# Retrieval of Similar Evolution Patterns from Satellite Image Time Series +
## 4 Discussion
### Comparison with Other State-of-the-Art SITS Analysis Methods  
As mentioned in the Introduction, the DTW-based K-means algorithm [7] and the LDA-based method described in [12] are unsupervised clustering methods for SITS analysis. We show a series of results obtained by applying the above mentioned methods over the experimental datasets in Figures 13-15. Following the recommendations in [12], the number of clusters considered was 15 and the dictionary was formed of 150 words. In the case of the DTW-based K-means method, we used the same number of clusters as for the LDA-based method. As it can be observed in Figure 15, both algorithms produce land use and land cover maps, for which the assignation of a temporal meaning (i.e., action name or evolution name) to the clusters is a difficult task to accomplish. Moreover, the extraction of particular temporal evolutions is not easy, since, most often, the spectral and spatial characteristics inhibit the temporal properties of spatio-temporal evolutions. This happens mostly when the number of clusters, \(K\), is small. However, in both cases, using a greater \(K\) leads to inconsistent results and to oversegmentation of the images  
Figure 12: Land use mapping in long Landsat SITS. (**a**) DTW distance image for a query made in the urban area. (**b**) Urban area delimitation using the proposed query-by-example retrieval method. (**c**) DTW distance image for a query made in the extra-urban area. (**d**) Extra-urban area delimitation using the proposed query-by-example retrieval method. (**d**) DTW distance image for a query made inside the agricultural area. (**e**) Agricultural area delimitation using the proposed query-by-example retrieval method. In the case of DTW distance images presented in (**a**,**c**,**e**), dark color represents similar evolutions and bright color represents non-similar evolutions, whereas in (**b**,**d**,**f**), white pixels correspond to spatio-temporal patterns that are similar to the query, which was selected from the region of interest. caused by nonhomogeneus spatio-temporal evolutions, cloud cluttering, noise, different illumination conditions, or seasonal changes. Our proposed approach aims to overcome these drawbacks by retrieving specific spatio-temporal evolutions that, at the end of the retrieval process, will receive the semantic label of the query. Figure 14: Analysis of Dobrogea SITS: (**a**) DTW-based K-means clustering [7], (**b**) Latent Dirichlet Allocation (LDA)-based clustering [12]. Figure 13: Analysis of short Landsat SITS: (**a**) DTW-based K-means clustering [7], (**b**) LDA-based clustering [12]. The LDA-based method performs an analysis of change map time series that is determined by applying different similarity measures. However, these similarity measures do not take the temporal extent of a transformation into account. This explains the insertion of the two different evolutions related to the building of accumulation lakes Morii & Dridu and Mihailesti into the same cluster as can be observed in Figure 13b. The DTW-based clustering divides the evolution of Mihailesti lake into two classes, one that corresponds to Morii & Dridu evolution and one that captures the evolution of Bucharest city. The SITS analysis method proposed in this paper is able to determine an optimal threshold that separates the two types of evolution related to the construction of the accumulation lakes to separate them from other types of evolutions. In contrast, the proposed query-by-example distinguishes between the two different spatio-temporal patterns, whose dissimilar evolutions can be observed in the corresponding spatio-temporal signatures shown in Figure 7.  
In the second use-case scenario, the DTW-based K-means method includes the flooded region in a category containing a portion of the Black Sea captured on the right hand side of Figure 14a, whereas the LDA-based analysis does not distinguish this particular evolution from the rest of evolution patterns.