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A Study on Continuous Max-Flow and Min-Cut Approaches

Yuan, Jing; Bae, Egil; Tai, Xue-Cheng
Chapter, Peer reviewed
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URI
https://hdl.handle.net/1956/5020
Date
2010
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  • Department of Mathematics [650]
Original version
https://doi.org/10.1109/cvpr.2010.5539903
Abstract
We propose and investigate novel max-flow models in the spatially continuous setting, with or without supervised constraints, under a comparative study of graph based max-flow / min-cut. We show that the continuous max-flow models correspond to their respective continuous min-cut models as primal and dual problems, and the continuous min-cut formulation without supervision constraints regards the well-known Chan-Esedoglu-Nikolova model [15] as a special case. In this respect, basic conceptions and terminologies applied by discrete max-flow / mincut are revisited under a new variational perspective. We prove that the associated nonconvex partitioning problems, unsupervised or supervised, can be solved globally and exactly via the proposed convex continuous max-flow and min-cut models. Moreover, we derive novel fast max-flow based algorithms whose convergence can be guaranteed by standard optimization theories. Experiments on image segmentation, both unsupervised and supervised, show that our continuous max-flow based algorithms outperform previous approaches in terms of efficiency and accuracy.
Description
2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. (An extended journal version).
Publisher
IEEE
Copyright
Copyright IEEE. All rights reserved.

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