# Multi-Constrained Optimization Method of Line Segment Extraction Based on Multi-Scale Image Space
## 3 Experiments and Analysis
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Data**} & \multirow{2}{*}{**Methods**} & **The Number of** & **Accuracy** & **Time-consuming** & **Total Length** & **Average Length** \\  & & **line Segments** & **Rate** & **(s)** & **(pixel)** & **(pixel)** \\ \hline \multirow{4}{*}{Indoor 1} & EDLines & 327 & 0.801 & 0.150 & 20633.7 & 63.1 \\  & **MSEDLines** & 215 & 0.842 & 0.359 & 18339.5 & **85.3** \\  & LSD & 445 & 0.879 & 0.586 & 22828.5 & 51.3 \\  & **MSLSD** & 238 & 0.874 & 0.636 & 20301.4 & **85.2** \\  & EDLines & 415 & 0.945 & 0.112 & 15977.5 & 38.5 \\  & **MSEDLines** & 276 & 0.960 & 0.122 & 14076.0 & **51.0** \\  & LSD & 463 & 0.944 & 0.214 & 16436.5 & 35.5 \\  & **MSLSD** & 303 & 0.967 & 0.269 & 13180.5 & **43.5** \\  & EDLines & 375 & 0.939 & 0.110 & 22950.0 & 61.2 \\  & **MSEDLines** & 253 & 0.960 & 0.133 & 18747.3 & **74.1** \\  & LSD & 487 & 0.959 & 0.221 & 26005.8 & 53.4 \\  & **MSLSD** & 299 & 0.963 & 0.272 & 21258.9 & **71.1** \\ \hline \multirow{4}{*}{Outdoor 1} & EDLines & 1854 & 0.944 & 0.476 & 64890.0 & 35.0 \\  & **MSEDLines** & 1147 & 0.969 & 0.711 & 53450.2 & **46.6** \\  & LSD & 2196 & 0.954 & 1.425 & 70930.8 & 32.3 \\  & **MSLSD** & 1274 & 0.973 & 1.452 & 57584.8 & **45.2** \\  & EDLines & 245 & 0.898 & 0.072 & 9016.0 & 36.8 \\  & **MSEDLines** & 158 & 0.810 & 0.084 & 8200.2 & **51.9** \\  & LSD & 265 & 0.894 & 0.237 & 8904.0 & 33.6 \\  & **MSLSD** & 162 & 0.907 & 0.273 & 7387.2 & **45.6** \\  & EDLines & 631 & 0.973 & 0.200 & 25997.2 & 41.2 \\  & **MSEDLines** & 436 & 0.975 & 0.249 & 22192.4 & **50.9** \\  & LSD & 836 & 0.982 & 0.376 & 31099.2 & 37.2 \\  & **MSLSD** & 510 & 0.982 & 0.456 & 24939.0 & **48.9** \\ \hline \multirow{4}{*}{Aerial 1} & EDLines & 395 & 0.975 & 0.112 & 12758.5 & 32.3 \\  & **MSEDLines** & 293 & 0.983 & 0.342 & 13448.7 & **45.9** \\  & LSD & 456 & 0.985 & 0.294 & 14044.8 & 30.8 \\  & **MSLSD** & 332 & 0.988 & 0.334 & 14342.4 & **43.2** \\  & EDLines & 901 & 0.964 & 0.230 & 33607.3 & 37.3 \\  & **MSEDLines** & 580 & 0.988 & 0.330 & 29580.0 & **51.0** \\  & LSD & 1064 & 0.963 & 0.785 & 31920.0 & 30.0 \\  & **MSLSD** & 642 & 0.989 & 1.142 & 26193.6 & **40.8** \\  & EDLines & 1126 & 0.947 & 0.546 & 34568.2 & 30.7 \\  & **MSEDLines** & 749 & 0.952 & 0.698 & 29735.3 & **39.7** \\  & LSD & 1313 & 0.950 & 0.753 & 33481.5 & 25.5 \\  & **MSLSD** & 875 & 0.966 & 1.029 & 29487.5 & **33.7** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Results of line segment extraction for indoor, outdoor, and aerial images using traditional and proposed methods. of extracted line segments was less than that of conventional methods. MSEDLines and MSLSD extracted 215 and 238 line segments respectively from Indoor 1, while EDLines and LSD extracted 327 and 445 line segments, respectively. However, the reduction in the number of line segments does not result in the sharp drop in the total length of line segments. Because proposed methods in this paper preserve and optimize the key geometric contour information on the image while removing the redundant line segments, they ensure that the total length does not change much. The extraction time of the four methods of MSEDLines, MSLSD, EDLines, and LSD is not much different, which indicates that the optimization steps in this paper's algorithm did not take much time. The quantification results of line segment extraction of the other eight sets of data have the same trend as Indoor 1. Generally, line segments extracted by MSLSD and MSEDLines were more complete than that extracted by traditional methods and they also alleviated the line segmentation fracture problem. Many broken line segments were optimized to be combined into a complete line feature, which completely expressed the geometric profile information of the target. Meanwhile, the proposed method eliminated redundant clutter in the line feature detection process. Quantitative results showed that the average length of optimized line segments extracted by the proposed method was greatly improved compared with that extracted by traditional methods.