# Object-Oriented Remote Sensing Image Change Detection Based on Color Co-Occurrence Matrix
## 2 Methods
### Optimal Object Construction Based on Multi-Scale Segmentation  
Due to the diversity of the surface object types and the complexity of the spatial distribution in remote sensing images, different regions also require different segmentation scales [36]. In order to obtain the optimal segmentation scale, the remote sensing image is first over-segmented into a series of smaller superpixels on the basis of the graph theory segmentation method, and then the adjacent superpixel blocks are merged on the basis of the FNEA algorithm to obtain the different scales of superpixel segmentation results, and the optimal segmentation scale is determined by OGF index to obtain the best object. The main idea of superpixel segmentation based on graph theory is to map the image into a weighted undirected graph \(G=(V,E)\), in which the set of vertexes \(V\) is composed of pixels of the image, and set of edges \(E\) corresponds to the adjacent relationship between  
Figure 1: Flow chart of the proposed algorithm. pixels. Each edge has a corresponding weight \(\mathbf{w}\), which is the dissimilarity between neighboring elements. The pixels are merged according to the criteria, and then the superpixels are formed [37]. The merger guidelines are as follows:  
\[Diff(C_{1},C_{2})\leq Mint(C_{1},C_{2}) \tag{1}\]  
\[Mint(C_{1},C_{2})=\min\{Int(C_{1})+\tau(C_{1}),Int(C_{2})+\tau(C_{2})\} \tag{2}\]  
where _Diff_ (\(C_{1}\), \(C_{2}\)) is the difference between regions \(C_{1}\) and \(C_{2}\), which is defined as the minimum weight edge connecting the two components. _Int_(\(C\)) is the internal difference of the regions \(C\), and it is defined as the largest weight in the minimum spanning tree of the component. \(\tau(C)=B/\left|\right.C\left|\right.\) is the threshold function to regulate the extreme case where both regions contain only one pixel; \(B\) is a constant parameter, and \(\left|\right.C\left|\right.\) is the size of component \(C\). FNEA is one of the most widely used methods of multi-scale segmentation, which has been commercially applied in eCognition software. Its principle is to form different scales by merging connected superpixels [38; 39]. The merge cost function is:  
\[f=w_{color}h_{color}+(1-w_{color})h_{shape} \tag{3}\]  
where \(h_{color}\) and \(h_{shape}\) are the costs of spectral heterogeneity and shape heterogeneity after the merger, respectively, and \(w_{color}\) is the weight of spectral heterogeneity. Spectral heterogeneity \(h_{color}\) is defined as:  
\[h_{color}=\sum_{c}w_{c}[n_{obj3}\sigma_{c}^{obj3}-(n_{obj1}\sigma_{c}^{obj1}+ n_{obj3}\sigma_{c}^{obj2})] \tag{4}\]  
where \(obj_{3}\) is the superpixel after merging \(obj_{1}\) and \(obj_{2}\), \(c\) is the band index, \(w_{c}\) is the band weight, \(\sigma\) is the standard deviation, and \(n\) is the number of pixels. Shape heterogeneity \(h_{shape}\) is defined as:  
\[h_{shape}=w_{compt}h_{compt}+(1-w_{compt})h_{smooth} \tag{5}\]  
where \(w_{compt}\) is the compactness weight. Assuming that the circumference of the superpixel is represented by \(l\), the compactness \(h_{compt}\) and edge smoothness \(h_{smooth}\) are:  
\[h_{compt}=n_{obj3}\cdot\frac{l_{obj3}}{\sqrt{n_{obj3}}}-\left(n_{obj1}\cdot \frac{l_{obj1}}{\sqrt{n_{obj1}}}+n_{obj2}\cdot\frac{l_{obj2}}{\sqrt{n_{obj2 }}}\right) \tag{6}\]  
\[h_{smooth}=n_{obj3}\cdot\frac{l_{obj3}}{b_{obj3}}-\left(n_{obj1}\cdot\frac{l _{obj1}}{b_{obj1}}+n_{obj2}\cdot\frac{l_{obj2}}{b_{obj2}}\right) \tag{7}\]  
where \(b\) is the perimeter of the object's bounding box. In order to determine the optimal segmentation scale among many scales, the segmentation results are evaluated on the basis of the OGF maximization criteria:  
\[OGF=(1+\alpha^{2})\frac{Ml_{norm}\times LV_{norm}}{\alpha^{2}\times Ml_{norm}+ LV_{norm}} \tag{8}\]  
where \(Ml_{norm}\) and \(LV_{norm}\) are the results after the normalization of the weighted variance \(LV\) of the segmentation object and Global Moran's I index \(M1\) (for detailed information, please see reference [40]).