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首页> 外文会议>Twenty-Sixth Australasian Computer Science Conference; Feb, 2003; Adelaide, Australia >A Useful Bound for Region Merging Algorithms in a Bayesian Model
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A Useful Bound for Region Merging Algorithms in a Bayesian Model

机译：贝叶斯模型中区域合并算法的有用界限

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摘要

A well known and effective approach to image segmentation is based on the Mumford-Shah model, where finding an optimal segmentation of an image is posed as the minimization of an energy functional. The simplest of these models is mathematically tractable and desirable properties of the resulting segmentations have been rigorously established. An important step in the proofs involves establishing an "inverse isoperimet-ric" type of bound. In particular, it can be shown that for segmentations where it is impossible to decrease the functional energy by merging any pair of regions, the length of the boundary between two regions must be bounded above by their areas and variation of the image itself. Recent work of one of the authors has extended the Mumford-Shah segmentation model to a Bayeasian setting. In this report we show that an "inverse isoperimetric" type of bound also exists in this new setting. The new bound can likewise be used to prove desirable properties of the corresponding segmentations.
机译：一种众所周知的有效的图像分割方法是基于Mumford-Shah模型的，其中将图像的最佳分割视为能量函数的最小化。这些模型中最简单的是在数学上易于处理的，并且已经严格建立了所得分割的所需属性。证明中的重要步骤涉及建立“逆等规”类型的绑定。特别地，可以显示出对于不可能通过合并任何一对区域来降低功能能量的分割，两个区域之间的边界的长度必须以它们的面积和图像本身的变化为界。一位作者的最新工作将Mumford-Shah分割模型扩展到Bayeasian环境。在此报告中，我们表明在此新设置中还存在“等距逆”绑定。新界限同样可以用于证明相应分段的理想属性。

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