Natural scene statistics

To organize our analysis of the statistics of depth edges in natural scenes, we defined five regions of interest (Figure 3C). These regions were the monocular region (green), the adjacent binocular foreground (orange), the adjacent binocular background (blue), and two transition regions from the binocular background to the monocular region and from the binocular foreground to the monocular region (black lines). The binocular regions consisted of the 0.5°-wide image areas neighboring the monocular region to the left or right. The transition regions contained 0.4°-wide image areas centered on the transition between the monocular region and the binocular background or foreground regions. The forthcoming results are similar for other region sizes.

From the distance maps, we calculated the mean distance of the surfaces in the monocular region, the adjacent binocular foreground region, and the adjacent binocular background region. From the luminance images, we computed the mean luminance and the mean contrast (i.e., square root of the mean squared luminance deviation) within each of these regions, as well. In the binocular–monocular transition regions, we focused on analyzing the changes in image properties associated with transitions between surfaces. For example, a large horizontal luminance derivative would reflect a strong vertical edge, suggesting a transition between two surfaces with different patterns. To quantify the strength of the vertical luminance edge between the monocular region and adjacent binocular regions, we used 5-tap derivative filters to compute the mean magnitude of the horizontal luminance derivative (Farid & Simoncelli, 2004). As a control measure, we repeated this analysis for vertical derivatives, which are not expected to be particularly strong at horizontal surface transitions.

Prior to statistical analyses, all of the image-based measurements described above were normalized; specifically, the mean luminance within each region and the mean magnitude of luminance derivatives within each transition region were normalized by the mean luminance of the entire patch. The mean contrast within each region was normalized by the mean contrast of the entire patch. Two-tailed Wilcoxon signed-rank tests were used to examine statistically significant differences in the visual properties of different regions. Non-parametric effect sizes for these tests were calculated as z/n, where z refers to the z-score of the Wilcoxon test statistic and n refers to the number of differences used to calculate the test statistic (Fritz, Morris, & Richler, 2012).

It is important to note that the natural scene dataset used here does not contain objects that are closer than 3 m. This limitation of the dataset should be considered when interpreting the results of our analysis, because prior work suggests that the prevalence of monocularly visible regions depends on the distribution of object distances in a scene (Langer & Mannan, 2012). That said, we later report the results of a geometric simulation that parametrically examined how object distance affects the geometric causes of monocular regions (see Results). The findings from the simulation suggest that the main conclusions of this natural scene analysis are likely to hold not only for surfaces that are far away but also for surfaces that are up close.