# Integrating Textural and Spectral Features to Classify Silicate-Bearing Rocks Using Landsat 8 Data
## 3 Methods  
### Extraction and Analysis of Spatial Textural Features  
#### 3.1.1 Box-Counting Dimension Method to Extract Textural Features  
The concept of fractal geometry, which was initially proposed by [PERSON] [50], provides a simple method to describe the irregularities of complex objects and objects with self-similar characteristics at different scales (spatial, temporal, or otherwise) in nature. Remote sensing images are not only spectrally and spatially complex, but they often exhibit certain self-similarities at different scales [51]. Therefore, increasing attention has been paid to fractal geometry in the remote sensing community. Fractal models have been used in a variety of image processing and pattern recognition applications [52]. For example, they have been used to describe image texture and to segment various types of images [30; 31; 35; 53]. In the past decades, fractal geometry has been one of the most popular techniques for texture extraction because of its robustness in image scaling [30; 31; 41; 54]. Fractals characterize the roughness or geometric complexity of surface features in remote sensing images. Roughness or geometric complexity, which is related to surface morphology, plays an important role in improving image understanding and classification. Applications of fractal models to image analysis mainly depend on the estimation of the fractal dimension (_FD_) [52]. More generally, the more irregular an object is, the higher its _FD_ value. Thus, _FD_ value is intimately linked to the concept of roughness or geometric complexity. In this way, different surface objects may have characteristic textures or  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Band Description** & **Wavelength (\(\mu\)m)** & **Spatial Resolution (m)** \\ \hline _Band_ 1 Coastal & 0.433–0.453 & \\ _Band_ 2 Blue & 0.450–0.515 & \\ _Band_ 3 Green & 0.525–0.600 & \\ _Band_ 4 Red & 0.630–0.680 & \\ _Band_ 5 NIR & 0.845–0.885 & \\ _Band_ 6 SWIR 1 & 1.560–1.660 & \\ _Band_ 7 SWIR 2 & 2.100–2.300 & \\ \hline _Band_ 8 Pan & 0.500–0.680 & 15 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Landsat 8 Operational Land Imager (OLI) band information.  
roughness that could be measured by different \(FD\) values. In this study, the box-counting method devised by [PERSON] [54] was used to calculate the fractal dimension. This method divides an area into regular boxes with the same box edge length. Here, \(M\) is the measured object, \(\varepsilon\) is the box edge length, \(M_{\varepsilon}\left(C\right)\) and \(C\) is the lowest number of boxes in the grid divided curve and scales, respectively, and \(FD\) is the fractal dimension of \(M\).  
\[FD=\lim_{\varepsilon\rightarrow\infty}\frac{\log M_{\varepsilon}\left(C \right)}{\log\varepsilon} \tag{1}\]  
The value of \(FD\) ranges from 1.0 to 2.0. To extract the fractal dimension of each pixel in remote sensing images, a 3 \(\times\) 3 moving window covering the neighboring pixels is used. In this way, a new layer is generated as the texture image. Each pixel in this layer is assigned an \(FD\) value.