# Multi-Constrained Optimization Method of Line Segment Extraction Based on Multi-Scale Image Space
## 5 Conclusions  
In this article, our proposed line detection method, MSLines, including MSLSD and MSEDLines, solves the line segmentation fracture problem. This novel method has the following advantages and characteristics: (1) Using advantages of down-sampling fuzzy processing, the influence of grayscale distortion on line segment extraction is reduced and the segmentation fracture effect of the traditional line feature extraction algorithm is alleviated. The continuity of line segments is improved. (2) Multi-scale image space line features are combined to construct an optimization and purification strategy with multiple constraints. The average length of extracted line segments is longer with higher integrity. Longer and accurate line segments provide a good research basis for line-based camera calibration, image matching, and 3D reconstruction. (3) Ineffective lines with partial redundancy and pseudo-lines are removed, as well as key line segments, such as geometric contours of the main object are optimized, which makes edge structures of the image be described more intuitively and clearly. (4) Only one parameter needs to be controlled manually, which makes the novel method more automated and parameter-less.  
We experimentally verified the validity and superiority of our proposed method. Compared with LSD and EDLines, our proposed method has a longer average length and higher line segment integrity, which alleviates the line segmentation fracture effect to some extent. Particularly, our approach can extract more complete and comprehensive details for structured buildings. The presented improvements also can provide better structural features for SLAM navigation and other line-based applications. However, the proposed method does not completely solve the segmentation fracture effect of line segment extraction. Later, we can consider the fusion of LiDAR (Light Detection And Ranging) point cloud data based on our proposed method to further optimize and eliminate the segmentation fracture effect of line segment extraction. It can also be considered from the classical LSD algorithm perspective to improve problems where the internal gradient direction angle of the algorithm is abruptly affected by the grayscale mutation of individual pixels, which leads to the interruption of region growing and insufficient density of the same points.  
[PERSON] and [PERSON] proposed the idea and methodology of the current research, while [PERSON] provided technical assistance in this regard. [PERSON] helped in providing image data and [PERSON] supported during conducting experiments. [PERSON] and [PERSON] put efforts into writing and reviewing this manuscript.  
This research was funded by the National Natural Science Foundation of China (Grant Nos. 61841101, 41571432) and National Key R&D Program of China (Grant No. 2017 YFB0503004).  
**Acknowledgments:** We would like to thanks the authors [PERSON] et al. (2010) and [PERSON] et al. (2011) for making their algorithms as open-source, which were helpful for research in this paper.  
**Conflicts of Interest:** The authors declare no conflicts of interest.