Geometric priors have been shown to be useful in image segmentation to regularize the results. For example, the classical Mumford–Shah functional uses region perimeter as prior. This has inspired much research in the last few decades, with classical approaches like the Rudin–Osher–Fatemi and most graph-cut formulations, which all use a weighted or binary perimeter prior. It has been observed that this prior is not suitable in many applications, for example for segmenting thin objects or some textures, which may have high perimeter/surface ratio. Mumford observed that an interesting prior for natural objects is the Euler elastical model, which involves the squared curvature. In other areas of science, researchers have noticed that some physical binarization processes, like emulsion unmixing, can be well-approximated by curvature-related flow like the Willmore flow. However, curvature-related flows are not easy to compute because curvature is difficult to estimate accurately, and the underlying optimization processes are not convex. In this article, we propose to formulate a digital flow that approximates an Elastica-related flow using a multigrid-convergent curvature estimator, within a discrete variational framework. We also present an application of this model as a post-processing step to a segmentation framework.

几何先验已显示在图像分割中使结果正规化很有用。例如，经典的Mumford-Shah函数使用区域周长作为先验。在过去的几十年中，这激发了许多研究的兴趣，其中包括经典的方法，如Rudin-Osher-Fatemi和大多数图形切割公式，这些方法以前都使用加权或二进制周长。已经观察到，该现有技术不适用于许多应用，例如用于分割可能具有高周长/表面比的薄物体或某些纹理。芒福德（Mumford）观察到，自然物体的一个有趣先验是欧拉弹性模型，该模型涉及平方曲率。在其他科学领域，研究人员注意到某些物理二值化过程，例如乳液分解，可以由与曲率相关的流（如Willmore流）很好地近似。但是，与曲率有关的流不容易计算，因为曲率难以准确估计，并且底层的优化过程也不是凸的。在本文中，我们建议在离散变分框架内使用多网格收敛曲率估计器来制定近似于Elastica相关流的数字流。我们还将当前模型的应用作为细分框架的后处理步骤。我们建议在离散变分框架内，使用多网格收敛曲率估计器来制定近似于Elastica相关流的数字流。我们还将当前模型的应用作为细分框架的后处理步骤。我们建议在离散变分框架内，使用多网格收敛曲率估计器来制定近似于Elastica相关流的数字流。我们还将当前模型的应用作为细分框架的后处理步骤。