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Portraying the religious activities of the Northern Wei imperial family, these reliefs hold substantial historical and artistic values. However, the reliefs have suffered severe damage because of both natural and human-induced factors. Although initial restoration efforts have taken place in museums, a considerable portion remains irrecoverable, with the facial features of the figures presenting the most formidable challenge for reconstruction. The precise and objective restoration of the missing facial portion in the reliefs is crucial. Although facial 3D reconstruction techniques from a single photograph exist, their stability and accuracy under complex imaging conditions often lack practical requirements. To enhance portrait relief restoration, we propose a method based on the Gaussian process model. Our approach leverages the surviving samples to learn prior shape knowledge, thereby establishing a Gaussian process model. Subsequently, observations from historical photographs and surviving fragments were used as input data to predict the damaged shape. Experimental validation via cross validation confirms the high precision and robustness of the proposed method.<\/jats:p>","DOI":"10.1145\/3717072","type":"journal-article","created":{"date-parts":[[2025,2,19]],"date-time":"2025-02-19T17:21:31Z","timestamp":1739985691000},"page":"1-22","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Automated Restoration of Portrait Reliefs in the Binyang Central Cave of the Longmen Grottoes"],"prefix":"10.1145","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6318-0649","authenticated-orcid":false,"given":"Qiang","family":"Chen","sequence":"first","affiliation":[{"name":"Art Department, Xi\u2019an Jiaotong University, Xi\u2019an, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8631-120X","authenticated-orcid":false,"given":"Tian-Ning","family":"Chen","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Manufacturing Systems Engineering, Xi\u2019an Jiaotong University, Xi\u2019an, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-1569-8153","authenticated-orcid":false,"given":"Wei-Cheng","family":"Lin","sequence":"additional","affiliation":[{"name":"Department of Art History, The University of Chicago, Chicago, Illinois, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-6604-9604","authenticated-orcid":false,"given":"Zhen-Yu","family":"Ou-Yang","sequence":"additional","affiliation":[{"name":"Art Department, Xi\u2019an Jiaotong University, Xi\u2019an, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-1331-6892","authenticated-orcid":false,"given":"Xiao-Yi","family":"Wang","sequence":"additional","affiliation":[{"name":"Art Department, Xi\u2019an Jiaotong University, Xi\u2019an, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2025,4,19]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.3390\/heritage6100357"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2007.383165"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.culher.2012.06.008"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2014.2377712"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.1109\/34.121791"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.1109\/34.24792"},{"key":"e_1_3_2_8_2","doi-asserted-by":"publisher","DOI":"10.1109\/ICCV.2017.116"},{"key":"e_1_3_2_9_2","doi-asserted-by":"crossref","unstructured":"Edouard Chavannes. 1909. 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