# A New Approach to Detect Hand-Drawn Dashed Lines in Engineering Sketches
## 7 Conclusions  
Although it may seem trivial, the development of an algorithm capable of detecting hand-drawn dashed lines addresses an unsolved problem in the field of industrial product design. This paper highlights the importance of such an algorithm, particularly in scenarios where designers must resort to drawing continuous lines and subsequently manually editing them into dashed lines. Our proposed algorithm represents a significant step towards improving user experience by allowing applications to accurately interpret dashed lines. However, it is worth noting that our current solution is partial, as it does not yet extend to detecting other types of dashed lines, such as dot or dash-dot patterns.  
To further highlight the novelty or complexity of the approach, we must remember that fixing dashed lines that are outlined with a ruler and compass is relatively straightforward. Simple algorithmic approaches based on geometric principles may work reasonably well. The problem becomes much more challenging when lines are hand-drawn. In this scenario, simple algorithms lack the human capability to perceive, balance, and make choices about small imperfections. Collinear dashes become \"nearly\" collinear, to cite but one example.  
The main contribution of this paper is the idea of \"following the path\" to find preceding or following dashes until completing the chain of dashes. The approach works with local information while favoring the formulation of the perceptual principles as cues and requisites. These cues are then managed as constraints, which are tuned by different parameters, with values supported by perceptual principles combined with our own experience.  
Finally, the algorithm, which was intended as a proof-of-concept, was validated with a wide and varied set of examples. We concluded that, with properly balanced parameters, the level of false negatives is acceptable, and the level of false positives is very small. These are good results, when put in the context of being one of the many stages that contribute to complete a complex vectorization and 3D reconstruction process. In these processes, false positives are difficult to detect and correct in later stages, whereas false negatives can be detected and \"repaired\" when global information comes into play in subsequent stages.  
The use of expert systems remains worthy of exploring in future research. Yet, the main guidelines of the current approach--which mimics human perception--can be useful to shorten the training period, and focus on the most critical aspects of detecting these geometrically imperfect, yet fully perceivable, hand-drawn dashed lines.  
Figure 22: Chaining from the intersection, vs. chaining from the extreme.  
**Author Contributions:** Conceptualization, R.P. and P.C.; methodology, R.P. and P.C.; software, R.P., M.C. and F.N.; validation, R.P., M.C. and F.N.; formal analysis, R.P., M.C. and F.N.; writing--original draft preparation, R.P. and P.C.; writing--review and editing, R.P., M.C., F.N. and P.C. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research received no external funding.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The full source code of the algorithm will be freely available on the Geometric Reconstruction Group website (REGEO), [[http://www.regoe.uji.es](http://www.regoe.uji.es)]([http://www.regoe.uji.es](http://www.regoe.uji.es)), (accessed on 19 April 2024) including examples that demonstrate the capabilities and limitations of the approach.  
**Acknowledgments:** Authors would like to extend their sincere gratitude to the reviewers for their valuable comments and constructive suggestions, which significantly improved the quality of this article.  
**Conflicts of Interest:** The authors declare no conflicts of interest.