# A New Approach to Detect Hand-Drawn Dashed Lines in Engineering Sketches
## 2 Related Work
[PERSON] and [PERSON] [7] contributed to finding hidden lines in a natural line-drawing, refining [PERSON]'s original approach [8; 9], and the approach provided by [PERSON] et al. [10; 11; 12]. All these approaches assume that the natural sketch is created in the most informative view, meaning that there is nothing on the \"back of the sketch\" that cannot be directly inferred from the visible part of it [11] and, most importantly, the user draws a sketch without hidden lines, which must be automatically inferred--and labeled as such--by the application. Therefore, dashed lines arise while parsing the sketch, but are missing at the input. Wireframe drawings include hidden lines, but these are not identified as such. Consequently, the well-known ambiguity of wireframes (Figure 4) is commonly solved by reconstruction approaches that cannot rely on the visibility of the edges. As the recent review by [PERSON] et al. shows [3], the reconstruction of wireframes operates by extracting alternative cues, such as faces and form features, while commonly avoiding trying to explicitly infer hidden edges. To the best of our knowledge, the only publicly available algorithm to distinguish visible edges from hidden edges in wireframe drawings was published by [PERSON] [13]; it was an exhaustive search of all possible permutations of hidden/visible edges, or exhaustive permutations of hidden/visible faces (if faces were calculated in advance, for instance, following the approach of [PERSON] et al. [14]). Figure 4: Wireframe model of polyhedral shape (**A**), with multiple volumetric interpretations in axonometric views (**B–D**). Figure 3: Wireframe (**left**), natural (**center**), and hidden lines (**right**) in isometric line-drawings. Some algorithms to detect dashed lines are used for other purposes, like human-tablet interaction [15]. However, they depend on assumptions that may be acceptable only while interactively interpreting simple diagrams. For instance, forcing the user to draw the strokes consecutively enables a trivial procedure to detect dashed lines interactively. The algorithm must simply group the strokes in the order the user introduces them. The problem becomes much more challenging when there is no time information available (off-line interpretation) or when the user does not follow a particular sequence for drawing the strokes (repaired or beautiful sketches). The works of [PERSON] and [PERSON] [16] and [PERSON] et al. [17] are some of the most representative of the initial works that were carried out in the field of the recognition and detection of dashed lines. [PERSON] and [PERSON] [16] attempted to recognize dashed lines by linking short and isolated bars in drawings and maps. [PERSON] et al. [17] investigated the detection of dashed lines with straight and curved shapes on a pixel basis. Both have served as inspiration for subsequent work in the development of algorithms for image processing. Finally, in recent years, the use of machine learning in image recognition has become widespread. In this regard, several methods with specific applications within engineering and design were developed. For instance, [PERSON] and [PERSON] [18] presented a method based on the use of a Convolutional Neural Network (CNN) as a trainable engineering symbol recognizer for network diagrams. The CNN can learn the visual characteristics of predefined symbol categories from a few diagrams provided by the user and a set of synthetically generated training samples. However, the method is not directly applicable to the recognition of dashed lines. Similarly, [PERSON] et al. [19] introduced a method for recognizing lines and flow arrows in piping and instrumentation diagrams. The model was trained by a combination of image processing techniques and deep neural networks.