# Multi-Constrained Optimization Method of Line Segment Extraction Based on Multi-Scale Image Space
## 4 Discussion
### The Impact of Image Noise  
Image noise tends to affect line segment extraction and causes serious line segmentation fracture problems. In order to analyze the influence of the proposed method on noise, we selected an aerial image with a resolution of \(1440\times 920\) for discussion. In the experimental analysis, the image was down-sampled twice, forming a three-layer multi-scale image space. Simultaneously, we added Gaussian white noise with different mean and variance to the image. We found that, when the noise variance was greater than 0.02, the image quality was seriously affected. Based on this, the traditional and proposed methods under different image noises with means of 0, 0.1, and 0.2 and variances of 0.005, 0.01, and 0.02 were analyzed. The partial line segment extraction result of the noisy image is shown in Figure 20.  
Figure 19: The line features of MSLSD without introducing low-resolution image line segment extraction error.  
Figure 20: The partial results of LSD and MSLSD line segment extraction of aerial image. **(a)** Original image. **(b)** Noisy image, mean = 0, variance (var) = 0.02. **(c)** Mean = 0, var = 0 LSD (1613/33.2). **(d)** Mean = 0, var = 0 MSLSD (998/43.4). **(e)** Mean = 0, var = 0.01 LSD (1156/18.7). **(f)** Mean = 0, var = 0.01 MSLSD (670/43.1). **(g)** Mean = 0, var = 0.02 LSD (825/17.8). **(h)** Mean = 0, var = 0.02 MSLSD (569/44.3). **(i)** Mean = 0.1, var = 0.01 LSD (1122/19.1). **(j)** Mean = 0.1, var = 0.01 MSLSD (648/44.1). **(k)** Mean = 0.2, var = 0.01 LSD (1143/19.0). **(l)** Mean = 0.2, var = 0.01 MSLSD (664/42.6).  
The complete line segment extraction results are shown in Figure 21, which reflects the average length of line segments for several methods under different noise conditions.  
Figure 21: The average lengths of line segment extraction of the conventional methods (LSD, EDLines) and proposed methods (MSLSD, MSEDLines) under noise interference. (**a**) Mean = 0, var = 0.005, 0.01, 0.02. (**b**) Mean = 0.1, var = 0.005, 0.01, 0.02. (**c**) Mean = 0.2, var = 0.005, 0.01, 0.02.  
Without image noise, LSD can extract 1613 line segments and the average length of line segments is 33.2 pixels, while MSLSD can detect 998 line segments and the average length of line segments is 43.4 pixels. In Figure 20, we find that the number of line segments extracted by the conventional methods and proposed methods is significantly reduced due to the influence of image noise.  
Meanwhile, it can be firstly found from Figure 21 that LSD is greatly affected by image noise. The larger the image noise, the more obvious the line segmentation fracture phenomenon, resulting in the shorter average length of the line segment. Secondly, MSLSD is robust to noise and is less affected by noise. Under different image noise environments, the average length of line segment extraction is basically unchanged. The average length of the MSLSD line segment extraction without noise is 43.4 pixels and the average length of the MSLSD line segment extraction under various noise conditions is maintained at 41.2-45.3 pixels. Thirdly, EDLines is less affected by image noise than LSD, but it still produces severe line segmentation fracture problems in noisy environments. In this article, MSEDLines can also alleviate the influence of image noise on line segment extraction and the average length of the line segment is greatly improved compared to EDLines. Through the discussion, MSLSD/MSEDLines can make the average length of lines longer than LSD/EDLines under different Gaussian noise conditions, respectively.