Supplemental Material
How can we interpret the spatio-temporal patterns observed in the human and
model classification images (CIs), and why did we find a strong tendency for position
cues to correlate with behavior in regions located at extreme points along the shape
templates (e.g. the feet of the walker or the corners of the squares)? In general, the
classification image technique is well suited for exploratory analysis and has the strength
of requiring few a priori assumptions about the outcome of the experiment or how the
experimental variables might affect perception and behavior. However, this technique
also has the power to reveal complex patterns and relationships in the data that must be
interpreted a posteriori to derive meaning from the resulting images (van Boxtel & Lu,
2015). To help explain the specific pattern of results revealed in the current study we
derived spatial and orientation distinctness maps, which represent the local difference in
these features between a given template and its counterpart, e.g. the template moving in
the opposite direction, owing to the fact that this comparison was the basis for the
discrimination task performed in the actual experiment. An example of this analysis is
illustrated in Supplemental Figure 1.
Supplemental Figure 1. Example frame to illustrate the creation of feature distinctness
maps. On the left, a reference template is shown (blue) with overlay of the opposing
frame from the same time point (red). On the right, smoothed distinctness maps are
shown for easy comparison to the smoothed classification image data from Experiment 1.
The rationale behind this analysis is that positions are sampled uniformly and
randomly from the underlying shape contour on each frame. Sometimes these locations
will overlap with the competing shape contour (e.g. a walker facing the opposite
direction) in which case positional information would not provide distinguishing
information for discriminating the templates. On the other hand, some locations will be
sampled that are distinctly specified by a particular template, thus providing
distinguishing positional information that could influence the globally perceived direction
of the hybrid stimulus. The same reasoning applies to orientation features of the
underlying templates. On each trial, the subtle but random pattern of relative sampling
from distinct and indistinct contour regions could provide an explanation for why
perception was nudged toward one direction or the other in the face of generally
ambiguous stimulus information.
When comparing a single template frame to its competing template frame, some
spatial regions are distinct and belong confidently to one shape or the other, while some
regions have distinct orientation information that is not shared with nearby regions of the
opposing template (Supplemental Figure 2). On the basis of these local spatial differences,
we computed spatial distinctness maps, predicting that distinct spatial regions would
correlate positively with decisions consistent with position cues and that indistinct
regions would potentially correlate with orientation, since orientation could provide
relatively more distinguishing information in these locations. For instance, imagine a case
where only indistinct or overlapping regions are sampled in each stimulus frame.
Discrimination between the two templates would be impossible on the basis of position
information alone because there would be no features to distinguish the opposing shapes.
Successful discrimination in such a case would necessarily require additional information
such as that provided by element orientation.
Supplemental Figure 2. Examples of spatial and orientation distinctness maps for each
selected frame to match the results reported in Figure 3 of the manuscript.
For easier comparison to human CIs, we spatially smoothed the spatial
distinctness maps with a two-dimensional Gaussian filter (sigma = 8). Regions that are
more distinct in terms of position or orientation, and hence belong with more certainty to
a particular object, are represented by positive values (e.g. orange-red) in the maps,
indicating larger distances between the templates. Comparing the distinctness maps to the
behavioral classification images revealed many qualitative similarities. To estimate the
relationship quantitatively, we computed the Pearson’s correlation coefficient between
CIs and distinctness maps across all pixels in the images, excluding background pixels
that never contained a signal or sample during the trials. Due to the large number of
degrees of freedom (262,978 pixels for biological stimuli, and 136,660 for non-biological
stimuli), we used a random permutation test to assess statistical significance of the
correlation coefficients. In the permutation test, we randomly scrambled the mapping
between subject responses and stimulus data, and processed this permuted data through
the same pipeline as the experimental data to derive permuted group CIs. This procedure
simulates a sample of observers using the same stimulus trial data, but with random
responses. We computed the correlation coefficient for each of 100 randomly permuted
CIs and used this null distribution to convert the experimental correlations to z-scores.
We found that the relationship between the human CI and the spatial distinctness
map was significant for both the biological stimulus (z=2.68, p<0.05), and non-biological
stimulus (z=4.91, p<0.05).To examine the contribution of orientation cues to the
responses, we performed a similar analysis based on maps that quantify the distinctness
of orientation cues by computing the difference in orientation between two templates. We
found that orientation distinctness on its own provided a poor fit to human data overall, as
revealed by weaker similarity between human CIs and the orientation distinctiveness map
for the biological (z = 0.4, p = 0.65), and non-biological stimulus (z = 0.73, p = 0.31).
This result demonstrates the primacy of positional information in guiding
perceptual discriminations on this task. In other words, if positions are sampled from
distinct regions, then this is the primary factor in determining which global stimulus
direction will be perceived by the observer. Only when indistinct regions are sampled at a
relatively high rate will orientation then have the opportunity to take precedent and
reverse the perceived direction. This interpretation makes sense intuitively as orientation
can never exist in isolation without being anchored to a particular location specified by
the center position of the Gabor window itself. Contrarily, position information can be
estimated independently from orientation features. For instance, in our prior study we
found that random and noisy orientation information could be easily discounted with no
cost to discrimination performance in the same task (Thurman & Lu, 2014b).
The spatial distinctness maps provide an intuitive and quantitative post-hoc
explanation for why the human and model CIs turned out the way that they did. Although
the stimuli were high ambiguous by design, perception of global movement direction was
apparently pushed one way or the other due to low-level feature differences in the
underlying shape templates. We view these results as complementary to those provided in
the main paper in comparing human performance to the Bayesian observer model.