Communications in Mathematical Sciences

Volume 9 (2011)

Number 2

Frame-based segmentation for medical images

Pages: 551 – 559



Aichi Chien (Division of Interventional Neuroradiology, David Geffen School of Medicine, University of California at Los Angeles)

Bin Dong (Department of Mathematics, University of California at San Diego)

Zuowei Shen (Department of Mathematics, National University of Singapore)


Medical image segmentation is an important but difficult problem that attracts tremendous attention from researchers in various fields. In this paper, we propose a frame based model, as well as a fast implementation, for general medical image segmentation problems. Our model combines ideas of the frame based image restoration model of [J. Cai, S. Osher, and Z. Shen, Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 8(2), 337–369, 2009] with ideas of the total variation based segmentation model of [T. Chan and L. Vese, Scale-Space Theories in Computer Vision, 141–151, 1999], [T. Chan and L. Vese, IEEE Transactions on image processing, 10(2), 266–277, 2001], [T. Chan, S. Esedoglu and M. Nikolova, ALGORITHMS, 66(5), 1632–1648], and [X. Bresson, S. Esedoglu, P. Vandergheynst, J. Thiran and S. Osher, Journal of Mathematical Imaging and Vision, 28(2), 151–167, 2007]. Numerical experiments show that the proposed frame based model outperforms the total variation based model in terms of capturing key features of biological structures. Successful segmentations of blood vessels and aneurysms in 3D CT angiography images are also presented.


image segmentation, level set method, sparse approximation, tight frame

2010 Mathematics Subject Classification

42C40, 62H35, 68U10, 70G75, 92C55

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