an annulus object with a 45 gap cut out of the ring. Annuli in the orientation averaging and integration trials contained only one 45 gap missing from the ring, but within the segregation blocks a second 45 gap 180 from the first was added. This extra gap was added for these trials due to motion cues of the edges of the ring making the split element too easy to identify, relative to the distractors. As compared to more conventional Gabor patch stimuli, this stimulus design eliminates the ambiguity of the direction of the orientation versus its 180 reflection by having a single orientation angle denoting gap. Therefore, subjects should not need to resolve whether the stimuli was oriented at, for example, 90 or 270.

To investigate the possibility of sub-sampling strategies, distributional properties of each frame were independently manipulated. Table 1 lists the full set of stimulus parameters to be detailed in this section. Within each block, each frame was set to one of 4 predetermined levels of variation in stimulus orientation within the frame (σc2= 0, 0.25, 0.39, 0.46, where σc2 denotes the circular variance). The number of presentations for each of these variance levels was equivalent within each task and within each frame, and the order of assignments to a frame was random across trials. As this random ordering was carried out separately for each frame, the particular combinations of variances for frames 1 and 2 were also random (though, again, an equal number of variance presentations for each variance was preserved for each frame). Further breakdowns of the distribution of stimuli parameter permutations is detailed within the Stimulus Distributions section2 of the Appendix.

Possible stimulus angle configurations for a frame

Each row of the table was assigned the same number of times (though in a random order across trials) to the frame in the experimental trials, and orientations within a given row were randomly assigned to locations within the frame. This logic was followed for each frame, meaning the specific combination of means (and variances) for frames 1 and 2 were randomly determined on each trial. See Text for further details

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