# Multi-Constrained Optimization Method of Line Segment Extraction Based on Multi-Scale Image Space
## 4 Discussion  
### Parameter Setting  
This part discusses the selection of problem-oriented parameters in the model construction process, providing the basis for constructing the most suitable multi-scale image space model for various resolution images. The image resolution is different, as is as the maximum number of down-sampling setting, which causes the number of multi-scale image space model layers formed to be different.  
In order to get a suitable multi-scale image space for a line feature extraction, the corresponding and reasonable maximum down-sampling number \(t_{max}\) should be set according to the image resolution. Regarding the construction of multi-scale image space, this article is consistent with the traditional empirical method. The scale space factor \(\sigma\) is 0.5 and the whole model has a total of N-layered images. To discuss the selection of model parameteres, an outdoor image (front view of the Grand Auditorium) with a resolution of approximatly 10 million pixels (\(3500\times 2625\)) was used as an example to down-sample from one to four times. The corresponding multi-scale image space model was constructed and the line features of the image were extracted by MSLSD. The results are shown in Figure 17 and Table 2.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Down-sampling Times** & **Resolution** & \begin{tabular}{c} **The Number of** \\ **Line Segments** \\ \end{tabular} & \
\begin{tabular}{c} **Time-consuming** \\ **(s)** \\ \end{tabular} &
\begin{tabular}{c} **Average Length** \\ **(pixel)** \\ \end{tabular} \\ \hline
0 & 9187500 & 8248 & 6.138 & 53.0 \\
1 & 2296000 & 4273 & 8.440 & 79.8 \\
2 & 574000 & 4191 & 8.836 & 92.9 \\
3 & 143664 & 4251 & 8.998 & 103.3 \\
4 & 35916 & 3393 & 10.574 & 110.4 \\ \hline \hline \end{tabular}
\end{table}
Table 2: MSLSD line segment extraction results under different down-sampling times.  
As we can see from Figure 17a, a line segment extracted from the original image suffers a severe fracture effect. Using our proposed method to construct a multi-scale image space model, we can effectively alleviate the fracture problem of extracted line segments, as can be seen from Figure 17b-e and Table 2, and the average length of the line segments is greatly improved. The continuity of line segment extracted by MSLSD with fusion of down-sampled images becomes better, but with the increase of down-sampling times, images, particularly those down-sampled four times, do not change the effect of extracted segments much. Moreover, the average length of line segments changed from  
Figure 17: Line segment extraction results of different multi-scale image space models. (**a**) Down-sampled zero times. (**b**) Down-sampled one time. (**c**) Down-sampled two times. (**d**) Down-sampled three times. (**e**) Down-sampled four times.  
103.3 to 110.4 pixels, which shows that the growth trend was not obvious. Therefore, to construct the multi-scale image space model, we set model parameters according to the proposed rules of Table 3.  
The super-resolution images of more than 10 million pixels were down-sampled at least three times to form more than four layers of the multi-scale image space model. High-resolution images with megapixel resolution were down-sampled three times to form an image pyramid model of four-layered multi-scale image space. Mid-resolution images were down-sampled twice to form a three-layered pyramid-like model. Low-resolution images with a pixel resolution of less than 100,000 pixels only needed to be down-sampled once to form a two-layered scale image space.