{"title":"基于缺失数据的三维结构恢复分解","authors":"Rui F. C. Guerreiro, P. Aguiar","doi":"10.1109/MMSP.2002.1203259","DOIUrl":null,"url":null,"abstract":"Matrix factorization methods are now widely used to recover 3D structure from 2D projections [C. Tomasi and T. Kanade. International Journal of Computer Vision, 9(2), 1992] . In this practice, the observation matrix to be factored out has missing data, due to the limited field of view and the occlusion that occur in real video sequences. In opposition to the optimality of the SVD to factor out matrices without missing entries, the optimal solution for the missing data case is not known. In R.F.C. Guerreiro and P.M.Q. Aguiar [IEEE ICIP, New York, USA, September 2002] we introduced suboptimal algorithms that proved to be more efficient than previous approaches to the factorization of matrices with missing data. In this paper we make an experimental analysis of the algorithms of R.F.C. Guerreiro and P.M.Q. Aguiar [IEEE ICIP, New York, USA, September 2002] and demonstrate their performance in virtual reality and video compression applications. We conclude that these algorithms are adequate to the amount of missing entries that may occur when processing real videos; robust to the typical level of noise in practical applications; and computationally as simple as the factorization of matrices without missing entries.","PeriodicalId":398813,"journal":{"name":"2002 IEEE Workshop on Multimedia Signal Processing.","volume":"3 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2002-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"12","resultStr":"{\"title\":\"Factorization with missing data for 3D structure recovery\",\"authors\":\"Rui F. C. Guerreiro, P. Aguiar\",\"doi\":\"10.1109/MMSP.2002.1203259\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Matrix factorization methods are now widely used to recover 3D structure from 2D projections [C. Tomasi and T. Kanade. International Journal of Computer Vision, 9(2), 1992] . In this practice, the observation matrix to be factored out has missing data, due to the limited field of view and the occlusion that occur in real video sequences. In opposition to the optimality of the SVD to factor out matrices without missing entries, the optimal solution for the missing data case is not known. In R.F.C. Guerreiro and P.M.Q. Aguiar [IEEE ICIP, New York, USA, September 2002] we introduced suboptimal algorithms that proved to be more efficient than previous approaches to the factorization of matrices with missing data. In this paper we make an experimental analysis of the algorithms of R.F.C. Guerreiro and P.M.Q. Aguiar [IEEE ICIP, New York, USA, September 2002] and demonstrate their performance in virtual reality and video compression applications. We conclude that these algorithms are adequate to the amount of missing entries that may occur when processing real videos; robust to the typical level of noise in practical applications; and computationally as simple as the factorization of matrices without missing entries.\",\"PeriodicalId\":398813,\"journal\":{\"name\":\"2002 IEEE Workshop on Multimedia Signal Processing.\",\"volume\":\"3 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2002-12-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"12\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2002 IEEE Workshop on Multimedia Signal Processing.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/MMSP.2002.1203259\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2002 IEEE Workshop on Multimedia Signal Processing.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/MMSP.2002.1203259","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 12
摘要
矩阵分解方法目前广泛用于从二维投影中恢复三维结构[C]。Tomasi和T. Kanade。国际计算机视觉学报,9(2),1992]。在这种实践中,由于有限的视场和真实视频序列中发生的遮挡,待分解的观测矩阵存在缺失数据。与SVD分解出没有缺失条目的矩阵的最优性相反,缺失数据情况的最优解是未知的。在R.F.C. Guerreiro和P.M.Q. Aguiar [IEEE ICIP, New York, USA, 2002年9月]中,我们介绍了次优算法,该算法被证明比以前的方法更有效地分解具有缺失数据的矩阵。本文对R.F.C. Guerreiro和P.M.Q. Aguiar [IEEE ICIP, New York, USA, September 2002]的算法进行了实验分析,并展示了它们在虚拟现实和视频压缩应用中的性能。我们得出的结论是,这些算法足以处理真实视频时可能出现的缺失条目的数量;在实际应用中对典型的噪声水平具有鲁棒性;计算上和矩阵的分解一样简单,没有缺失的元素。
Factorization with missing data for 3D structure recovery
Matrix factorization methods are now widely used to recover 3D structure from 2D projections [C. Tomasi and T. Kanade. International Journal of Computer Vision, 9(2), 1992] . In this practice, the observation matrix to be factored out has missing data, due to the limited field of view and the occlusion that occur in real video sequences. In opposition to the optimality of the SVD to factor out matrices without missing entries, the optimal solution for the missing data case is not known. In R.F.C. Guerreiro and P.M.Q. Aguiar [IEEE ICIP, New York, USA, September 2002] we introduced suboptimal algorithms that proved to be more efficient than previous approaches to the factorization of matrices with missing data. In this paper we make an experimental analysis of the algorithms of R.F.C. Guerreiro and P.M.Q. Aguiar [IEEE ICIP, New York, USA, September 2002] and demonstrate their performance in virtual reality and video compression applications. We conclude that these algorithms are adequate to the amount of missing entries that may occur when processing real videos; robust to the typical level of noise in practical applications; and computationally as simple as the factorization of matrices without missing entries.