## 3 Results
### Effects of Building Materials on NDVI  
To investigate the effects of building materials on the NDVI, the NDVI\({}_{\text{mean}}\) of scenes with the same H/W, \(\lambda_{\text{p}}\), and materials reflectance are presented in Figures 4 and 5. Table 2 illustrates the reflectance of different R\({}_{\text{walls}}\) in the red and near-infrared bands. The characteristics of homogeneous and heterogeneous buildings are explained in Section 2.1.1.  
Figure 4: NDVI changes with building density and building height when building materials are the same: (**a**) with shadow conditions and FVC = 0.1; (**b**) under sunlit conditions and FVC = 0.1; (**c**) with shadow conditions and FVC = 0.2; (**d**) under sunlit conditions and FVC = 0.2; (**e**) with shadow conditions and FVC = 0.3; and (**f**) under sunlit conditions and FVC = 0.3.  
Figure 5: NDVI changes with building density and building height when building materials are heterogeneous: (**a**) with shadow conditions and FVC = 0.1; (**b**) under sunlit conditions and FVC = 0.1; (**c**) with shadow conditions and FVC = 0.2; (**d**) under sunlit conditions and FVC = 0.2; (**e**) with shadow conditions and FVC = 0.3; and (**f**) under sunlit conditions and FVC = 0.3.  
Figure 4 displays the NDVI\({}_{\text{mean}}\) values for mixed scenes with homogeneous buildings, wherein a notable negative correlation is observed between the NDVI\({}_{\text{mean}}\) and the R\({}_{\text{wall}}\). Specifically, for scenes under shadow conditions (Figure 4a,c,e), when the building density is low (\(\lambda_{\text{p}}\) = 0.1, 0.1875), the NDVI is almost unaffected by the H/W and shows a highly overlapping scatter. In contrast, when the building density is high (\(\lambda_{\text{p}}\) = 0.3, 0.4375, 0.6), there is a negative correlation between the NDVI and both the H/W and R\({}_{\text{wall}}\). Moreover, when R\({}_{\text{wall}}\) = 0.3R\({}_{\text{stdW}}\), the negative correlation between the NDVI\({}_{\text{mean}}\) and the building density (i.e., \(\lambda_{\text{p}}\)) gradually diminishes with the increase of the FVC, and their correlation even becomes positive when FVC = 0.3 (Figure 4).  
Figure 5 illustrates that for scenes with heterogeneous buildings, both the NDVI\({}_{\text{mean}}\) and R\({}_{\text{wall}}\) are weakly positively correlated. This positive correlation remains relatively consistent as the FVC increases. However, this positive correlation is marginally weaker in scenes under sunlit conditions than in scenes with shadow conditions. Only two observation times were considered for mixed scenes. This correlation is also likely to increase further if the observation time corresponds to a smaller solar elevation angle (i.e., a larger shaded area). However, at least in unshaded scenes, the effects of building materials on the NDVI are essentially negligible when the wall and roof materials are heterogeneous.  
When both the scene geometry and vegetation components are the same, the NDVI\({}_{\text{mean}}\) of a mixed scene with heterogeneous buildings is not always greater than the NDVI\({}_{\text{mean}}\) of a mixed scene with homogeneous buildings. Heterogeneous buildings, however, cause the range of variation of the NDVI with the geometry to be significantly reduced (Figures 4 and 5). This suggests that heterogeneous buildings weaken the effects of geometry on the NDVI. Additionally, the difference in the NDVI\({}_{\text{mean}}\) between heterogeneous and homogeneous buildings becomes more pronounced as the \(\lambda_{\text{p}}\) increases. This is because a high building density increases the scattering within pixels; thus, the effects of material heterogeneity within pixels on the NDVI are higher.