# Object-Oriented Remote Sensing Image Change Detection Based on Color Co-Occurrence Matrix
## 2 Methods
### Feature Filtering Based on the Cumulative backward Search Strategy  
The random forest (RF) algorithm is an integrated algorithm that takes the decision tree model as the basic classification model. The final result is obtained by establishing multiple decision tree classifiers and voting, or averaging, their predicted values. Compared with a single decision tree, the RF has higher accuracy and stability by using random sampling of samples and features. The RF can solve classification and regression problems and can estimate the importance of features at the same time [41; 42].  
In order to effectively utilize the characteristic information of changed and unchanged samples and to ensure that the selected features are stable and representative, a cumulative backward search strategy is proposed based on the random forest framework. In the proposed strategy, the traditional way of determining feature ranking by a single search is abandoned [43], and the cumulative value of the feature contributions by multiple searches is regarded as the foundation for sorting the features. This approach can enhance the accuracy of the feature sorting and avoid the impact of randomness and volatility of the model on the sorting results. The details are elucidated as follows, and the flow chart is shown in Figure 3.  
First, after determining the changed and unchanged object samples, 70% of the samples are selected as training samples to train the model. The test set, including all the samples and many additional superpixels, is used to evaluate the model training accuracy. The difference images of the spectral and color texture feature sets are input into the random forest, and the importance of each feature of a single training round is estimated. In order to ensure the stability of filtering features, the model is trained many times, and the features are re-sorted according to the cumulative value of the feature importance of each training. On the basis of the spectral features, the least important color texture features are eliminated successively, and a new feature combination is formed and re-input into the random forest for training. The training is stopped once the number of features reaches the minimum  
\begin{table}
\begin{tabular}{c c} \hline
**Feature Names** & **Feature Description** & **Calculation Formula** \\ \hline Angular Second Moment & The evenness of the grayscale & \(\text{ASM}=\sum_{e\in\mathcal{S}}^{N}p_{e\in\mathcal{S}}^{2}\) \\ (ASM) & distribution of the image & \(\text{Con}=\sum_{e\in\mathcal{S}}^{N}p_{e\in\mathcal{S}}(e-o)^{2}\) \\ Contrast (Con) & Graphic sharpness & \(\text{Con}=\sum_{e\in\mathcal{S}}^{N}p_{e\in\mathcal{S}}(e-o)^{2}\) \\ Correlation (Cor) & Consistency of image texture & \(\text{Cor}=\sum_{e\in\mathcal{S}}^{N}p_{e\in\mathcal{S}}\left[\frac{(e-p_{e \in\mathcal{S}})(e-p_{e})}{\sqrt{(e^{2})(e^{2})}}\right]\) \\ Inverse Different Moment (IDM) & Homogeneity of image texture & \(\text{IDM}=\sum_{e\in\mathcal{S}}^{N}\frac{p_{e}}{1+(e-o)^{2}}\) \\ \hline \end{tabular}
\end{table}
Table 1: Statistical variables of the texture features.  
Figure 2: Color co-occurrence matrix. (**a**) Subregion and grayscale; (**b**) Color co-occurrence matrix about bands R and G.  
given value. Finally, according to the fluctuation of the test accuracy under the condition of multiple feature combinations, the feature combination with fewer features and higher test accuracy is selected as the optimal feature combination.