{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,17]],"date-time":"2026-02-17T13:24:25Z","timestamp":1771334665567,"version":"3.50.1"},"reference-count":50,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2019,1,23]],"date-time":"2019-01-23T00:00:00Z","timestamp":1548201600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003787","name":"Natural Science Foundation of Hebei Province","doi-asserted-by":"publisher","award":["F2017205066"],"award-info":[{"award-number":["F2017205066"]}],"id":[{"id":"10.13039\/501100003787","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61802109"],"award-info":[{"award-number":["61802109"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Science Foundation of Hebei Normal University","award":["L2017B06"],"award-info":[{"award-number":["L2017B06"]}]},{"name":"Science Foundation of Hebei Normal University","award":["L2018K02"],"award-info":[{"award-number":["L2018K02"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Face reconstruction is a popular topic in 3D vision system. However, traditional methods often depend on monocular cues, which contain few feature pixels and only use their location information while ignoring a lot of textural information. Furthermore, they are affected by the accuracy of the feature extraction method and occlusion. Here, we propose a novel facial reconstruction framework that accurately extracts the 3D shapes and poses of faces from images captured at multi-views. It extends the traditional method using the monocular bilinear model to the multi-view-based bilinear model by incorporating the feature prior constraint and the texture constraint, which are learned from multi-view images. The feature prior constraint is used as a shape prior to allowing us to estimate accurate 3D facial contours. Furthermore, the texture constraint extracts a high-precision 3D facial shape where traditional methods fail because of their limited number of feature points or the mostly texture-less and texture-repetitive nature of the input images. Meanwhile, it fully explores the implied 3D information of the multi-view images, which also enhances the robustness of the results. Additionally, the proposed method uses only two or more uncalibrated images with an arbitrary baseline, estimating calibration and shape simultaneously. A comparison with the state-of-the-art monocular bilinear model-based method shows that the proposed method has a significantly higher level of accuracy.<\/jats:p>","DOI":"10.3390\/s19030459","type":"journal-article","created":{"date-parts":[[2019,1,24]],"date-time":"2019-01-24T03:52:32Z","timestamp":1548301952000},"page":"459","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Three-Dimensional Face Reconstruction Using Multi-View-Based Bilinear Model"],"prefix":"10.3390","volume":"19","author":[{"given":"Liang","family":"Tian","sequence":"first","affiliation":[{"name":"The Key Laboratory of Augmented Reality, College of Mathematics and Information Science, Hebei Normal University, No.20 Road East, 2nd Ring South, Yuhua District, Shijiazhuang 050024, Hebei, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1444-190X","authenticated-orcid":false,"given":"Jing","family":"Liu","sequence":"additional","affiliation":[{"name":"The Key Laboratory of Augmented Reality, College of Mathematics and Information Science, Hebei Normal University, No.20 Road East, 2nd Ring South, Yuhua District, Shijiazhuang 050024, Hebei, China"}]},{"given":"Wei","family":"Guo","sequence":"additional","affiliation":[{"name":"The Key Laboratory of Augmented Reality, College of Mathematics and Information Science, Hebei Normal University, No.20 Road East, 2nd Ring South, Yuhua District, Shijiazhuang 050024, Hebei, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,1,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1016\/j.jvcir.2017.06.008","article-title":"Wide-angle and long-range real time pose estimation: A comparison between monocular and stereo vision systems","volume":"48","author":"Ferrara","year":"2017","journal-title":"J. Vis. Commun. Image Represent."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"4508","DOI":"10.1109\/JSEN.2017.2703829","article-title":"On the performance of the Intel SR300 depth camera: Metrological and critical characterization","volume":"17","author":"Carfagni","year":"2017","journal-title":"IEEE Sens. J."