# Multi-Temporal Sentinel-1 Backscatter and Coherence for Rainforest Mapping
## 3 Method  
As stated in the introduction, the methodology adopted in our system is based on the one developed in [7], which relies on the use of a monthly interferometric time-series. Figure 1 depicts the new processing chain with the integration of the SADH textures. The pre-processing steps for the generation of the feature matrices in input to the classifier consist of a coregistration between the interferometric pair followed by an independent analysis of the information retrieved from the radar backscatter and interferometric coherence. As usually done in differential InSAR (DInSAR) applications, all the images in the time-series are coregistered with respect to a common master acquisition, selected as the one in the middle of the temporal stack. Secondly, the backscatter and the coherence from all the possible image pair combinations are estimated by using a moving average filter with a common window size. A boxcar filter with a fixed-size window of \(5\times 19\) pixels was chosen according to:  
1. the resolution of S-1 IW mode along azimuth and ground range, 14 m \(\times\) 3.7 m respectively,
2. the common goal of having a window centered in the current estimated pixel. Accordingly, the output resolution is an almost square cell of 70 m \(\times\) 70.3 m. Regarding the multi-temporal InSAR processing chain, we used the exponential decay model proposed in [7], and recalled in Section 2.1, to fit for each pixel the estimated coherence samples at different temporal baselines. Two key parameters, namely the decorrelation constant \(\tau\) and the long-term coherence \(\rho_{\text{LT}}\), are eventually retrieved. For the backscatter measurement, we consider the projection of the radar brightness on the plane perpendicular to the line of sight, known in literature as the \(\gamma^{0}\) coefficient [21], and we investigate its spatial dependencies in order to extract texture features. On the one hand, we estimated  
Figure 1: Developed processing chain for short-time-series, based on the architecture presented in [7], with the integration of Sum and Difference Histograms (SADH) textures. the multi-temporal \(\gamma^{0}\) coefficient by averaging along the temporal dimension and then spatially multi-looking using the same boxcar filter used for the InSAR processing, as suggested in [7]. On the other hand, for the computation of the spatial textures, we considered the multi-temporal mean \(\gamma^{0}\) without applying any spatial multi-looking process. Indeed, at full resolution, the characteristics of different scattering mechanisms can be better preserved. For the application of the SADH method, we set the domain \(D\) to \(5\times 19\) pixels and the number of gray levels \(N_{\text{g}}=20\), in order to obtain a final output resolution which is consistent with the one of the other estimated parameters \(\gamma^{0}\), \(\tau\), and \(\rho_{\text{LT}}\). Finally, the feature extraction using the SADH method is repeated twice, considering the most significant displacement vectors along both the azimuth \(d=(1,0)\) and the slant-range \(d=(0,1)\) directions. In Figure 1 we named these two set of textures as \(SADH_{(1,0)}\) and \(SADH_{(0,1)}\), respectively. After geocoding, all the previously described feature maps are posted to the final resolution of 50 m \(\times\) 50 m and serve as input to a Random Forests (RF) classifier. As in [7], we considered the Gini index as impurity measurement for the classifier and we set the number of estimators, that is, the number of decision trees, and the minimum number of samples in a leaf node to 50. Following the branches of the block diagram in Figure 1, a set of S-1 short-time-series can be downloaded and processed, deriving a total of 22 feature maps, 18 textures plus the 4 parameters proposed in [7]. Table 1 summarizes the complete set of features considered in this work.