Spatial frequency distribution was characterized by the slope of the power spectrum because the logarithmic value of Fourier power spectra of natural images tends to be inversely proportional to the power of spatial frequency as
f−s, where
f and
s indicate spatial frequency and a constant (
Burton & Moorhead, 1987;
Field, 1987;
Tolhurst, Tadmor, & Chao, 1992;
van der Schaaf & van Hateren, 1996). We calculated the Fourier power spectra as radially averaged two-dimensional Fourier power computed from the 1,024-by-1,024-pixel images resized from the 3,840-by-3,840-pixel center square area of the original images. We averaged the power spectra over 10 image frames extracted in intervals of 0.5 s for each motion picture, similar to the processes for luminance statistics (
Figure 13A). Subsequently, the slopes of the regression lines for the spectral power against the spatial frequency in the log-log domain were computed. Pearson's product-moment correlation coefficient between the slopes and the preferred image size was significant,
r(41) = 0.40,
p = 0.008 (
Figure 13B). In addition, the slopes showed a significant difference among the categories determined in
Experiment 2 based on an analysis of variance with those three categories,
F(2, 35) = 3.68,
p = 0.035, ω
2 = 0.12, and a post hoc Tukey test showed that the difference between
scenery and
person was significant (0.35, 95% CI [0.03, 0.67],
p = 0.032), but the other differences,
person-
object (–0.13, 95% CI [–0.43, 0.15],
p = 0.50) and
scenery-
object (0.21, 95% CI [–0.06, 0.49],
p = 0.15), were not (
Figure 13C). This trend regarding the image statistics is consistent with that found in a previous study (
Redies, Hänisch, Blickhan, & Denzler, 2007) that reported that photos of human faces showed a steeper slope than natural scenes did. Therefore, it is plausible that the relationship between the preferred image size and the categories found in
Experiment 2 could be accounted for by the spatial frequency characteristics, at least partially. However, since the correlation coefficients of the preferred size to the power spectrum distribution were smaller than those to the evaluated size of the main objects,
rslope = 0.39,
rsize = 0.68,
z = 1.69,
p = 0.090 (
Pearson & Filon, 1898), it does not seem that spatial frequency distribution plays a deterministic role exclusively, and it would not be reasonable to rule out the idea that the size of main objects in the images played some role related to the participants’ size preference. This view was supported by the result of the multiple regression analysis testing if the spatial frequency distribution (the slopes of the regression lines of the power spectra) and the evaluated size of the main subject predicted the preferred image size. The results of the regression indicated the two predictors explained 49.1% of the variance [adjusted
R2 =0.491,
F(2, 27) = 15,
p < 0.0001] and found that the evaluated size significantly predicted the preferred size (
β = 0.085, 95% CI [0.047, 0.122],
p < 0.0001) but the slope did not (
β = 0.112, 95% CI [–0.014, 0.239],
p = 0.08).