# RSB: Robust Successive Binarization for Change Detection in Bitemporal Hyperspectral Images
## 4 Post-Processing
### Supervised Classifier  
Regarding the other two datasets, _USA_ and _River_, the produced change maps (Figure 9, first pictures in the second row and in the third row, respectively) look very detailed and, hence, it is not advisable to use a pixel-wise noise removal filter, as important information could be lost. Therefore, the obtained binary change maps are used as pseudo-labels to train a supervised classifier. Note that this step is now performed without using the exact ground truth. In particular, a Gaussian Naive Bayes algorithm is applied. Naive Bayes methods are a set of supervised learning algorithms based on applying [PERSON] theorem with the \"naive\" assumption of conditional independence between every pair of features, given the value of the class variable. Therefore, every feature distribution can be individually estimated: this implies an ability to solve many mono-dimensional problems, which in turn can alleviate the computational cost when large matrices or tensors are processed. Moreover, besides being rather efficient, Naive Bayes are considered optimal in many applications [47]. In our specific case, the likelihood of every feature is assumed to be modeled by a Gaussian distribution, where the unknown mean and standard deviation, for every Gaussian, are estimated via the maximum likelihood algorithm. The Gaussian Naive Bayes (GNB) is run twice. The first time, for the training and test set, the difference image \(|I_{1}-I_{2}|\) for the _USA_ and _River_ dataset is constructed and the output of the RSB change maps are used as \"exact\" labels. The second time, the \"exact\" labels are replaced by the output produced by the first iteration. The implementation is done by using scikit-learn[48], and on the first iteration, the algorithm is run with the default parameters, while on the second iteration, the parameter var_smoothing is set to \(1.125210^{-3}\) for the _USA_ dataset and to \(1.0\) for the _River_ dataset. The finetuning of such parameters is not a trivial task; although quite elaborate techniques exist, since this is outside the scope of the current paper, for our purpose, the chosen values have been experimentally found. The obtained results after this PP step are shown in Table 2. Applying GNB, after the first iteration, remarkably improves both OA and K for the _USA_ dataset, while, for the _River_ dataset, the OA is slightly reduced, but K is largely increased. After the second iteration, for both datasets, the OA indicator is slightly increased, but \(K\) is highly improved, hence providing a more accurate output. The final produced change maps are shown in Figure 10, in the second and third picture for the _USA_ and _River_ dataset, respectively.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Datasets**} & \multicolumn{2}{c}{**1 Iteration**} & \multicolumn{2}{c}{**2 Iterations**} \\  & **OA** & **K** & **OA** & **K** \\ \hline _USA_ & 0.9535 & 0.8609 & 0.9579 & 0.8781 \\ _River_ & 0.9609 & 0.7711 & 0.9681 & 0.8014 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Output of the Gaussian Naive Bayes.  
Figure 10: The obtained final binary change maps. From leftmost to rightmost: _Hermiston_, _USA_, _River_, and _Bay Area_ datasets.