SIAM Journal on Imaging Sciences, Volume 13, Issue 1, Page 497-534, January 2020.
In this paper, we propose a high-order accurate scheme for image segmentation based on the level-set method. In this approach, the curve evolution is described as the 0-level set of a representation function, but we modify the velocity that drives the curve to the boundary of the object in order to obtain a new velocity with additional properties that are extremely useful to develop a more stable high-order approximation with a small additional cost. The approximation scheme proposed here is the first 2D version of an adaptive “filtered" scheme recently introduced and analyzed by the authors in one dimension. This approach is interesting since the implementation of the filtered scheme is rather efficient and easy. The scheme combines two building blocks (a monotone scheme and a high-order scheme) via a filter function and smoothness indicators that allow one to detect the regularity of the approximate solution adapting the scheme in an automatic way. Some numerical tests on synthetic and real images confirm the accuracy of the proposed method and the advantages given by the new velocity.

中文翻译：

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通过改进的水平集方法进行图像分割的高阶方案

SIAM影像科学杂志，第13卷，第1期，第497-534页，2020年1月。
在本文中，我们提出了一种基于水平集方法的高阶精确图像分割方案。在这种方法中，曲线演化被描述为表示函数的0级集，但是我们修改了将曲线驱动到对象边界的速度，以便获得具有其他特性的新速度，这些特性对于用较少的额外费用开发出更稳定的高阶近似。本文中提出的近似方案是作者最近在一个维度上引入和分析的自适应“滤波”方案的第一个2D版本，这种方法很有趣，因为滤波方案的实现非常有效且容易。该方案通过过滤器功能和平滑度指示器将两个构造块（单调方案和高阶方案）组合在一起，使人们可以自动检测适应方案的近似解的规律性。在合成图像和真实图像上进行的一些数值测试证实了该方法的准确性以及新速度带来的优势。