# An Object- and Shapelet-Based Method for Mapping Planted Forest Dynamics from Landsat Time Series
## 2 Materials and Methods
### Methods
#### 2.2.2 Forest Object Generation
\begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Category** & **Variables** & **Acronym** & **Equations or Descriptions** & **References** & **Importance** \\ \hline Topographic & Slope & - & Slope/elevation calculated from & - & 1 \\ index & Elevation & - & digital elevation model (DEM) data & - & 4 \\ \hline \multirow{7}{*}{Textural index} & Variance (VAR) & VAR\_64 & VAR = \(\sum_{i=1}\sum_{j=1}(i-u)^{2}\text{P}(i,j)\) & & 2 \\  & & SAVG\_64 & & & 7 \\  & & SAVG\_8 & & & 8 \\  & Sum average (SAVG) & SAVG\_3 & & [40] & 9 \\  & & SAVG\_16 & SAVG = k \(\sum_{k=2}^{2\text{G}}\sum_{i=1}^{\text{G}}\text{P}(i,j)\) & & 12 \\  & & SAVG\_32 & & & 14 \\  & Correlation (CORR) & CORR\_64 & CORR = \(\frac{\sum_{i=1}\sum_{j=1}(i)\text{P}(i)-\mu_{i}\mu_{j}}{\sigma_{\sigma}\sigma_{ j}}\) & & 11 \\ \hline \multirow{3}{*}{Spectral band} & Blue & B1 & - & - & 3 \\  & Red & B3 & - & - & 6 \\ \hline \multirow{7}{*}{Spectral index} & Modified normalized & \multirow{2}{*}{MNDWI} & \multirow{2}{*}{MNDWI} & \multirow{2}{*}{\(\text{Green}=\frac{\text{Green}-\text{SWIRI}}{\text{Green}+\text{SWIRI}}\)} & \multirow{2}{*}{[41]} & \multirow{2}{*}{5} \\  & difference water index & & & & \\ \cline{1-1} \cline{5-5}  & Enhanced vegetation index & EVI & EVI & \(\text{EVI}=\frac{25\times(\text{NIR}-\text{Red})}{\text{NIR}+6\times\text{ red}-7\,5\times\text{Blue}+1}\) & [42] & 10 \\ \cline{1-1} \cline{5-5}  & Normalized difference & \multirow{2}{*}{NDBI} & \multirow{2}{*}{NDBI} & \multirow{2}{*}{NDBI} & \multirow{2}{*}{NDBI} & \multirow{2}{*}{[43]} & \multirow{2}{*}{13} \\ \cline{1-1} \cline{5-5}  & built-up index & & & & & \\ \cline{1-1} \cline{5-5}  & Land surface water index & & & & & \\ \hline \hline \end{tabular} Variables in the textural index are calculated using GLCM based on corresponding window sizes; for instance, VAR_64 represents the textural index variance of a window of size 64. P(i,i) represents the probability of occurrences for the (i,j) the entry in a joint probability distribution of pairs of gray levels, G represents the number of gray levels in the quantized image, and x and y represent the rows and columns of the GLCM, respectively.  
\end{table} 
Table 1: Top 15 variables ordered by their importance in the land-cover classification. where \(\rm var_{ij}\) and \(\rm a_{ij}\) represent the NDVI variance of superpixel i in layer j; and l and n are the number of NDVI layers, and the total number of superpixels, respectively. \[\rm{MIL}=\sum_{k=1}^{1}\frac{n*\sum_{i=1}^{n-1}\sum_{j=1}^{n}w_{ij}(v_{ij}-\overline {v})*(v_{ij}-\overline{v})}{(\sum_{i=1}^{n}\sum_{j=1}^{n}w_{ij})*\sum_{i=1}^{n} (v_{ij}-\overline{v})}/1 \tag{2}\]  
where \(\rm w_{ij}\) represents a value (1 is adjacent and 0 is non-adjacent) of the adjacency matrix value between superpixels i and j; and \(\rm v_{i}\) and \(\rm\overline{v}\) are the means of superpixels i and layer k, respectively. \[\rm WS=0.5\;*\;\rm{ALV}+0.5\;*\;\rm{MIL} \tag{3}\]  
The minimum of WS corresponded to an optimum scale parameter of 20, as shown in Figure 4. As such, the SNIC was conducted under the optimal parameters to yield homogenous forest objects in the NHAR, and the superpixels spanning less than 0.5 hectares were subsequently eliminated according to the requirements outlined by [52]. Finally, the object-level NDVI (the pixel-level mean value) time series were built according to the SNIC superpixels.