Girshick, Landy & Simoncelli
c
Variability (deg)
b
50 S2
30
S3
S4
S5
10
0
L vs. L data
H vs. H data
L vs. L fit
H vs. H fit
Relative bias (deg)
a
Variability (deg)
SUPPLEMENTARY MATERIALS
50
30
10
0
10
0
–10
H vs. L data
0
90
180
Orientation (deg)
Predictions based on:
Observer's prior
Environmental prior
Uniform prior
Supplementary Figure 1 Experimental data for observers S2, S3, S4, and S5 (four columns,
respectively). The horizontal axis is orientation (in deg) in all cases. (a) Variability of same-noise
conditions (L vs. L and H vs. H). Same format as Fig. 2b. (b) Cross-noise variability with
predictions of three Bayesian-observer models: observers’ priors (black), environmental
distribution prior (medium gray), and uniform prior (light gray). Same format as Fig. 5b. (c)
Relative bias with the predictions the same three Bayesian-observer models. Same format as
Fig. 5c.
Supplementary Materials 1
Nature Neuroscience: doi:10.1038/nn.2831
b
Relative bias (deg)
a
Variability (deg)
Girshick, Landy & Simoncelli
50 S1
30
Mean
10
10
0
–10
0
90
180
Orientation (deg)
H vs. L data
Predictions based on
observer's prior with:
MAP estimate
Circular mean estimate
Supplementary Figure 2 Comparison of two decision rules: maximum a posteriori (MAP) and
circular mean for representative observer S1 and the mean observer. (a) Variability in same
format as Fig. 5b and Supplementary Fig. 1b. (b) Relative bias in same format as Fig. 5c and
Supplementary Fig. 1c. Black solid curves (from Fig. 5) are the predictions of the Bayesian
observer using the recovered observers’ priors and MAP estimation. Gray dashed curves are
the predictions of the Bayesian observer using the same recovered observers’ priors and a
circular mean estimate.The MAP and mean estimates would be identical if the posteriors were
symmetric. In our case, the posteriors were asymmetric due to slight asymmetry in the
recovered priors and likelihoods.
Supplementary Materials 2
Nature Neuroscience: doi:10.1038/nn.2831
Probability
Girshick, Landy & Simoncelli
S2
S3
S4
S5
0.01
0.00
0
90
180
Orientation (deg)
Recovered
observer's prior
Uniform prior
Supplementary Figure 3 Recovered priors for observers S2, S3, S4, and S5. Same format as
Fig. 3.
Probability
Natural
Blend
Human-made
All
0.02
0.01
0
0
90
180
Orientation (deg
2560 x 1920
1280 x 960
640 x 480
320 x 240
160 x 120
80 x 60
Supplementary Figure 4 Orientation distributions measured at different scales in a multi-scale
decomposition, for four different photographic image collections. From left to right, distributions
for photographs containing: mostly natural content (653 images), a blend of natural and humanmade content (e.g., a scene with a tree and a house; 151 images), mostly human-made content
(221 images), and the full database (1025 images). Human-made scenes are dominated by
buildings, and exhibit the sharpest and largest peaks at verticals. Natural scenes, which contain
objects such as flowers and foliage, have a reduced dominance of the cardinals and softer
peaks. Scenes of blended content lie in-between. Intensity of grey curves corresponds to six
image resolutions. The error regions, ±
1 s.d. from bootstrapping the data 1000 times, are
smaller than the line widths.
Supplementary Materials 3
Nature Neuroscience: doi:10.1038/nn.2831
Girshick, Landy & Simoncelli
a
b
Measured
orientation (deg)
180
m(! )
90
0!
0
!
90
180
Stimulus
orientation (deg)
0.1
0.025
0.06
0.015
0.02
0.005
!
Supplementary Figure 5 Matrices for the mean observer, in the same format as Fig. 7, upperright panel. Columns are measurement distributions, rows are likelihood functions, and color
corresponds to probability. Variance of measurement distributions comes from the fits to the
same-noise variability (Fig. 2b). Each observer had a corresponding pair of matrices generated
from their data. (a) Matrix for the low-noise stimuli. Likelihoods are asymmetric, skewed away
from the cardinals due to the orientation-dependent change of variance (i.e., the oblique effect).
(b) Matrix for the high-noise stimuli. Likelihoods are broader and less asymmetric than in a.
(Note change of scale between a and b.)
Supplementary Materials 4
Nature Neuroscience: doi:10.1038/nn.2831