[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-650294-105":3,"doc-detail-650294-en":80,"detail-sidebar-cat-0-en-105":97},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":73,"head_meta":75,"extra_data":77,"updated_unix":79},105,"en","3d-object-reconstruction-from-a-single-2d-line-drawing-without-hidden-lines-paper","3D Object Reconstruction from a Single 2D Line Drawing without Hidden Lines - Paper","","Human vision can interpret a single 2D line drawing as a 3D object even when the object’s hidden lines are not visible. Existing reconstruction methods cannot recover the complete object if the hidden lines are missing. This paper proposes a novel approach for complete 3D reconstruction without hidden lines, first deriving constraints and properties for inferring topology of invisible edges and vertices, then reconstructing the full shape using perceptual symmetry and planarity, supported by multiple examples.",{"@graph":14,"@context":72},[15,34,55],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/research-report/","Research & Report",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/3d-object-reconstruction-from-a-single-2d-line-drawing-without-hidden-lines-paper/650294/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/3d-object-reconstruction-from-a-single-2d-line-drawing-without-hidden-lines-paper/650294.png","ImageObject",300,407,{"name":42,"@type":43},"Aria Callaghan","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-31","2026-10-24",true,{"@type":52,"interactionType":53,"userInteractionCount":26},"InteractionCounter",{"@type":54},"ViewAction",{"@type":56,"mainEntity":57},"FAQPage",[58,64,68],{"name":59,"@type":60,"acceptedAnswer":61},"Why is reconstructing a complete 3D object from a 2D line drawing difficult without hidden lines?","Question",{"text":62,"@type":63},"Because the invisible edges and vertices are not provided, many existing methods rely on assumptions or formulations that require hidden-line visibility to recover the full structure.","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"What are the two main elements of the proposed method?",{"text":67,"@type":63},"The method consists of inferring the topology of the hidden part of the object and reconstructing the complete 3D shape.",{"name":69,"@type":60,"acceptedAnswer":70},"Which geometric and perceptual cues does the reconstruction rely on?",{"text":71,"@type":63},"Reconstruction is based on perceptual symmetry and the planarity of the object.","https://schema.org",{"og:url":32,"og:type":74,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":76,"canonical":32},"index,follow",{"doc_id":78,"site_id":7},650294,1792823838,{"code":4,"msg":81,"data":82},"success",{"doc_id":78,"user_id":83,"nickname":42,"user_avatar":84,"doc_module":4,"category_id":85,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":86,"file_id":87,"file_url":88,"file_type":89,"file_size":90,"view_count":26,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":91,"language":92,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":93,"faqs":94,"seo_title":95,"seo_description":12,"update_tm":79,"read_time":96},962084926284,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"3D Object Reconstruction from a Single 2D Line Drawing without Hidden Lines  \nLiangliang Cao and Jianzhuang Liu Department of Information Engineering The Chinese University of Hong Kong {llcao3,[jzliu](jzliu}@ie.cuhk.edu.hk)[}](jzliu}@ie.cuhk.edu.hk)[@ie.cuhk.edu.hk](jzliu}@ie.cuhk.edu.hk)  \nXiaoou Tang Microsoft Research Asia Beijing, China [xitang@microsoft.com](xitang@microsoft.com)  \nAbstract  \nThe human vision system can interpret a single 2D line drawing as a 3D object without much difficulty even if the hidden lines of the object are invisible. Several reconstruction approaches have tried to emulate this ability, but they cannot recover the complete object if the hidden lines of the object are not shown. This paper proposesa novel approach for reconstructing complete 3D objects from line drawings without hidden lines. First, we develop some constraints and properties for the inference of the topology of the invisible edges and vertices of an object. Then we present areconstruction method based on perceptual symmetry and planarity of the object. We give a number of examples to demonstrate the ability of our approach.  \n1. Introduction  \nA line drawing is defined as a 2D projection of the edgesand vertices of a 3D object in a generic view, with or without hidden lines visible. The human vision system has the ability to interpret 2D line drawings as 3D objects without difficulty. Emulating this ability is an interesting research topic for machine vision. The applications include providing 2D sketch query interface for 3D object retrieval from large databases or from the web [1], interactive generation of 3D models from images [2], [3], and flexible sketching interface for designers to sketch ideas in object design [4],[5] .  \nSince the early stage of computer vision , a large amount of work called line labeling has been carried out for line drawing interpretation [6], [7] . Line labeling focuses on finding a set of consistent labels from a line drawing without hidden lines, and does not explicitly give the 3D structure represented by a line drawing. Another body of work online drawing interpretation is related to judging the correctness of line drawings and give their possible reconstruction based on algebra test with linear equalities and inequalities [8], [9], [10] . The common problem of these methods is that the formulation is superstrict and not robust; an origi-  \nnally correct line drawing will be judged as impossible after a little deviation of one or more vertices, causing a 3D reconstruction to fail [10] .  \nRecently, some researchers formulated the 3D reconstruction as an optimization problem based on different objective functions. Marill proposed a criterion, minimizing the standard deviation of the angles (MSDA) in a reconstructed object to emulate human 3D perception of 2D line drawings [11] . This idea is followed by the researchers in [4], [5], [12], [13] . This approach is tolerant of freehand sketching errors, but cannot reconstruct complete 3D objects if their hidden lines are not drawn.  \nThis paper proposes an approach to the 3D reconstruction from line drawings without hidden lines. Compared with the line drawings with hidden lines visible, these line drawings are easier and more natural to draw. In addition, if we want to recover the complete 3D shape of an object inan image, we usually do not have the invisible edges. Our approach mainly consists of two elements: inference of the topology of the hidden part of an object and reconstruction of the complete shape of the object. Fig. 1 shows the two steps with an example.  \nFig. 1: (a) A line drawing without hidden lines. (b) The inferred hidden topological structure. (c) Reconstructed complete 3D object.  \nFor easier understanding of the technical content of our approach, we first summarize the terms that will be used in the rest of the paper. Some of these terms are illustrated with Fig. 2.  \n• Degree. The degree d(v) of a vertex v is the number of edges me","cbCaioYJR04Cotw9","https://ap.wps.com/l/cbCaioYJR04Cotw9","pdf",375447,6,"English","# Abstract\n# Introduction\n## Line drawing interpretation\n## Related work\n## Proposed approach overview\n# Theoretical Inference of the Hidden Topological Structure\n## Assumptions","[{\"question\":\"Why is reconstructing a complete 3D object from a 2D line drawing difficult without hidden lines?\",\"answer\":\"Because the invisible edges and vertices are not provided, many existing methods rely on assumptions or formulations that require hidden-line visibility to recover the full structure.\"},{\"question\":\"What are the two main elements of the proposed method?\",\"answer\":\"The method consists of inferring the topology of the hidden part of the object and reconstructing the complete 3D shape.\"},{\"question\":\"Which geometric and perceptual cues does the reconstruction rely on?\",\"answer\":\"Reconstruction is based on perceptual symmetry and the planarity of the object.\"}]","3D Object Reconstruction from a Single 2D Line Drawing without Hidden Lines - Paper | PDF",15,{"code":4,"msg":81,"data":98},[99,103,107,111,116,120,125,128,133,136,140],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":100,"show_sort_weight":101,"slug":102},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":104,"show_sort_weight":105,"slug":106},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":108,"show_sort_weight":109,"slug":110},"Exam",70,"exam",{"id":112,"doc_module":4,"doc_module_name":25,"category_name":113,"show_sort_weight":114,"slug":115},5,"Comic",60,"comic",{"id":91,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":118,"slug":119},"Technology",50,"technology",{"id":121,"doc_module":4,"doc_module_name":25,"category_name":122,"show_sort_weight":123,"slug":124},7,"Healthcare",40,"healthcare",{"id":85,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":126,"slug":127},30,"research-report",{"id":129,"doc_module":4,"doc_module_name":25,"category_name":130,"show_sort_weight":131,"slug":132},9,"Religion & Spirituality",20,"religion-spirituality",{"id":131,"doc_module":4,"doc_module_name":25,"category_name":134,"show_sort_weight":131,"slug":135},"World Cup","world-cup",{"id":137,"doc_module":4,"doc_module_name":25,"category_name":138,"show_sort_weight":137,"slug":139},10,"Lifestyle","lifestyle",{"id":141,"doc_module":4,"doc_module_name":25,"category_name":142,"show_sort_weight":112,"slug":143},19,"General","general"]