a School of Software, Tsinghua University, Beijing 100084, PR China b Department of Computer Science and Technology, Tsinghua University, Beijing 100084, PR China c Key Laboratory for Information System Security, Ministry of Education, Beijing 100084, PR China d Tsinghua National Laboratory for Information Science and Technology, Beijing 100084, PR China e Information Center, Hunan Tobacco, Changsha 410004, PR China h i g h l i g h t s • Our work improves the level of semantic understanding of 2D projections in 3D solids reconstruction. • It is the first trial to formulate the parts identification task into a classification problem. • We employ an advanced classification model, CRFs, to identify the elemental parts. a r t i c l e i n f o
Received 23 March 2012
Accepted 30 October 2014
Keywords: 3D reconstruction
Conditional random fields (CRFs) model a b s t r a c t
Semantic information is very important for understanding 2D engineering drawings. However, this kind of information is implicit so that it is hard to be extracted and understood by computers. In this paper, we aim to identify the semantic information of shafts from their 2D drawings, and then reconstruct the 3D models. The 2D representations of shafts are diverse. By analyzing the characteristics of 2D drawings of shafts, we find that there is always a view which represents the projected outline of the shaft, and each loop in this view corresponds to an elemental part. The conditional random fields (CRFs) model is a classification technique which can automatically integrate various features, rather than manually organizing of heuristic rules. We first use a CRFs model to identify elemental parts with semantic information. The 3D elemental parts are then constructed by a parameters template method. Compared with the existing 3D reconstruction methods, our approach can obtain both geometrical information and semantic information of each part of shafts from 2D drawings. Several examples are provided to demonstrate that our algorithm can accurately handle diverse 2D drawings of shafts. © 2014 Elsevier Ltd. All rights reserved. 1. Introduction 2D engineering drawings have been taken as a standard language to carry out mechanical designs since the 19th century .
From then on, many engineering drawings have been accumulated which are useful for design reuse. Currently, they still play a key role in engineering practices since many product designs are definitively represented in the format of 2D engineering drawings. Moreover, many small to medium size manufacturing com✩ This paper has been recommended for acceptance by Dr. Vadim Shapiro.∗ Corresponding author at: School of Software, Tsinghua University, Beijing 100084, PR China. Tel.: +86 10 62795459; fax: +86 10 62795460.
E-mail address: firstname.lastname@example.org (H. Zhang). panies directly use the 2D CAD software to do design work. However, 3D solid models have become more useful CAD tools  for visualization, modification and some other operations in downstream computer-aided manufacturing processes . Considering that much of the existing product design documentation is described by 2Dengineering drawings, it is necessary to convert them to 3D solid models. 1.1. Related work
Since Idesawa  published the first paper on reconstructing 3D models from 2D vector drawings in 1973, many researchers have studied on the field and made great improvements.
There are two main approaches used in the existing 3D reconstruction research : wireframe-based approach and volumebased approach. The wireframe-based approach was presented by http://dx.doi.org/10.1016/j.cad.2014.10.008Computer-Aided Des
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Identifying and constructing elemental p conditional random fields model✩
Yamei Wen b,c,d,e, Hui Zhang a,c,d,∗, Fangtao Li b, Jiagua0010-4485/© 2014 Elsevier Ltd. All rights reserved.ign 62 (2015) 10–19 ble at ScienceDirect ided Design .elsevier.com/locate/cad arts of shafts based on ng Sun a,b,c,d
Y. Wen et al. / Computer-Aid
Idesawa  firstly, and then it was formalized by Markowsky and
Wesley [6,7]. This approach generates 3D vertices, edges and faces by matching projection relations among 2D vertices and edges of different views. The volume-based approach identifies elemental entities bymatching predefined patterns, and then combines them together using Boolean operations. The former approach has one important advantage over the latter, since it covers wider domain of objects. The latter approach is limited to extrusions of uniform thickness [8,9] and axis-aligned revolutions [10,11]. The former approach can reconstruct more complicated objects, including polyhedrons [12,13] and quadric surfaces [3,14]without restrictions on their axes. However, the former is generally applicable to three orthographic views, and the latter is more suitable for handling sectional views [2,15,16] which are commonly used in engineering practices .
In the last few years, many nontraditional algorithms have been provided to deal with 3D reconstruction from 2D drawings.
Ibrahim  proposed a new 3D reconstruction framework. It considers the initial object as a prismatic volume at first, and then uses the proposed 3-Spacemethod to identify features which would be removed. Wen et al.  presented a new feature identification algorithm to handle sectional views. The desired features, including explicit features and implicit features, can be recognized by extracting semantic information of incomplete projections in sectional views. In addition, a novel confidence-based algorithm was proposed to validate features. 1.2. This work
The current researches are focused on identifying 3D geometric information from 2D engineering drawings . A 3D object usually consists of several elemental entities. Using the existing volume-based methods, the reconstructed 3D entities just contain 3D geometric information and topological relations. However, their real semantic names in mechanical parts, which can be easily identified by human engineers, are unknown.Moreover, semantics are useful for the manufacture in subsequent processes.