[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83251-en":3,"doc-seo-83251-105":30,"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":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},83251,962075114101,"Seraphina","https://ap-avatar.wpscdn.com/avatar/e000253a75eb197efd?x-image-process=image/resize,m_fixed,w_180,h_180&k=1780044092746381165",8,"Research & Report","Discovering Geometric Biases in 3D Face Reconstruction","3D Morphable Models (3DMMs) remain the default parametric priors for 3D face reconstruction, yet their dependence on limited training samples introduces morphological biases that can hinder generalization across global populations. This work proposes a curvature-aware spectral framework to discover, quantify, and visualize reconstruction biases using Laplace-Beltrami-based curvature error maps. A derived error metric is validated via a user study and shows stronger alignment with human perception than Euclidean metrics. Extensive experiments reveal systematic age-related biases and preliminary evidence for gender and ethnicity effects.","arXiv :2607 .07486v 1 [ cs .CV] 8 Jul 2026  \nDiscovering Geometric Biases in 3D Face Reconstruction: A Curvature-Aware Spectral Framework for Fairness Evaluation  \nVeronika Shilova 1 ,2 , Emmanuel Malherbe 1 , Giovanni Palma3 , Panagiotis-Alexandros Bokaris3 , Laurent Risser2 , and Jean-Michel Loubes2 ,4 ,5  \n1 Artefact Research Center, Paris, France  \n2 Institut de Mathématique de Toulouse, CNRS, Toulouse, France  \n3 L’Oréal Recherche et Innovation, Paris, France  \n4 Université de Toulouse, ANITI, Toulouse, France  \n5 INRIA Regalia, Bordeaux, France  \nAbstract. 3D Morphable Models (3DMMs) remain the standard parametric shape priors for many state-of-the-art 3D face reconstruction algorithms. However, as these models are derived from a finite number of 3D face samples, they inherit the morphological biases of their training data, potentially limiting their generalizability across diverse global populations. In this paper, we propose a novel framework to analyze 3DMM reconstructions through the lens of surface curvature, with the objective to discover, quantify and visualize biases. While standard evaluation metrics often rely on Euclidean distances, our reconstruction error captures subtle surface nuances such as local topology or undulations.  \nTo do so, we leverage the Laplace-Beltrami Operator (LBO) to generate high-resolution curvature error maps, providing a localized and geometrically meaningful visualization of discrepancies between ground truth faces and reconstructed meshes. We derive from it an error metric that we validated through a user study, observing a significantly higher correlation to human perception compared to traditional methods. Furthermore, we conduct extensive experiments across several 3DMM bases and fitting algorithms, uncovering systematic age-related biases and providing preliminary evidence of biases associated with gender and ethnicity.  \nOur findings highlight the necessity of adopting curvature-aware evaluation protocols to ensure demographic fairness and geometric precision in future 3D face reconstruction research. The code and annotation data are available at [https://github.com/artefactory/3dface-fairness](https://github.com/artefactory/3dface-fairness).  \nKeywords: Fairness · 3D Face Reconstruction · Computer Vision  \n1 Introduction  \nThe field of 3D face reconstruction from images has become important in computer vision, as it makes it possible to compute accurate representations of the human facial morphology, with many applications such as in the field of cinema  \n2 V. Shilova et al.  \nFig. 1: Overview of our curvature-aware evaluation framework for bias discovery. Given a ground truth scan and its corresponding 3D reconstruction, we perform an anatomical segmentation of the reconstructed mesh. We compute Curvature-Based Error Maps using the Laplace-Beltrami Operator to isolate localized geometric discrepancies that Euclidean metrics often overlook. By performing spectral clustering on these error maps, we identify distinct failure modes and correlate them with demographic factors.  \n[17], virtual reality [24,36], cosmetics [39], biometric security [21] or medicine [27] . An underlying component of any face reconstruction is the parametrization of the 3D shapes, for which 3D Morphable Models (3DMM) [5] have established themselves as fundamental parametric shape priors for 3D face reconstruction [13] .  \nThe 3DMM formalism is based on two fundamental assumptions. First, it establishes a dense, point-to-point correspondence across registered face scansin its database. This shared topology allows for the generation of anatomically plausible identities through linear combinations of basis shapes. Second, the model explicitly disentangles facial shape and texture, and separates them from extrinsic scene parameters, such as illumination and camera parameters. The classic 3DMM formulation decomposes facial geometry and texture using Principal Component Analysis (PCA) bases derived on a finite","cbCaiofG72ZntQW0","https://ap.wps.com/l/cbCaiofG72ZntQW0","pdf",4520688,3,1,18,"English","en",105,"# Introduction\n## Curvature-Aware Evaluation Framework\n## Perceptual Validation\n## Systematic Bias Discovery","[{\"question\":\"Why can 3D Morphable Models produce demographic bias in 3D face reconstruction?\",\"answer\":\"3DMMs are built from a finite set of 3D face samples, so they inherit morphological biases from training data. This can yield poor performance on specific demographic categories such as age, gender, or geographical origin.\"},{\"question\":\"What role does the Laplace-Beltrami Operator play in the proposed fairness evaluation?\",\"answer\":\"The method uses the Laplace-Beltrami Operator to generate high-resolution curvature error maps, providing a localized and geometrically meaningful visualization of discrepancies between ground truth faces and reconstructed meshes.\"},{\"question\":\"How is the curvature-aware error metric validated, and what does it improve over?\",\"answer\":\"The paper derives an error metric from the curvature error maps and validates it through a user study. The results show a significantly higher correlation with human perception compared with traditional Euclidean-based evaluation approaches.\"}]",1784186265,45,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"discovering-geometric-biases-in-3d-face-reconstruction","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":20},"https://docshare.wps.com/document/research-report/",{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/discovering-geometric-biases-in-3d-face-reconstruction/83251/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-24","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},"Why can 3D Morphable Models produce demographic bias in 3D face reconstruction?","Question",{"text":75,"@type":76},"3DMMs are built from a finite set of 3D face samples, so they inherit morphological biases from training data. This can yield poor performance on specific demographic categories such as age, gender, or geographical origin.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What role does the Laplace-Beltrami Operator play in the proposed fairness evaluation?",{"text":80,"@type":76},"The method uses the Laplace-Beltrami Operator to generate high-resolution curvature error maps, providing a localized and geometrically meaningful visualization of discrepancies between ground truth faces and reconstructed meshes.",{"name":82,"@type":73,"acceptedAnswer":83},"How is the curvature-aware error metric validated, and what does it improve over?",{"text":84,"@type":76},"The paper derives an error metric from the curvature error maps and validates it through a user study. The results show a significantly higher correlation with human perception compared with traditional Euclidean-based evaluation approaches.","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":25},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]