# A New Approach to Detect Hand-Drawn Dashed Lines in Engineering Sketches
## 2 Related Work  
The problem of reconstructing 3D shapes from 2D drawings is challenging, as the information provided by the user is a flat image and the output is a volumetric shape. It  
Figure 1: An example diagram illustrating the use of dashed lines to represent relationships between classes in computer code. is, thus, necessary to bring out the hidden third dimension. In addition, drawings may be hand-drawn, which prevents the problem from being solved by applying only geometric principles. The use of hand-drawn sketches remains significant in the early stages of conceptual design. [PERSON] et al. (2019) argued that sketching improves the designer's spatial ability, which is positively correlated with their ability to generate technical artifacts. In short, input 2D sketches contain insufficient geometric information and may be \"geometrically corrupted.\" This problem is at the core of the field of sketch-based modeling (SBM). Readers interested in this topic can find a recent state of the art by [PERSON], [PERSON] and [PERSON] (2019), where balancing geometric rules with perceptual principles is repeatedly advocated for. A recent work by [PERSON] et al. (2019) builds on the so-called \"design principles\" (previously explored by other authors like [PERSON] et al. (2019)), which the authors define as \"insights about sketching and design practices\" (based on recommendations of expert designers on how to sketch). We consider them quite promising as a third type of information that may complement and enrich geometric and perceptual information. However, we have not included these principles in our study as we do not want to limit our study to the sequential placement of dashes, which is the primary principle related to the identification of dashed lines. Vectorization is just one of the stages in SBM (Figure 2). For instance, after fitting lines to strokes, the 2D refinement stage contributes to remove the imperfections of the line-drawing, such as fitting vertices ([PERSON] et al., 2019). SBM leverages the fact that sketches convey valuable information through cues, which, when perceived, reveal regularities and features of the object. Bringing out as many cues as possible facilitates the reconstruction process. Regarding the lines that depict edges, they may represent visible or hidden edges. The removal of hidden edges from a drawing makes it appear as representing a \"solid\" and \"opaque\" object. Hence, they are more \"natural,\" as most of the objects we see are not transparent. We \"perceive\" the shapes more easily when looking at a natural line-drawing. However, from the point of view of communicating geometrical information, they are less rich than wireframes, as the back of the object is not depicted and must be \"inferred\". In principle, there are two classical approaches to deal with hidden edges in SBM. In the first, the user creates a natural drawing and then the system tries to automatically infer the back of it (which is not provided by the user). In the second, the user draws a wireframe  
Figure 2: Main stages in SBM. representation of the solid shape without distinguishing that hidden from visible edges. Both are drawn as solid lines. Reconstruction approaches cannot rely on the visibility of the edges, which is generally unknown. There is, however, a third alternative. A common artifact that is successfully used to convey information of the back of an object while increasing the perceptual sensation of volume involves the use of dashed lines to represent surfaces, edges, or corners of objects that are hidden from view (Figure 3). A review of all three approaches concludes that drawing with hidden lines communicates higher-level geometric information more effectively than the other two approaches. However, it has not been explored extensively, presumably because detecting hand-drawn dashed lines remains an open problem.