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Prior work has focused on computing efficient maps between pairs of shapes, and has shown a quantifiable benefit of joint map synchronization, where a collection of shapes are used to improve (denoise) the pairwise maps for consistency and correctness. However, these existing map synchronization techniques place very strong assumptions on the input shapes collection such as all the input shapes fall into the same category and\/or the majority of the input pairwise maps are correct. In this paper, we present a multiple map synchronization approach that takes a heterogeneous shape collection as input and simultaneously outputs consistent dense pairwise shape maps. We achieve our goal by using a novel tensor-based representation for map synchronization, which is efficient and robust than all prior matrix-based representations. We demonstrate the usefulness of this approach across a wide range of geometric shape datasets and the applications in shape clustering and shape co-segmentation.<\/jats:p>","DOI":"10.1145\/3306346.3322944","type":"journal-article","created":{"date-parts":[[2019,7,12]],"date-time":"2019-07-12T19:04:08Z","timestamp":1562958248000},"page":"1-18","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":8,"title":["Tensor maps for synchronizing heterogeneous shape collections"],"prefix":"10.1145","volume":"38","author":[{"given":"Qixing","family":"Huang","sequence":"first","affiliation":[{"name":"The University of Texas at Austin"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhenxiao","family":"Liang","sequence":"additional","affiliation":[{"name":"The University of Texas at Austin"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haoyun","family":"Wang","sequence":"additional","affiliation":[{"name":"Tsinghua University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Simiao","family":"Zuo","sequence":"additional","affiliation":[{"name":"The University of Texas at Austin"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chandrajit","family":"Bajaj","sequence":"additional","affiliation":[{"name":"The University of Texas at Austin"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2019,7,12]]},"reference":[{"key":"e_1_2_2_1_1","first-page":"1","article-title":"Tensor Decompositions for Learning Latent Variable Models","volume":"15","author":"Anandkumar Animashree","year":"2014","journal-title":"J. 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