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首页> 外文会议>Conference on Image Extraction, Segmentation, and Recognition Oct 22-24, 2001, Wuhan, China >Level Set Methods and Image Segmentation
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Level Set Methods and Image Segmentation

机译：水平集方法和图像分割

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摘要

In this article, some basic problems on the level set methods are discussed, such as the method used to preserve the distance function, the existence and uniqueness of the solutions for the level set equations and the analysis of the singular points. It is presented that if the solutions of the level set equations with the distance function restriction exist, they must be the signed distance function to the evolving surface. And it is presented that there exists a unique solution in a neighborhood of the initial zero level set. However, the uniqueness of the solutions is hard to be guaranteed away from the initial zero level set. An important property of the singular points is given, which is a sufficient and necessary condition in distinguishing the singular points from ordinary points. The above results consummate the theoretical base of the level set methods. At meantime, the estimate method of the width of the narrow band is presented in order to avoid the singular points during the iterative process of the level set methods. The implementations of our theory are shown on real images and synthetic images.
机译：本文讨论了有关水平集方法的一些基本问题，例如用于保留距离函数的方法，水平集方程解的存在性和唯一性以及奇异点的分析。提出了如果存在具有距离函数限制的水平集方程的解，则它们必须是到演化表面的有符号距离函数。提出了在初始零水平集附近存在唯一解。但是，很难保证解决方案的独特性远离初始的零水平设置。给出了奇异点的重要性质，这是区分奇异点和普通点的充分必要条件。以上结果完善了水平集方法的理论基础。同时，提出了窄带宽度的估计方法，以避免在水平集方法的迭代过程中出现奇异点。我们的理论的实现在真实图像和合成图像上显示。

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