CLC number: O242; TP391
On-line Access: 2021-09-10
Received: 2020-05-25
Revision Accepted: 2020-09-27
Crosschecked: 2021-08-19
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Yingshi Wang, Xiaopeng Zheng, Wei Chen, Xin Qi, Yuxue Ren, Na Lei, Xianfeng Gu. Robust and accurate optimal transportation map by self-adaptive sampling[J]. Frontiers of Information Technology & Electronic Engineering,in press.https://doi.org/10.1631/FITEE.2000250 @article{title="Robust and accurate optimal transportation map by self-adaptive sampling", %0 Journal Article TY - JOUR
基于自适应采样的鲁棒精确最优传输映射1内蒙古财经大学计算机系,中国呼和浩特市,010010 2大连理工大学软件学院,中国大连市,116620 3首都师范大学北京成像理论与技术高精尖创新中心,中国北京市,100048 4石溪大学计算机系,美国纽约州石溪镇,11794 摘要:最优传输在工程、医疗等各领域扮演着重要角色,包括图形学中的曲面参数化、计算机视觉中的注册、深度学习中的生成模型等。对于平方距离传输成本,最优传输映射是Brenier势的梯度,可通过求解Monge-Ampère方程得到。此外,最优传输映射可归结为几何凸优化问题。Monge-Ampère方程高度非线性,在求解过程中,中间解需要始终保持严格凸。特别地,离散解的精确性严重依赖于目标测度的采样。因此,提出一种自适应采样算法,极大减少采样偏差,同时提高离散解的精确性和鲁棒性。实验结果验证了所提算法的有效性和高效性。 关键词组: Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article
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