Extending continuous cuts: Anisotropic metrics and expansion moves
Extending continuous cuts: Anisotropic metrics and expansion moves
复制标题
扩展连续切割：各向异性度量和扩展移动
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
Fredrik Kahl
中科院分区：
文献类型：
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作者：
Carl Olsson;Martin Byröd;N. C. Overgaard;Fredrik Kahl
图切割的概念现在是解决各种低级视觉问题的标准方法。它的流行很大程度上是由于这样一个事实，即全局或接近全局最优的解决方案可以使用有效的最大流算法计算。另一方面，已经观察到这种方法可能遭受公制误差。最近的工作已经开始研究连续版本的图切割，这给较小的度量误差。另一个优点是，连续切割是直接并行化。在本文中，我们扩展了类的泛函，可以优化的连续设置，包括各向异性TV-规范。我们表明，有一个所谓的coarea公式，这些泛函，使之有可能通过解决凸问题，以尽量减少他们。我们还表明，a-膨胀移动的概念可以重新制定，以适应连续的配方，我们推导出近似界类比离散的情况下。给出了多类分割问题的Potts模型的一个连续版本，并展示了如何使用连续α-展开来获得可证明的好解。
The concept of graph cuts is by now a standard method for all sorts of low level vision problems. Its popularity is largely due to the fact that globally or near globally optimal solutions can be computed using efficient max flow algorithms. On the other hand it has been observed that this method may suffer from metrication errors. Recent work has begun studying continuous versions of graph cuts, which give smaller metrication errors. Another advantage is that continuous cuts are straightforward to parallelize. In this paper we extend the class of functionals that can be optimized in the continuous setting to include anisotropic TV-norms. We show that there is a so called coarea formula for these functionals making it possible to minimize them by solving a convex problem. We also show that the concept of a-expansion moves can be reformulated to fit the continuous formulation, and we derive approximation bounds in analogy with the discrete case. A continuous version of the Potts model for multi-class segmentation problems is presented, and it is shown how to obtain provably good solutions using continuous α-expansions.