## 4 Results
### Image Texture as a Proxy for DEM Quality
#### 4.3.3 Flat-Area DEM Variance versus Image Texture
The density is logarithmically scaled, and we see that darker parts of the 2D histogram are several orders of magnitude less common; nevertheless, the densest area still exhibits significant spread across values. Thus, to better characterize the relationship between our variables, we employ an additional smoothing step, achieved by blocking the map-view PAN variance and DEM variance in 50 \(\times\) 50 pixel areas, and obtaining the median value in these blocks (Figure 7A,B). Following this, the median values are plotted graphically for all blocks (\(\sim\)2400 values), and a binned median is taken through these blocked points (Figure 7D). Under this smoothing, the banana shape of the relationship becomes apparent, with a steeply dipping improvement in DEM quality (DEM variance) with increasing image texture (PAN variance) that plateaus at high image texture. We further highlight the relationship between PAN variance, DEM variance, and the intersection error (shown as blocked values in Figure 7C), by coloring the points by intersection error variance in each block (Figure 7D). We use the variance of intersection error rather than the raw intersection error for consistency with our other variance variables plotted. The point here is to highlight that areas of lower PAN variance and higher DEM variance (i.e., lower-quality parts of the DEM) are also associated with a mix of very high and very low intersection error values (high intersection error variance). This further emphasizes the high stereo-correlation uncertainties and resulting lower DEM quality in areas of low image texture and confirms observations made on the maps and hillsades in Figure 4.  
When reducing the scatter by blocking and taking a binned median line as in Figure 7D for all SPOT6 DEMs (Table 1), the parameter's relationships can be plotted together to view differences between stereo-matching algorithms and processing parameters. This is shown in Figure 8 for the DEM and PAN variance calculations in a 5 \(\times\) 5 pixel window. These relationships are almost identical (only translated within \(\sim\)1 order of magnitude on the x- and y-axes) for 3 \(\times\) 3, 7 \(\times\) 7, or 9 \(\times\) 9 window calculations. We note the reduction in DEM variance (i.e., improvement in quality on the flat salar) as the CK size is increased for both the BM (Figure 8A) and MGM (Figure 8B) algorithms. The BM algorithm also has a much steeper decrease in DEM variance with increasing PAN variance, exhibiting the plateau at \(\sim\)10\({}^{3}\) PAN variance across all tested CK sizes. On the other hand, the MGM approach exhibits a more gentle (less steep) shape, but we do still observe a slight breakpoint in slope at \(\sim\)10\({}^{3}\) PAN variance, followed by a plateauing behavior. For the MGM-ck5 DEM (the smallest CK tested), the DEM variance never falls below 10\({}^{-3}\) m\({}^{2}\) (0.03 m standard deviation). Figure 8: Median binned line generated in Figure 7D for BM-ck25, here shown for (**A**) all BM DEMs and (**B**) all MGM DEMs (cf. Table 1). The BM algorithm has a more steeply dipping relationship, but both BM and MGM have a plateauing behavior above \(\sim\)10\({}^{3}\) PAN variance. Larger CK sizes preserve the shape of the relationship but result in lower DEM variance for the same PAN variance. Figure 7: (**A**) 5 \(\times\) 5 pixel windowed PAN variance and (**B**) 5 \(\times\) 5 pixel windowed DEM variance for the SPOT6 BM-ck25 3 m DEM, both blocked into 50 \(\times\) 50 pixel (150 \(\times\) 150 m) areas, with the median value in each block given by the color scale; (**C**) the same 5 \(\times\) 5 pixel variance calculation and blocking carried out on the intersection error output from the ASP; (**D**) the blocked variables in (**A**) and (**B**) plotted against each other and colored by (**C**), with a binned median taken through all \(\sim\)2400 blocks.