# A New Approach to Detect Hand-Drawn Dashed Lines in Engineering Sketches
###### Abstract  
Sketched drawings sometimes include non-solid lines drawn as sets of consecutive strokes. They represent dashed lines, which are useful for various purposes. Recognizing such dashed lines while parsing drawings is reasonably straightforward if they are outlined with a ruler and compass but becomes challenging when they are hand-drawn. The problem is manageable if the strokes are drawn consecutively so we can leverage the entire sequence. However, it becomes more challenging if they are drawn unordered, and/or we do not have access to the sequence (like in batch vectorization). In this paper, we describe a new approach to identify groups of strokes as depicting single hand-drawn dashed lines. The approach does not use sequence information and is tolerant with irregularities and imprecisions of the strokes. Our goal is to identify hidden lines of sketched engineering line-drawings, which would enable the interpretation of line-drawings with hidden edges, which currently cannot be efficiently vectorized. We speculate that other fields like hand-drawn graph interpretation may also benefit from our approach. vectorization; dashed lines; hidden lines; hand-drawn sketches; sketch-based modeling 2024202020242  
In this paper, we describe a new approach to identify hand-drawn dashed lines. Although the approach is intended to be as generic as possible, we are mainly interested in dashed lines used in line-drawings. In this regard, there are typically two types of line-drawings of solid shapes: natural and wireframe. Neither of them includes dashed lines. However, there is also a hybrid type of line-drawings: wireframes with hidden edges represented as dashed lines. This type of drawing is supported by drawing standards (such as ISO 128-2:2020 [1]) and has been--and continues to be--widely used in engineering drawings. It has been historically less common in sketch-based modeling (SBM) because it requires an additional workload from the part of the designer, and it is more challenging for the computer. In this context, an algorithm that could detect hand-drawn dashed lines would enable SBM approaches to process line-drawings that include hidden edges represented as dashed lines. Such an algorithm would obviously provide information about the type of the edge (visible or hidden) represented by each line, thus easing the procedure to find the 3D shape depicted by the 2D line-drawing. The grouped line would be marked as \"dashed\", facilitating the subsequent detection of hidden edges. In addition, such an algorithm would also facilitate the vectorization process by grouping non-solid strokes before they may be--incorrectly--parsed as independent edges. To sum up, an algorithm to detect dashed lines eases vectorization, while providing high-level semantic information that may improve the subsequent reconstruction process. After justifying the benefits of an algorithm to detect hand-drawn dashed lines, the rest of the paper is organized as follows: We first review the related work to conclude that--to the best of our knowledge--no similar algorithms have been published so far. The problems the algorithm could solve are faced by alternative approaches that require human intervention and/or limit the scope of the automatic approaches. In Section 3, we describe the general process of vectorization to provide context and understanding of the objective and tasks of the algorithm under consideration in this work. In Section 4, we detail the main guidelines of our approach. In short, we assume that short strokes are candidate dashes, and then we recursively find chains of such candidate dashes by searching for dashes that precede or follow the current chain until no more candidates remain and/or they do not meet the requirements. We use a set of geometric and perceptual criteria to guide the search for the most plausible dashes. The tuning parameters that govern those criteria are first introduced in Section 4 and summarized in Section 5.