最优传输理论及其在图像处理中的应用

A review of optimal transport in image processing∗
MA Litao1,2 BIAN Wei2,†
Abstract The optimal transport problem which has attracted wide attentions in many fields in recent years, is a special kind of optimization problem discussed in the probabilistic measure space. In order to overcome the disadvantages of traditional optimal transport models, such as complex computation and lack of regularity, many different kinds of improved optimal transport models and algorithms are proposed to deal with various practical problems. Firstly, this paper briefly describes the basic theory and methods of optimal transport, and further introduces the concept of Wasserstein distance and Wasserstein barycenters. And then, the discrete optimal transport model and the improved regularization models are discussed. Besides, a short summary of the algorithms to solve optimal transport problem is given. Then, from Wasserstein distance aspect, a review of applications in several areas of image processing is briefly discussed. At last, the further research work is prospected.
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ÂvFÏ: 2019-03-31 * Ä7‘8: I[g,‰ÆÄ7¡þ‘8(Nos. 11871178, 61773136) 1. à ó§ŒÆên‰Æ†ó§Æ §à ·ý 056038; School of Mathematics and Physics, Hebei University of Engineering, Handan 056038, Hebei, China 2. M Tó’ŒÆêÆÆ , M T 150001; School of Mathematics, Harbin Institute of Technology, Harbin 150001, China † Ï&Šö E-mail: bianweilvse520@163.com
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2010 êÆ©aÒ 90C30§90C08
Keywords optimal transport, image processing, regularization, Wasserstein distance
Chinese Library Classification O29§O224 2010 Mathematics Subject Classification 90C30§90C08
2019c9 Sept., 2019
பைடு நூலகம்
$ÊÆÆ Operations Research Transactions
DOI: 10.15960/j.cnki.issn.1007-6093.2019.03.008
123ò 13Ï Vol.23 No.3
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