Area-preservation mapping using optimal mass transport

Xin Zhao Zhengyu Su Xianfeng David Gu Arie Kaufman Jian Sun Jie Gao Feng Luo

Numerical Analysis and Scientific Computing mathscidoc:1912.43778

IEEE transactions on visualization and computer graphics, 19, (12), 2838-2847, 2013.10
We present a novel area-preservation mapping/flattening method using the optimal mass transport technique, based on the Monge-Brenier theory. Our optimal transport map approach is rigorous and solid in theory, efficient and parallel in computation, yet general for various applications. By comparison with the conventional Monge-Kantorovich approach, our method reduces the number of variables from O(n<sup>2</sup>) to O(n), and converts the optimal mass transport problem to a convex optimization problem, which can now be efficiently carried out by Newton's method. Furthermore, our framework includes the area weighting strategy that enables users to completely control and adjust the size of areas everywhere in an accurate and quantitative way. Our method significantly reduces the complexity of the problem, and improves the efficiency, flexibility and scalability during visualization. Our framework, by combining
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@inproceedings{xin2013area-preservation,
  title={Area-preservation mapping using optimal mass transport},
  author={Xin Zhao, Zhengyu Su, Xianfeng David Gu, Arie Kaufman, Jian Sun, Jie Gao, and Feng Luo},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205736413003342},
  booktitle={IEEE transactions on visualization and computer graphics},
  volume={19},
  number={12},
  pages={2838-2847},
  year={2013},
}
Xin Zhao, Zhengyu Su, Xianfeng David Gu, Arie Kaufman, Jian Sun, Jie Gao, and Feng Luo. Area-preservation mapping using optimal mass transport. 2013. Vol. 19. In IEEE transactions on visualization and computer graphics. pp.2838-2847. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205736413003342.
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