DocumentCode :
53582
Title :
Area-Preservation Mapping using Optimal Mass Transport
Author :
Xin Zhao ; Zhengyu Su ; Gu, Xianfeng David ; Kaufman, Arie ; Jian Sun ; Jie Gao ; Feng Luo
Volume :
19
Issue :
12
fYear :
2013
fDate :
Dec. 2013
Firstpage :
2838
Lastpage :
2847
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.
Keywords :
Newton method; convex programming; data visualisation; Monge-Brenier theory; Monge-Kantorovich approach; Newton method; area weighting strategy; area-preservation flattening method; area-preservation mapping method; conformal mapping; convex optimization problem; graphics application; medical imaging application; optimal mass transport technique; visualization application; Area measurement; Conformal mapping; Convex functions; Shape analysis; Transportation; Area measurement; Area-preservation mapping; Conformal mapping; Convex functions; Monge-Brenier theory; Shape analysis; Transportation; optimal transport map; surface flattening; visualization and graphics applications; Algorithms; Computer Graphics; Computer Simulation; Image Enhancement; Image Interpretation, Computer-Assisted; Imaging, Three-Dimensional; Models, Theoretical; Reproducibility of Results; Rheology; Sensitivity and Specificity; User-Computer Interface;
fLanguage :
English
Journal_Title :
Visualization and Computer Graphics, IEEE Transactions on
Publisher :
ieee
ISSN :
1077-2626
Type :
jour
DOI :
10.1109/TVCG.2013.135
Filename :
6634117
Link To Document :
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