{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/nonlinear-3d-face-morphable-model","title":"Nonlinear 3D Face Morphable Model","arxiv_id":"1804.03786","date":"2018-04-11","proceeding":"CVPR 2018 6","authors":["Luan Tran","Xiaoming Liu"],"abstract":"As a classic statistical model of 3D facial shape and texture, 3D Morphable\nModel (3DMM) is widely used in facial analysis, e.g., model fitting, image\nsynthesis. Conventional 3DMM is learned from a set of well-controlled 2D face\nimages with associated 3D face scans, and represented by two sets of PCA basis\nfunctions. Due to the type and amount of training data, as well as the linear\nbases, the representation power of 3DMM can be limited. To address these\nproblems, this paper proposes an innovative framework to learn a nonlinear 3DMM\nmodel from a large set of unconstrained face images, without collecting 3D face\nscans. Specifically, given a face image as input, a network encoder estimates\nthe projection, shape and texture parameters. Two decoders serve as the\nnonlinear 3DMM to map from the shape and texture parameters to the 3D shape and\ntexture, respectively. With the projection parameter, 3D shape, and texture, a\nnovel analytically-differentiable rendering layer is designed to reconstruct\nthe original input face. The entire network is end-to-end trainable with only\nweak supervision. We demonstrate the superior representation power of our\nnonlinear 3DMM over its linear counterpart, and its contribution to face\nalignment and 3D reconstruction.","url_abs":"http://arxiv.org/abs/1804.03786v3","url_pdf":"http://arxiv.org/pdf/1804.03786v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"nonlinear-3d-face-morphable-model","repo_url":"https://github.com/tranluan/Nonlinear_Face_3DMM","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"tf","reach":{"status":"ok","spdx":"Apache-2.0"}}],"tasks":[{"task_slug":"3d-reconstruction","task_name":"3D Reconstruction"},{"task_slug":"face-alignment","task_name":"Face Alignment"},{"task_slug":"image-generation","task_name":"Image Generation"},{"task_slug":"model","task_name":"model"}],"methods":[{"method_slug":"pca","method_name":"PCA"}],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/face-alignment-on-aflw2000","task":"Face Alignment","dataset":"AFLW2000","model":"Nonlinear 3D Face Morphable Model","rank_in_archive_order":2,"of":5,"metrics":{"Error rate":"4.70"},"uses_additional_data":false}],"syntology":{"syntology_url":"https://syntology.ai/paper/1804.03786","atlas_url":"https://app.syntology.ai/?focus=1804.03786","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}