A study on continuous max-flow and min-cut approaches
A study on continuous max-flow and min-cut approaches
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DOI：
10.1109/cvpr.2010.5539903
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发表时间：
2010-06
期刊：
影响因子：
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通讯作者：
Jing Yuan;Egil Bae;X. Tai
中科院分区：
文献类型：
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作者：
Jing Yuan;Egil Bae;X. Tai
我们提出并研究了新的最大流模型，在连续设置，直接映射的离散图为基础的最大流问题，其连续优化配方。我们表明，这样一个连续的最大流模型导致一个等价的最小割问题，在一个自然的方式，作为相应的对偶模型。在这方面，我们重新审视离散最大流/最小割模型中使用的基本概念，并从变分的角度给出了新的解释。我们还提出了相应的连续最大流和最小割模型约束的先验监督信息，并将其应用于交互式图像分割/标记问题。我们证明了所提出的连续最大流和最小割模型，有或没有监督约束，产生一系列全局二元解λ <$（x）<${0，1}，全局解决了原来的非凸图像分割问题。此外，我们提出了新的和可靠的基于乘数的最大流算法。它们的收敛性由经典优化理论保证。通过无监督和有监督的图像分割实验，验证了所讨论的连续最大流和最小割模型以及基于最大流的算法的有效性。
We propose and study novel max-flow models in the continuous setting, which directly map the discrete graph-based max-flow problem to its continuous optimization formulation. We show such a continuous max-flow model leads to an equivalent min-cut problem in a natural way, as the corresponding dual model. In this regard, we revisit basic conceptions used in discrete max-flow / min-cut models and give their new explanations from a variational perspective. We also propose corresponding continuous max-flow and min-cut models constrained by priori supervised information and apply them to interactive image segmentation/labeling problems. We prove that the proposed continuous max-flow and min-cut models, with or without supervised constraints, give rise to a series of global binary solutions λ∗(x) ∊ {0,1}, which globally solves the original nonconvex image partitioning problems. In addition, we propose novel and reliable multiplier-based max-flow algorithms. Their convergence is guaranteed by classical optimization theories. Experiments on image segmentation, unsupervised and supervised, validate the effectiveness of the discussed continuous max-flow and min-cut models and suggested max-flow based algorithms.