## 3 Methodology
### Columns and Walls Recognition using GLH Statistical Parameters  
The GLH is innovatively used in this proposed study to recognize structural elements from detected sub-regions in an image. The meanings of the five GLH statistical parameters are described as follows: mean is the average gray value of a GLH; integrated density is the sum of the gray values of a GLH; variance indicates the degree of spread from the mean of a GLH; skewness represents the dissymmetric degree of the distribution of a GLH; and kurtosis reflects the tailedness of the distribution of a GLH. By investigating GLHs of detected sub-regions, the authors found that, comparing with the GLH of the adjacent sub-regions that contain various objects, the GLH of a structural element sub-region showed a more concentrated, symmetric distribution with fat tailedness due to relatively uniform gray levels on the surface of the element (also discussed in Section 4.2.1), while differences of the gray values between structural element regions and nonstructural element regions are inconspicuous. Therefore, only variance, skewness, and kurtosis are used to differentiate GLHs between structural element sub-regions and nonstructural element sub-regions. These three statistical parameters of a GLH can be calculated by Equations (8)-(13):  
\[H(i)=\frac{n_{i}}{m\times n},\;i=0,\;1,\;2,\ldots,\;L-1, \tag{8}\]  
\[\mu=\sum_{i=0}^{L-1}i\times H(i),\;i=0,\;1,\;2,\ldots,\;L-1, \tag{9}\]  
\[\sigma=\left[\sum_{i=0}^{L-1}(i-\mu)^{2}H(i)\right]^{1/2}, \tag{10}\]  
\[\text{Variance}=\sum_{i=0}^{L-1}(i-\mu)^{2}H(i), \tag{11}\]\[\text{Skewness}=\frac{1}{\sigma^{3}}\sum_{i=0}^{L-1}(i-\mu)^{3}H(i), \tag{12}\]  
\[\text{Kurtosis}=\frac{1}{\sigma^{4}}\sum\
olimits_{i=0}^{L-1}(i-\mu)^{4}H(i), \tag{13}\]  
where \(i\) is the gray level of a pixel ranging from 0 to 255; \(H(i)\) is the proportion of pixels in the gray level \(i\); \(n_{i}\) is the number of pixels in the gray level \(i\) of a sub-region; and \(m\) and \(n\) are the numbers of pixels in the rows and columns of a sub-region, respectively; \(\mu\) is the average gray level of pixels; \(\sigma\) is the standard deviation of pixels' gray levels; \(L\) is the RGB color space, which is equal to 256. Accordingly, three GLH statistical parameters of every sub-region are calculated. Based on the preliminary study, the authors conclude that (1) the variance and skewness values of a sub-region that is a structural element is smaller than the values of adjacent sub-regions that contain complex surrounding environment, respectively; (2) the kurtosis value of a sub-region that is a structural element is larger than the kurtosis values of adjacent sub-regions that contain complex surrounding environment. The first conclusion can be explained by the concentrated distributions of the gray levels of structural element sub-regions in narrow ranges as a result of the relatively uniform color of columns' and walls' surfaces, while gray levels of sub-regions containing complex surrounding environment distribute in wide ranges, leading to large variance values. Meanwhile, the centralization of gray level distributions also results in the low skewness values of structural element sub-regions because the concentration of gray level distributions leads to a relatively symmetric distribution compared with the random distribution of non-structural element sub-regions' gray levels. Finally, based on Equation (13), for a concentrated distribution, a few pixels with extreme values (i.e., the values considerably deviate from the mean value) can lead to an extreme large skewness value of a structural element sub-region.