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"You, Y., Shen, Y., Zhang, G., and Xing, X. (2017). Real-Time and High-Resolution 3D Face Measurement via a Smart Active Optical Sensor. Sensors, 17.","DOI":"10.3390\/s17040734"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"6279","DOI":"10.3390\/s140406279","article-title":"Random-Profiles-Based 3D Face Recognition System","volume":"14","author":"Kim","year":"2014","journal-title":"Sensors"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"19561","DOI":"10.3390\/s141019561","article-title":"A multi-modal face recognition method using complete local derivative patterns and depth maps","volume":"14","author":"Yin","year":"2014","journal-title":"Sensors"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1016\/j.patcog.2013.07.018","article-title":"An efficient 3D face recognition approach using local geometrical signatures","volume":"47","author":"Lei","year":"2014","journal-title":"Pattern Recognit."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1109\/TVCG.2013.249","article-title":"Facewarehouse: A 3d facial expression database for visual computing","volume":"20","author":"Cao","year":"2014","journal-title":"IEEE Trans. Vis. Comput. Gr."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Dong, Y., Wang, Y., Yue, J., and Hu, Z. (2016). Real Time 3D Facial Movement Tracking Using a Monocular Camera. Sensors, 16.","DOI":"10.3390\/s16081157"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"12870","DOI":"10.3390\/s121012870","article-title":"3D face modeling using the multi-deformable method","volume":"12","author":"Hwang","year":"2012","journal-title":"Sensors"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Suwajanakorn, S., Kemelmacher-Shlizerman, I., and Seitz, S.M. (2014, January 6\u201312). Total moving face reconstruction. Proceedings of the European Conference on Computer Vision, Zurich, Switzerland.","DOI":"10.1007\/978-3-319-10593-2_52"},{"key":"ref_11","unstructured":"Liang, S., Kemelmacher-Shlizerman, I., and Shapiro, L.G. (2014, January 8\u201311). 3D face hallucination from a single depth frame. Proceedings of the 2014 2nd IEEE International Conference on 3D Vision (3DV), Tokyo, Japan."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1493","DOI":"10.1109\/TPAMI.2013.235","article-title":"A two-stage framework for 3D facereconstruction from RGBD images","volume":"36","author":"Wang","year":"2014","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_13","unstructured":"Roth, J., Tong, Y., and Liu, X. (July, January 26). Adaptive 3D face reconstruction from unconstrained photo collections. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Las Vegas, NV, USA."},{"key":"ref_14","first-page":"75","article-title":"High-quality passive facial performance capture using anchor frames","volume":"30","author":"Beeler","year":"2011","journal-title":"ACM Trans. Gr. (TOG)"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1561\/0600000007","article-title":"3D reconstruction from multiple images part 1: Principles","volume":"4","author":"Moons","year":"2010","journal-title":"Found. Trends\u00ae Comput. Gr. Vis."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"878","DOI":"10.1109\/TPAMI.2007.70752","article-title":"Nonrigid structure-from-motion: Estimating shape and motion with hierarchical priors","volume":"30","author":"Torresani","year":"2008","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_17","first-page":"28","article-title":"Reconstruction of personalized 3D face rigs from monocular video","volume":"35","author":"Garrido","year":"2016","journal-title":"ACM Trans. Gr. (TOG)"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Sucontphunt, T. (2014). 3D Face Reconstruction from a Single Shaded Image Using Subspace Crossing Engine. Iberoamerican Congress on Pattern Recognition, Springer.","DOI":"10.1007\/978-3-319-12568-8_96"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1109\/TPAMI.2010.63","article-title":"3D face reconstruction from a single image using a single reference face shape","volume":"33","author":"Basri","year":"2011","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Uchida, N., Shibahara, T., Aoki, T., Nakajima, H., and Kobayashi, K. (2005, January 11\u201314). 