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Recent approaches are either data-driven or learning-based: Data-driven approaches rely on a shape model whose parameters are optimized to fit the observations; Learning-based approaches, in contrast, avoid the expensive optimization step by learning to directly predict complete shapes from incomplete observations in a fully-supervised setting. However, full supervision is often not available in practice. In this work, we propose a weakly-supervised learning-based approach to 3D shape completion which neither requires slow optimization nor direct supervision. While we also learn a shape prior on synthetic data, we amortize, i.e.,<jats:italic>learn<\/jats:italic>, maximum likelihood fitting using deep neural networks resulting in efficient shape completion without sacrificing accuracy. On synthetic benchmarks based on ShapeNet (Chang et\u00a0al.\u00a0Shapenet: an information-rich 3d model repository, 2015.<jats:ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"http:\/\/arxiv.org\/abs\/1512.03012\" ext-link-type=\"uri\">arXiv:1512.03012<\/jats:ext-link>) and ModelNet (Wu et\u00a0al., in: Proceedings of IEEE conference on computer vision and pattern recognition (CVPR), 2015) as well as on real robotics data from KITTI (Geiger et al., in: Proceedings of IEEE conference on computer vision and pattern recognition (CVPR), 2012) and Kinect (Yang et\u00a0al., 3d object dense reconstruction from a single depth view, 2018.<jats:ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"http:\/\/arxiv.org\/abs\/1802.00411\" ext-link-type=\"uri\">arXiv:1802.00411<\/jats:ext-link>), we demonstrate that the proposed amortized maximum likelihood approach is able to compete with the fully supervised baseline of Dai et\u00a0al. (in: Proceedings of IEEE conference on computer vision and pattern recognition (CVPR), 2017) and outperforms the data-driven approach of Engelmann et\u00a0al.\u00a0(in: Proceedings of the German conference on pattern recognition (GCPR), 2016), while requiring less supervision and being significantly faster.<\/jats:p>","DOI":"10.1007\/s11263-018-1126-y","type":"journal-article","created":{"date-parts":[[2018,10,29]],"date-time":"2018-10-29T07:02:01Z","timestamp":1540796521000},"page":"1162-1181","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":72,"title":["Learning 3D Shape Completion Under Weak Supervision"],"prefix":"10.1007","volume":"128","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6286-1805","authenticated-orcid":false,"given":"David","family":"Stutz","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andreas","family":"Geiger","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2018,10,29]]},"reference":[{"key":"1126_CR1","volume-title":"Handbook of mathematical functions, with formulas, graphs, and mathematical tables","author":"M Abramowitz","year":"1974","unstructured":"Abramowitz, M. 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