基于高维点云分布的最优传输问题的研究

阮一鸣

基于高维点云分布的最优传输问题的研究

引用本文：阮一鸣.基于高维点云分布的最优传输问题的研究[J].计算技术与自动化,2022,(1):141-147

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作者	单位
阮一鸣	（河海大学理学院，江苏南京 211100）

中文摘要:最优传输问题是寻求相对于给定的代价函数,把一种分布转化为另一种分布的最有效的方式，其具有较为深远的价值，其中基于点云的最优传输问题更是得到广泛的关注。针对高维的点云分布的最优传输问题，利用了分片最优传输的理论及其对应的优化模型，提出一个改进梯度迭代的算法，以二维、三维点云分布为例进行数值实验，并将其与经典的方法进行比较，验证模型与算法的有效性。实验结果表明，本文模型及其算法在标准差、峰值信噪比、平均梯度等指标均有更高的性能。

中文关键词:最优传输 Wasserstein距离点云分布随机梯度迭代

Research on Optimal Transport Problem Based on High Dimensional Point Cloud Distribution

Abstract:The problem of optimal transport is to find the most effective way to transform one distribution into another relative to a given cost function. It has far-reaching value, among which the problem of optimal transport based on point cloud has gained wide attention. Aiming at the problem of optimal transport of high-dimensional point cloud distribution, using the theory of piecewise optimal transport and its corresponding optimization model, this paper proposes an improved gradient iterative algorithm. Taking two-dimensional and three-dimensional point cloud distribution as examples, numerical experiments are carried out and compared with classical methods to verify the effectiveness of the model and algorithm. Experimental results show that the model and its algorithm have higher performance in Standard Deviation, Peak Signal to Noise Ratio, Average Gradient and other indicators.

keywords:optimal transport Wasserstein distance point cloud distribution random gradient iteration

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