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首页> 外文期刊>Journal of visual communication & image representation >Multiphase image segmentation via equally distanced multiple well potential
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Multiphase image segmentation via equally distanced multiple well potential

机译：通过等距多井势进行多相图像分割

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摘要

Variational models for image segmentation, e.g. Mumford-Shah variational model and Chan-Vese model, generally involve a regularization term that penalizes the length of the boundaries of the segmentation. In practice often the length term is replaced by a weighted length, i.e., some portions of the set of boundaries are penalized more than other portions, thus unbalancing the geometric term of the segmentation functional. In the present paper we consider a class of variational models in the framework of Γ-convergence theory. We propose a family of functionals defined on vector valued functions that involve a multiple well potential of the type arising in diffuse-interface models of phase transitions. A potential with equally distanced wells makes it possible to retrieve the penalization of the true (i.e., not weighted) length of the boundaries as the Γ-convergence parameter tends to zero. We explore the differences and the similarities of behavior of models in the proposed class, followed by some numerical experiments.
机译：图像分割的变体模型，例如Mumford-Shah变分模型和Chan-Vese模型通常包含一个正则化项，该项会惩罚分割边界的长度。在实践中，通常用加权长度代替长度项，即，边界集的某些部分比其他部分受到更多的惩罚，从而使分割函数的几何项失去平衡。在本文中，我们在Γ收敛理论的框架内考虑了一类变分模型。我们提出了一个在向量值函数上定义的函数族，这些函数涉及在相变的扩散接口模型中出现的多种势阱类型。当Γ收敛参数趋于零时，势阱等距的势能使边界的真实（即未加权）长度的损失成为可能。我们在提出的类中探索模型行为的异同，然后进行一些数值实验。

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