## 4 Experiment I--DSM Quality Evaluation
### Statistical Evaluation for Different Land Cover Types  
In addition to the visual comparison and correlation coefficients, the DSMs have been evaluated using more statistical features. Over the 13 years in which the data were acquired, some changes may have influenced the forest structure. Therefore, we have manually selected some high-dense and low-dense forest areas unrelated to visible change. As the inventory plots only cover the forest region, LiDAR2001 and LiDAR2010 are again used as reference for the two defined groups. As shown in Table 5, the accuracy assessment is based on the absolute vertical height differences (\(\Delta\)h) between the DSMs and the reference height model. The mean error (\(\hat{\mu}\)) represents the mean absolute shift value for all pixels, while the standard deviation (\(\hat{\sigma}\)) is derived from the difference of the two DSMs, which also indicates the surface smoothness of the generated DSM. Another robust, statistically-based accuracy measurement is the Normalized Median Absolute Deviation (NMAD) [44]. NMAD can be used to evaluate the quality of the DSMs in the presence of outliers and non-normal distributions, and it is proportional to the median of the absolute differences between errors and the median error. It can be considered as an estimate for the standard deviation which is more resilient to outliers [44]. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**Land Cover Type**} & \(\mathbf{N}\) & **Sensor** & **ME (m)** & **STD (m)** & **NMAD (m)** \\ \hline \multirow{6}{*}{High-density forest area} & \multirow{6}{*}{11,173} & HRSC2003 & 5.72 & 7.25 & 4.45 \\  & & ALOS2008 & 5.36 & 7.49 & 5.42 \\  & & Cartosat2008 & 4.27 & 6.56 & 4.02 \\  & & RapidEye2009 & **6.23** & **7.62** & **5.67** \\  & & WorldView2012 & 4.47 & 6.27 & 3.66 \\  & & Aerial2012 & **3.62** & **5.62** & **2.45** \\  & & TamDEM-X2013 & 4.71 & 7.09 & 4.47 \\ \hline \multirow{6}{*}{Low-density forest area} & \multirow{6}{*}{16,017} & HRSC2003 & 7.08 & 9.54 & 5.93 \\  & & ALOS2008 & 9.67 & 11.77 & 10.10 \\ \cline{1-1}  & & Cartosat2008 & 9.21 & **12.29** & 8.77 \\ \cline{1-1}  & & RapidEye2009 & **9.88** & 11.09 & **13.36** \\ \cline{1-1}  & & WorldView2012 & 7.44 & 10.88 & 5.25 \\ \cline{1-1}  & & Aerial2012 & **5.02** & **8.50** & **2.72** \\ \cline{1-1}  & & TamDEM-X2013 & 9.04 & 11.06 & 11.30 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Quality assessment for low-density and high-density forest based on the quality measures in Table 5 by using LiDAR data from 2001 as reference for HRSC2003 and from 2010 as references for the other DSMs (the highest and lowest values are marked in bold). \begin{table}
\begin{tabular}{c c} \hline \hline Number of checkpoints (\(N\)) & \(n\) \\ \hline Vertical errors (Error) & \(\Delta h=\left|h_{DSM}-h_{ref\_Height}\right|\) \\ \hline Mean errors (ME) & \(\hat{\mu}=\frac{1}{n}\sum\limits_{i=1}^{n}\Delta h_{i}\) \\ \hline Standard Deviation (STD) & \(\hat{\sigma}=\sqrt{\frac{1}{(n-1)}\sum\limits_{i=1}^{n}\left(\Delta h_{i}-\hat{ \mu}\right)^{2}}\) \\ \hline Normalized Median Absolute Deviation (NMAD) & \(NMAD=1.4826\times median(\left|\Delta h_{i}-median(\Delta h)\right|)\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Accuracy measures for DSM quality assessment. In Table 6 the calculated \"ME\", \"STD\" and \"NMAD\" values illustrate the characteristics of all DSMs. More than 10,000 pixels are selected for each land cover type. The best results in each comparison group are highlighted in bold with black color and the worst results are highlighted in grey-bold. However, by comparing the accuracies of these DSMs for each land cover type, it becomes clear that DSMs in high-density forest regions generally match better the reference DSM than in the low-density ones. In high-density forest, the mean errors range from 3.62 to 5.72 m: the range is very small, considering the resolution of the original images. The differences are also larger for low-density forest regions. All DSMs are instead less accurate in low-density forest areas.