3D face recognition using passive stereo vision. Proceedings of the IEEE International Conference on Image Processing, ICIP 2005, Genoa, Italy.","DOI":"10.1109\/ICIP.2005.1530214"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"3635","DOI":"10.1007\/s11042-013-1791-3","article-title":"Fast 3D face reconstruction based on uncalibrated photometric stereo","volume":"74","author":"Sun","year":"2015","journal-title":"Multimed. Tools Appl."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Nigam, A., Chhalotre, G., and Gupta, P. (2015, January 16\u201319). Pose and illumination invariant face recognition using binocular stereo 3D reconstruction. Proceedings of the 2015 Fifth National Conference on Computer Vision, Pattern Recognition, Image Processing and Graphicsc, Patna, India.","DOI":"10.1109\/NCVPRIPG.2015.7489941"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/j.cviu.2015.08.012","article-title":"Statistical 3D face shape estimation from occluding contours","volume":"142","author":"Smith","year":"2016","journal-title":"Comput. Vis. Image Underst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1063","DOI":"10.1109\/TPAMI.2003.1227983","article-title":"Face recognition based on fitting a 3D morphable model","volume":"25","author":"Blanz","year":"2003","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"426","DOI":"10.1145\/1073204.1073209","article-title":"Face transfer with multilinear models","volume":"24","author":"Vlasic","year":"2005","journal-title":"ACM Trans. Gr. (TOG)"},{"key":"ref_26","first-page":"130","article-title":"Video face replacement","volume":"30","author":"Dale","year":"2011","journal-title":"ACM Trans. Gr. (TOG)"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Bolkart, T., and Wuhrer, S. (2015, January 7\u201313). A groupwise multilinear correspondence optimization for 3d faces. Proceedings of the IEEE International Conference on Computer Vision, Santiago, Chile.","DOI":"10.1109\/ICCV.2015.411"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Zollh\u00f6fer, M., Thies, J., Garrido, P., Bradley, D., Beeler, T., P\u00e9rez, P., Stamminger, M., Nie\u00dfner, M., and Theobalt, C. (2018, January 8). State of the Art on Monocular 3D Face Reconstruction, Tracking, and Applications. Proceedings of the Computer Graphics Forum, Brno, Czech Republic.","DOI":"10.1111\/cgf.13382"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Moeini, A., Moeini, H., and Faez, K. (2014, January 24\u201328). Expression-invariant face recognition via 3D face reconstruction using Gabor filter bank from a 2D single image. Proceedings of the 2014 22nd International Conference on Pattern Recognition (ICPR), Stockholm, Sweden.","DOI":"10.1109\/ICPR.2014.805"},{"key":"ref_30","unstructured":"Piotraschke, M., and Blanz, V. (July, January 26). Automated 3d face reconstruction from multiple images using quality measures. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Las Vegas, NV, USA."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Zhu, X., Yi, D., Lei, Z., and Li, S.Z. (2014, January 24\u201328). Robust 3d morphable model fitting by sparse sift flow. Proceedings of the 2014 22nd International Conference on Pattern Recognition (ICPR), Stockholm, Sweden.","DOI":"10.1109\/ICPR.2014.693"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"11469","DOI":"10.1007\/s11042-015-2864-2","article-title":"Self-adaptive morphable model based collaborative multi-view 3D face reconstruction in visual sensor network","volume":"75","author":"Lin","year":"2016","journal-title":"Multimed. Tools Appl."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Booth, J., Antonakos, E., Ploumpis, S., Trigeorgis, G., Panagakis, Y., and Zafeiriou, S. (2017, January 21\u201326). 3D face morphable models in-the-wild. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Honolulu, HI, USA.","DOI":"10.1109\/CVPR.2017.580"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Tran, A.T., Hassner, T., Masi, I., and Medioni, G. (2017, January 21\u201326). Regressing robust and discriminative 3D morphable models with a very deep neural network. Proceedings of the 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Honolulu, HI, USA.","DOI":"10.1109\/CVPR.2017.163"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Tran, L., and Liu, X. (arXiv, 2018). On Learning 3D Face Morphable Model from In-the-wild Images, arXiv.","DOI":"10.1109\/CVPR.2018.00767"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1111\/cgf.13127","article-title":"Multi-View Stereo on Consistent Face Topology","volume":"36","author":"Fyffe","year":"2017","journal-title":"Comp. Graph. Forum."