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CLC number: O242; TP391
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
Crosschecked: 2021-08-19
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Robust and accurate optimal transportation map by self-adaptive sampling
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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, 2021, 22(9): 1207-1220.
@article{title="Robust and accurate optimal transportation map by self-adaptive sampling",
author="Yingshi Wang, Xiaopeng Zheng, Wei Chen, Xin Qi, Yuxue Ren, Na Lei, Xianfeng Gu",
journal="Frontiers of Information Technology & Electronic Engineering",
volume="22",
number="9",
pages="1207-1220",
year="2021",
publisher="Zhejiang University Press & Springer",
doi="10.1631/FITEE.2000250"
}
%0 Journal Article
%T Robust and accurate optimal transportation map by self-adaptive sampling
%A Yingshi Wang
%A Xiaopeng Zheng
%A Wei Chen
%A Xin Qi
%A Yuxue Ren
%A Na Lei
%A Xianfeng Gu
%J Frontiers of Information Technology & Electronic Engineering
%V 22
%N 9
%P 1207-1220
%@ 2095-9184
%D 2021
%I Zhejiang University Press & Springer
%DOI 10.1631/FITEE.2000250
TY - JOUR
T1 - Robust and accurate optimal transportation map by self-adaptive sampling
A1 - Yingshi Wang
A1 - Xiaopeng Zheng
A1 - Wei Chen
A1 - Xin Qi
A1 - Yuxue Ren
A1 - Na Lei
A1 - Xianfeng Gu
J0 - Frontiers of Information Technology & Electronic Engineering
VL - 22
IS - 9
SP - 1207
EP - 1220
%@ 2095-9184
Y1 - 2021
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/FITEE.2000250
Abstract: optimal transportation plays a fundamental role in many fields in engineering and medicine, including surface parameterization in graphics, registration in computer vision, and generative models in deep learning. For quadratic distance cost, optimal transportation map is the gradient of the Brenier potential, which can be obtained by solving the monge-Ampère equation. Furthermore, it is induced to a geometric convex optimization problem. The monge-Ampère equation is highly non-linear, and during the solving process, the intermediate solutions have to be strictly convex. Specifically, the accuracy of the discrete solution heavily depends on the sampling pattern of the target measure. In this work, we propose a self-adaptive sampling algorithm which greatly reduces the sampling bias and improves the accuracy and robustness of the discrete solutions. Experimental results demonstrate the efficiency and efficacy of our method.
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