An Algorithm for Grouping Lines Which Converge to Vanishing Points in Perspective Sketches of Polyhedra

Abstract

Abstract. We seek to detect the vanishing points implied by design sketches of engineering products. Adapting previous approaches, developed in computer vision for analysis of vectorised photographic images, is unsatisfactory, as they do not allow for the inherent imperfection of sketches. Human perception seems not to be disturbed by such imperfections. Hence, we have designed and implemented a vanishing point detection algorithm which mimics the human perception process and tested it with perspective line drawings derived from engineering sketches of polyhedral objects. The new algorithm is fast, easilyimplemented, returns the approximate locations of the main vanishing points and identifies those groups of lines in 2D which correspond to groups of parallel edges in the 3D object.Keywords: Sketches; Perspective; Vanishing points; Parallel edges IntroductionOur area of interest is creating computer-based tools to help design engineers during conceptual design (the first stage of the design process). For sketch-based modelling (SBM) systems to become a valid alternative to both current WIMP-based CAD systems and traditional paper and pencil sketching, they must cope with the full range of conceptual design sketches. Although most such sketches are done in orthographic projection style [1], it is also important to allow for perspective projection. As explained in Section 2, some of the most popular vanishing point detection algorithms are compatible with human interpretation and may be tuned to mimic human perception [1][2][3], but none of them copes satisfactorily with the inherent imperfection of sketches. Hence, we have designed and implemented a new algorithm, specifically aimed at finding vanishing points (VPs) in sketches of engineering design products. Our algorithm clusters candidate vanishing points instead of clustering lines, and measures cluster similarity by angular difference in orientation. This deals naturally with sketching errors, as, when judging where VPs should be located, people are far more tolerant of discrepancies in distance than discrepancies in orientation [4].Section 3 describes our algorithm. Section 4 presents our test results. Section 5 presents conclusions and recommendations for future work. Related WorkThe input to our algorithm is a set of lines. In discussing related work, we only consider approaches which takes lines as input (we exclude those such as Barnard [5] and Magee and Aggarwal [6] which require bitmaps). We also exclude those such as Varley [7] which use (or attempt to deduce) higher semantic level information. We note that most methods for detecting VPs are intended for 2D camera images. The errors they deal with (lens imperfections and noise in line segment extraction) are much smaller than typical sketching errors. Of these methods, the clustering approach of McLean and Kotturi [2] is most tolerant to noisy data.Tardif [8] is interesting as it deals with one of the problems we consider here: its input is a set of N sparse edges, and its output is a set of VPs an...

Sketch-Based Modeling in Mechanical Engineering Design: Current Status and Opportunities

“…Recent contributions are due to Governi et al [GFP13] and Han et al, who used multiple views that are not necessarily orthographic [HML20]. Pictorial views used as input are usually axonometric and single views, but some approaches based on perspective views can also be found in the literature [PCV13], [CVP14]. If the original drawing is created on paper, the electronic input can be obtained by scanning the drawing and producing a raster image, which is then vectorized as a series of strokes [WD99].…”