The stimuli were Gabor patterns with an orientation and central spatial frequency. In Experiment 1, the orientation of the stimulus was randomly chosen from eight possible angles (−78
o, −55.5°, −33°, −10.5°, 12°, 34.5°, 57°, or 79.5°), with its central spatial frequency at one or more spatial frequencies. In pre- and post-tests, the spatial frequency of the stimulus was randomly chosen on each trial from five possible ones (0.7, 1.0, 1.4, 2.0, or 2.8 cycles per degree [cpd]). In the training sessions between pre- and post-tests, orientation identification was trained in separate groups with stimuli with a designated spatial frequency (low at 0.7 cpd, middle at 1.4 cpd, and high at 2.8 cpd, or randomized over all five spatial frequencies as in pre- and post- tests). Training consisted of five sessions in high external noise and then two sessions in zero external noise. Experiment 2 evaluated learning and transfer in spatial-frequency identification and followed the same design, with the spatial frequency randomly chosen on each trial from eight possible ones (0.5, 0.7, 1.0, 1.4, 2.0, 2.8, 4.0, or 5.6 cpd). In pre- and post-tests, spatial-frequency identification was tested at five orientations, randomized over trials (−55.5°, −33°, −10.5°, 12°, or 34.5°). In training phases, the stimuli used one orientation (left at −55.5°, middle at −10.5°, or right at 34.5°) or all five orientations (as in pre- and post-tests), depending on the group. (See
Figure 2 for an example of all stimuli in high noise.) Thus, each experiment included four groups of observers in the various training conditions and one group of observers in the control condition.
On each trial, the Gabor stimulus was displayed either at the top left or bottom right corner of the screen. The 64 × 64 pixel patch is defined by \(l( {x,y} ) = {{l}_0}(1.0 + c{\rm{sin}}( {2{\rm{\pi }}f( {y{\rm{sin}}( {\rm{\theta }} ) + x{\rm{cos}}( {\rm{\theta }} )} ) \times {{e}^{\frac{{{{x}^2} + {{y}^2}}}{{2{{{\rm{\sigma }}}^2}}}}}} )\), where θ and f are the chosen orientation and spatial frequency, respectively; σ = 0.7°, the standard deviation of the Gaussian envelope; c is the maximum contrast; and l0 is the mid-gray background luminance. In our experiment, c was one of the three contrasts: 0.3, 0.6, or 1.0.
The external noise images were generated independently for each trial. Each noise image was composed of 2 × 2-pixel noise elements, whose contrasts were randomly chosen from a Gaussian distribution with mean 0 and standard deviation 0.33 (for the orientation task) or 0.25 (for the spatial frequency task) and filtered through a second-order Butterworth bandpass filter (cut-off frequencies at 1.4 cpd and 5.6 cpd, respectively). On each trial, the stimulus sequence was two external noise images followed by one signal image and then followed by two more external noise images (NNSNN). Each external noise image was independently generated. These images were flashed through quickly at the refresh rate, and participants perceived a single noisy Gabor through temporal integration. Stimuli were generated using MATLAB (MathWorks, Natick, MA) with Psychtoolbox 3 on a Dell PC (Dell Technologies, Round Rock, TX) and displayed on a 20-inch monitor (ViewSonic, Brea, CA). The color monitor was set at a refresh rate of 60 Hz and resolution of 640 × 480 pixels and in a pseudo-monochrome with luminance linearized into 127 levels by a visual calibration procedure (
Lu & Dosher, 2013). The minimum, maximum, and mid-gray background luminance values were 1, 67, and 34 cd/m
2, respectively. Images were presented at 5.3° visual angle eccentricity, subtended 2.8° × 2.8°. Participants sat 83 cm from the monitor, and a chin rest was used to stabilize the distance.