# Object-Oriented Remote Sensing Image Change Detection Based on Color Co-Occurrence Matrix
## 2 Methods
### Object-Oriented Multi-Feature Extraction
#### 2.2.2 Texture Features Based on Color Co-Occurrence Matrix  
The remote sensing image is divided into \(N\) gray levels, that is \(\mathbf{I}=\{\mathbf{I}_{i}^{*},\,i=1,\,\dots,\,n\}\) and \(\mathbf{I}_{i}^{*}=\{I_{ic}^{*},\,c=1,\,\dots,\,h\}\), where \(I_{ic}^{*}\) represents the gray level of pixel \(i\) in \(c\) band, which satisfies \(I_{ic}^{*}\in\{1,\,\dots,\,N\}\). A color co-occurrence matrix about two bands is established, i.e., CCMcs(\(e\), \(o\), \(d\), \(\theta\)), where \(c\) and \(s\) represent the bands; \(e\) and \(o\) represent gray levels, such that \(e\), \(o\in\{1,\,\dots,\,N\}\); \(d\) is the spatial distance of two pixels; and \(\theta\) is the texture direction. Generally, the value of \(\theta\) is 4 or 8; when \(\mid\theta\mid\) = 4, we have \(\theta\) = [0\({}^{\circ}\), 90\({}^{\circ}\), 180\({}^{\circ}\), 270\({}^{\circ}\)], and when \(\mid\theta\mid\) = 8, we have \(\theta\) = [0\({}^{\circ}\), 45\({}^{\circ}\), 90\({}^{\circ}\), 135\({}^{\circ}\), 180\({}^{\circ}\), 225\({}^{\circ}\), 270\({}^{\circ}\), 315\({}^{\circ}\)]. CCMcs(\(e\), \(o\), \(d\), \(\theta\)) represents the probability of two pixels, which have \(d\) distance in the \(\theta\) direction and gray levels \(e\) and \(o\), respectively, i.e.,  
\[\text{CCM}_{cs}(e,o,d,\theta)=\text{Pr}\big{\{}I_{ic}^{*}=e\wedge I_{i^{\prime} s}^{*}=o\big{|}\big{|}i-i^{\prime}\big{|}=d,\,\angle ii^{\prime}\,=\theta\big{\}} \tag{11}\]  
In particular, when \(c=s\) and \(d=1\), the color co-occurrence matrix degenerates into the traditional gray level co-occurrence matrix. According to the number of bands, \(C_{h}^{2}+h\) co-occurrence matrices can be established. If \(h\) = 3, i.e., R, G, B, the six co-occurrence matrices will be CCM\({}_{RR}\), CCM\({}_{GG}\), CCM\({}_{BB}\), CCM\({}_{RG}\), CCM\({}_{RB}\), and CCM\({}_{GB}\).  
Taking the 3 \(\times\) 3 local region as an example, we assume that there are 3 bands and 8 gray levels in the local region, as shown in Figure 2a. The number of pixel pairs of the color co-occurrence matrix about bands \(R\) and \(G\) with \(d=1\) and \(\theta=0\) is shown in Figure 2b. In the local region, there are two pairs of pixels that meet the requirements of \(I_{ic}^{*}=1\), \(I_{fc}^{*}=1\), and \(\mid i-i^{\prime}\mid\) = 1, \(\angle ii^{\prime}=0\), as shown by the red lines. In fact, the local region can have an irregular shape because the real boundary is constrained by objects, which ensures the homogeneity of the texture feature description.  
Based on the CCM, the four statistical variables of the texture features are extracted [27], as shown in Table 1, including angular second moment (ASM), contrast (Con), correlation (Cor), and inverse different moment (IDM). The ASM represents the evenness of the grayscale distribution of the image, Con represents the sharpness, Cor represents the consistency of image texture, and IDM represents the homogeneity of image texture. \(P_{e,o}\) is the probability value of the occurrence of the element at the position (\(e\), \(o\)) in the matrix, and \(\mu\) and \(\sigma\) are the mean and variance of the corresponding gray level, respectively. The mean values of the statistical variables in different directions compose the color texture feature set of the object.