[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84487-en":3,"doc-seo-84487-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},84487,549758146520,"Patrick","https://ap-avatar.wpscdn.com/avatar/80002397d8c0411e94?_k=1775819394049821470",8,"Research & Report","TriP: A Triangle Puzzle Approach to Robust Translation Averaging","Translation averaging recovers camera locations from pairwise relative translation directions, serving as a key component in global Structure-from-Motion pipelines. Direction-only measurements are highly ill-conditioned because they lack distance information and can be corrupted by mismatched correspondences, RANSAC failures, and error propagation. TriP introduces a triangle-based framework that infers local edge scales from triangle geometry, then synchronizes overlapping triangle scales in the logarithmic domain for globally consistent edge lengths and camera locations. By exploiting higher-order triangle consistency, TriP is robust to structured, cycle-consistent corruptions, avoids collapse by construction via log-scale synchronization, and provides strong exact-recovery theory while remaining parallelizable, efficient, and scalable to graphs with millions of cameras, outperforming prior methods on synthetic and real data.","arXiv :2605 .07143v2 [ cs .CV] 12 Jul 2026  \nTriP: A Triangle Puzzle Approach to Robust Translation Averaging  \nZhekai Fan 1 ∗ Wanze Li2 ∗ Jinxin Wang2 Yunpeng Shi 1  \n1 UC Davis 2 University of Chicago  \n[zkfan@ucdavis.edu](zkfan@ucdavis.edu) [wanzeli@uchicago.edu](wanzeli@uchicago.edu) [wangjinxin68@gmail.com](wangjinxin68@gmail.com) [ypshi@ucdavis.edu](ypshi@ucdavis.edu)  \nAbstract  \nTranslation averaging aims to recover camera locations from pairwise relative translation directions and is a fundamental component of global Structure-from-Motion pipelines. The problem is challenging because direction measurements contain no distance information, making the estimation problem highly ill-conditioned and highly sensitive to corrupted observations. In this paper, we propose TriP, a triangle-based framework for robust translation averaging. TriP first infers local relative edge scales from triangle geometry, and then synchronizes the scales of overlapping triangles in the logarithmic domain to recover globally consistent edge lengths and camera locations. By leveraging higher-order consistency across triangles, the proposed method is robust to adversarial, cycle-consistent, and other structured corruptions. In addition, TriP avoids the collapse issue without requiring any extra anti-collapse constraints, since log-scale synchronization excludes the degenerate zero-scale solution by construction. These structural advantages enable a particularly strong theory for exact location recovery. On the practical side, TriP is fully parallelizable, computationally efficient, and naturally scalable to graphs with millions of cameras. Moreover, it outperforms all previous translation averaging methods by a large margin on both synthetic and real datasets.  \n1 Introduction  \nStructure-from-Motion (SfM) [17] is a fundamental problem in 3D vision that aims to recover camera poses and scene structure from a collection of 2D images. Given multiple images of the same scene, SfM typically establishes feature correspondences across images and estimates pairwise geometric relationships between cameras. A central step in this pipeline is global camera pose estimation, namely recovering camera rotations and camera locations from noisy pairwise measurements.  \nIn this work, we focus on camera location estimation from pairwise relative translation directions, also known as translation averaging (TA) . Mathematically, TA solves the following problem: given a viewing graph G = ([n], E), where each node i ∈ [n] = {1, 2 , 3 ,..., n} is assigned underlying camera location x∗i ∈ R3 . Here, we use star superscript to emphasize the ground truth. In this graph, each edge (i, j) ∈ E is associated with a relative direction measurement dij, whose clean counterpart is d∗ij = (x∗i − x∗j)/∥x∗i − x∗j∥ . The goal of TA is to recover the unknown camera locations {x∗1} i∈[n] from these possibly noisy and corrupted direction measurements {dij}(i,j)∈E . Since these relative measurements contain no distance information, the camera locations can only be determined up toa global translation and scaling. If reliable relative scales were also available, the problem would become significantly easier and closer in spirit to a synchronization problem over translations [10] . In practice, however, relative direction measurements are often severely corrupted due to mismatched  \nfeature correspondences, RANSAC [2] failures, and error propagation from earlier stages, especially ∗ Equal contribution.  \nrotation estimation [6, 21 , 14] . In real data, these corrupted directions can be self-consistent [23, 16], typically due to symmetry and repetitive patterns ([e.g. windows](e.g. windows) on a building) in a 3D scene.  \nThe adverse effects of structured corruption can be mitigated by robust formulations, commonly written as  \nmin {xi} i∈[n], {ℓij}(i,j)∈E  \nX ρ (∥xi − xj − ℓijdij∥) ,(i,j)∈E  \n(1)  \nwhere ρ is a user-specified robust loss function. However, without suitable constraints on t","cbCaiowATU6zGcjA","https://ap.wps.com/l/cbCaiowATU6zGcjA","pdf",1680971,1,68,"English","en",105,"# Introduction\n## Related work","[{\"question\":\"What problem does TriP address?\",\"answer\":\"TriP addresses translation averaging: recovering camera locations from noisy pairwise relative translation direction measurements used in global Structure-from-Motion pipelines.\"},{\"question\":\"Why is translation averaging difficult with direction-only measurements?\",\"answer\":\"Because direction measurements contain no distance information, the estimation is highly ill-conditioned and sensitive to corrupted observations.\"},{\"question\":\"How does TriP achieve robustness and avoid degenerate collapse solutions?\",\"answer\":\"TriP infers local edge scales from triangle geometry and synchronizes scales across overlapping triangles in the logarithmic domain. Log-scale synchronization excludes the degenerate zero-scale solution by construction, while higher-order consistency across triangles improves robustness to structured corruptions.\"}]",1784195984,171,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":27},"trip-a-triangle-puzzle-approach-to-robust-translation-averaging","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/trip-a-triangle-puzzle-approach-to-robust-translation-averaging/84487/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What problem does TriP address?","Question",{"text":75,"@type":76},"TriP addresses translation averaging: recovering camera locations from noisy pairwise relative translation direction measurements used in global Structure-from-Motion pipelines.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Why is translation averaging difficult with direction-only measurements?",{"text":80,"@type":76},"Because direction measurements contain no distance information, the estimation is highly ill-conditioned and sensitive to corrupted observations.",{"name":82,"@type":73,"acceptedAnswer":83},"How does TriP achieve robustness and avoid degenerate collapse solutions?",{"text":84,"@type":76},"TriP infers local edge scales from triangle geometry and synchronizes scales across overlapping triangles in the logarithmic domain. Log-scale synchronization excludes the degenerate zero-scale solution by construction, while higher-order consistency across triangles improves robustness to structured corruptions.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":45,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":45,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":45,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":45,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":45,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":45,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":45,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]