# Retrieval of Similar Evolution Patterns from Satellite Image Time Series +
## 4 Discussion  
### Discovery of Similar Patterns in SITS  
In the first setup, we aimed to discover two types of spatio-temporal evolution related to the formation of three accumulation lakes in the Bucharest region, namely Morii, Dridu and Mihailesti. If compared to the Morii and Dridu lakes, Lake Mihailesti has a distinct spatio-temporal evolution because this accumulation lake was emptied several times (in 1987 and in 1992) during its construction. The spectro-temporal differences between the two queries can also be observed from the spectro-temporal signatures shown in Figure 7. In this sense, the user performs two independent queries, each selected from the regions of interest. The analyzed period of time was between 1984 and 1993 and the dataset considered for retrieval was the short Landsat SITS composed of 10 images captured in the mentioned period (i.e., one image per year). The results of the proposed query-by-example retrieval method are shown in Figure 8, whereas the ground truth is presented in Figure 9. The first row of Figure 8 represents all the DTW distances measured between the query and the rest of the spatio-temporal sequences, whereas the second row shows the output of the retrieval system (i.e., after applying the optimal threshold over the DTW distance image). For a numerical evaluation of the performances reached by the system, we measured the overall accuracy (OA), the missed alarm rate (MAR) and the false alarm rate (FAR), which are defined as  
Figure 6: Long Landsat SITS comprised of 88 images captured in 1984–2011. Only the first and the last images of the series are shown, namely **(a)** 1984 and **(b)** 2011. The distribution of the acquisition moments is shown in **(c)**. \[OA=\frac{TP+TN}{TP+TN+FP+FN} \tag{17}\]  
\[MAR=\frac{FN}{TP+FN} \tag{18}\]  
\[FAR=\frac{FP}{TN+FP} \tag{19}\]  
where _TP_ indicates the number of similar spatio-temporal evolutions that were correctly identified, _TN_ indicates the number of non-similar spatio-temporal evolutions that were correctly identified, _FP_ is the number of non-similar spatio-temporal evolutions that were determined as similar, and _FN_ is the number of similar spatio-temporal evolutions that were determined to be non-similar to the given query. The results, reported in Table 2, show that the system is able to accurately determine similar spatio-temporal patterns with respect to the given queries in term of overall accuracy and false alarm rate. The missed alarm rate can still be decreased if spatial constraints are imposed (i.e., similar sequences are more likely to be close to the query location, and, conversely, non-similar spatio-temporal evolutions are likely to be surrounded by other non-similar spatio-temporal evolutions). In this case, Markov Random Fields models can be employed [1], but they are difficult to use in SITS analysis due to their computational complexity. In addition, if the searched spatio-temporal evolutions are not compact (e.g., construction of new buildings), the solution may not achieve satisfactory results. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Query** & **Overall** & **Missed** & **False** \\  & **Accuracy** & **Alarm Rate** & **Alarm Rate** \\ \hline Morii and Dridu & 99.68\% & 26.84\% & 0.23\% \\ Mihailesti & 99.36\% & 30.36\% & 0.56\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Performance evaluation on short SITS. Figure 7: Spectro-temporal signatures during the construction of the accumulation lakes. The two spectro-temporal signatures are characterized by different temporal evolutions in the period that corresponds to their construction, namely 1984–1993. Figure 8: Pattern discovery in short Landsat SITS. (**a**) DTW distance image for a query marked inside the Morii & Dridu accumulation lakes. (**b**) DTW distance image for a query marked inside Mihailesti accumulation lake. (**c**) Pattern discovery using the proposed method for Morii & Dridu accumulation lakes. (**d**) Pattern discovery using the proposed method for Mihailesti accumulation lake.