## 4 Implementation and Results
### Implementation and Discussion  
#### 4.2.1 column Detection Results and Discussion  
The detection precision for all 20 column images in Table 1 is 100%, while detection recall ranges from 50% to 100% with an average of 78.4%. The No. 1 column image, in which all five columns were correctly detected, is taken as an example to explain the whole procedure of the proposed method. Firstly, by using Equation (1), the original RGB image (Figure 2a) was converted into a grayscale image (Figure 2b), which served as the basis of edge detection. Then, discrete edge points were detected using the Prewitt Operator, generating the edge map. As shown in Figure 2c, the edge map is a binary image in which white points are edge points and black points are the background. Next, long vertical lines, potentially to be boundaries of structural elements, were retrieved by the Hough Transform from the edge map. In this study, the authors defined a vertical line whose length is longer than a quarter of the height of the image as a long vertical line. Moreover, slightly inclined lines could also be retrieved by setting the allowed inclination of \(\pm\) 5\({}^{\circ}\) with the vertical direction. Consequently, 20 vertical boundary lines were detected, dividing the image into 19 sub-regions, as shown in Figure 2d. Accordingly, the variance, skewness, and kurtosis of the GLHs of every sub-regions were calculated, and sub-regions with variance and skewness values being local minimum and kurtosis values being local maximum were identified as structural elements. Finally, these detected structural elements were regarded as columns because their ratios of length to width were no less than two. As shown in Figure 3a-c, sub-region 3, 7, 12, 16, 19 are columns. It can be observed that non-column sub-regions contain various objects in different gray levels: windows in high gray levels and retaining walls in low gray levels, while column sub-regions only contain columns in similar gray levels. To further illustrate the differences of variance, skewness, and kurtosis among a column sub-region and its two adjacent non-column sub-regions, the GLHs of the column sub-region 7 and the two adjacent non-column sub-region 6 and 8 in Figure 2d are shown in Figure 3d-f respectively. Three peaks exist in Figure 3d,f but only one peak in Figure 3e, which means that in non-column sub-region 6 and 8, gray levels of pixels dispersedly distribute in wide ranges while in the column sub-region 7, gray levels of pixels concentrate on a narrow range. Therefore, compared with the GLH of adjacent non-column sub-regions, the GLH of a column sub-region shows a more concentrated and symmetric distribution, with fat tailedness. Figure 2: The preprocessing of the No. 1 image in Table 1: (**a**) the original image; (**b**) converting the RGB image into a grayscale image; (**c**) generating the edge map using the Prewitt Operator; (**d**) detecting long vertical lines by the Hough transform. The column detection results prove that columns with tiled or painted surfaces can be detected, overcoming the shortage of color/texture-based methods. For example, in Figure 4a, both column 1 and column 2 were successfully detected although they are tiled with colorful tiles--the top and bottom parts are tiled with dark tiles while the middle parts with light tiles. Moreover, columns with a small tilt, which commonly occur due to camera tilting or perspective illusion, can be detected by this method. As shown in Figure 4b, three tilted columns (column 2, 3 and 4) in the image, with tilt angles between their boundary lines and the vertical direction ranging from \(1^{\circ}\) to \(5^{\circ}\), were detected as a result of the maximum allowed tilt angle set as \(5^{\circ}\) in this study.