Area-preservation mapping using optimal mass transport

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

Research output: Contribution to journalArticlepeer-review

52 Scopus citations

Abstract

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(n2) 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 conformal mapping and optimal mass transport mapping, serves as a powerful tool for a broad range of applications in visualization and graphics, especially for medical imaging. We provide a variety of experimental results to demonstrate the efficiency, robustness and efficacy of our novel framework.

Original languageEnglish (US)
Article number6634117
Pages (from-to)2838-2847
Number of pages10
JournalIEEE Transactions on Visualization and Computer Graphics
Volume19
Issue number12
DOIs
StatePublished - 2013

All Science Journal Classification (ASJC) codes

  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Computer Graphics and Computer-Aided Design

Keywords

  • Area-preservation mapping
  • Monge-Brenier theory
  • optimal transport map
  • surface flattening
  • visualization and graphics applications

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