Optimizing parametric total variation models
Optimizing parametric total variation models
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优化参数总变分模型
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
N. C. Overgaard
中科院分区：
文献类型：
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作者：
Petter Strandmark;Fredrik Kahl;N. C. Overgaard
最近的能量最小化方法成功的关键因素之一是它们寻求计算全局解决方案。即使对于非凸能量泛函，图割等优化方法已被证明可以通过基于大邻域的迭代最小化产生高质量的解决方案，从而使它们不易受到局部最小值的影响。我们的方法通过扩大一维搜索邻域来更进一步。在本文中，我们考虑依赖于一组附加参数的二元全变分问题。例子包括：（i）我们全局解决的 Chan-Vese 模型（ii）比率和约束最小化，可以表述为参数问题，以及（iii）Mumford-Shah 泛函的变体。我们的方法基于最近的 Chambolle 定理，该定理指出，解决单参数二元问题族相当于解决单个凸变分问题。我们证明了该结果的概括，并展示了如何将其应用于参数优化。
One of the key factors for the success of recent energy minimization methods is that they seek to compute global solutions. Even for non-convex energy functionals, optimization methods such as graph cuts have proven to produce high-quality solutions by iterative minimization based on large neighborhoods, making them less vulnerable to local minima. Our approach takes this a step further by enlarging the search neighborhood with one dimension. In this paper we consider binary total variation problems that depend on an additional set of parameters. Examples include: (i) the Chan-Vese model that we solve globally (ii) ratio and constrained minimization which can be formulated as parametric problems, and (iii) variants of the Mumford-Shah functional. Our approach is based on a recent theorem of Chambolle which states that solving a one-parameter family of binary problems amounts to solving a single convex variational problem. We prove a generalization of this result and show how it can be applied to parametric optimization.