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"939","DOI":"10.1007\/s11042-016-4325-y","article-title":"Coarse-to-fine multiview 3D face reconstruction using multiple geometrical features","volume":"77","author":"Dai","year":"2018","journal-title":"Multimed. Tools Appl."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Kazemi, V., and Sullivan, J. (2014, January 23\u201328). One millisecond face alignment with an ensemble of regression trees. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Columbus, OH, USA.","DOI":"10.1109\/CVPR.2014.241"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.cag.2014.01.002","article-title":"Parallel L-BFGS-B algorithm on gpu","volume":"40","author":"Fei","year":"2014","journal-title":"Comput. Gr."},{"key":"ref_40","unstructured":"ESRC (2013, August 11). Image Database. Available online: http:\/\/pics.psych.stir.ac.uk\/ESRC\/."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Thies, J., Zollh\u00f6fer, M., Stamminger, M., Theobalt, C., and Nie\u00dfner, M. (2016, January 24\u201328). Demo of Face2Face: Real-time face capture and reenactment of RGB videos. Proceedings of the ACM SIGGRAPH 2016 Emerging Technologies, Anaheim, CA, USA.","DOI":"10.1145\/2929464.2929475"},{"key":"ref_42","first-page":"222","article-title":"Automatic acquisition of high-fidelity facial performances using monocular videos","volume":"33","author":"Shi","year":"2014","journal-title":"ACM Trans. Gr. (TOG)"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/j.cag.2017.05.008","article-title":"Accurate 3D Face Reconstruction via Prior Constrained Structure from Motion","volume":"66","author":"Hernandez","year":"2017","journal-title":"Comput. Gr."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Aissaoui, A., Martinet, J., and Djeraba, C. (October, January 30). 3D face reconstruction in a binocular passive stereoscopic system using face properties. Proceedings of the 2012 19th IEEE International Conference on Image Processing (ICIP), Orlando, FL, USA.","DOI":"10.1109\/ICIP.2012.6467228"},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Fransens, R., Strecha, C., and Van Gool, L. (2005, January 16). Parametric stereo for multi-pose face recognition and 3D-face modeling. Proceedings of the International Workshop on Analysis and Modeling of Faces and Gestures, Beijing, China.","DOI":"10.1007\/11564386_10"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1977","DOI":"10.1109\/JPROC.2006.886019","article-title":"Face recognition using 3-D models: Pose and illumination","volume":"94","author":"Romdhani","year":"2006","journal-title":"Proc. IEEE"},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Chang, F.J., Tran, A.T., Hassner, T., Masi, I., Nevatia, R., and Medioni, G. (2018, January 15\u201319). ExpNet: Landmark-free, deep, 3D facial expressions. Proceedings of the 2018 13th IEEE International Conference on Automatic Face & Gesture Recognition (FG 2018), Xi\u2019an, China.","DOI":"10.1109\/FG.2018.00027"},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Feng, Y., Wu, F., Shao, X., Wang, Y., and Zhou, X. (arXiv, 2018). Joint 3D Face Reconstruction and Dense Alignment with Position Map Regression Network, arXiv.","DOI":"10.1007\/978-3-030-01264-9_33"},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Jackson, A.S., Bulat, A., Argyriou, V., and Tzimiropoulos, G. (2017, January 22\u201329). Large pose 3D face reconstruction from a single image via direct volumetric CNN regression. Proceedings of the 2017 IEEE International Conference on Computer Vision (ICCV), Venice, Italy.","DOI":"10.1109\/ICCV.2017.117"},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Dou, P., Shah, S.K., and Kakadiaris, I.A. (2017, January 21\u201326). End-to-end 3D face reconstruction with deep neural networks. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Honolulu, HI, USA.","DOI":"10.1109\/CVPR.2017.164"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/3\/459\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:28:09Z","timestamp":1760185689000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/3\/459"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,23]]},"references-count":50,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2019,2]]}},"alternative-id":["s19030459"],"URL":"https:\/\/doi.org\/10.3390\/s19030459","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1,23]]}}}