SIAM Journal on Imaging Sciences, Volume 14, Issue 3, Page 1184-1205, January 2021.
Active contour models have been widely used in image segmentation, and the level set method (LSM) is the most popular approach for solving the models, via implicitly representing the contour by a level set function. However, the LSM suffers from high computational burden and numerical instability, requiring additional regularization terms or reinitialization techniques. In this paper, we use characteristic functions to implicitly represent the contours, propose a new representation to the geodesic active contours, and derive an efficient algorithm termed the iterative convolution-thresholding method (ICTM). Compared to the LSM, the ICTM is simpler and much more efficient. In addition, the ICTM enjoys most desired features of the level set--based methods. Extensive experiments, on two-dimensional (2D) synthetic, 2D ultrasound, 3D computed tomography, and 3D magnetic resonance images for nodule, organ, and lesion segmentation demonstrate that the proposed method not only obtains comparable or even better segmentation results (compared to the LSM) but also achieves significant acceleration.

中文翻译：

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一种基于特征函数的测地线活动轮廓算法

SIAM 成像科学杂志，第 14 卷，第 3 期，第 1184-1205 页，2021 年 1 月。
主动轮廓模型已广泛用于图像分割，水平集方法（LSM）是解决模型最流行的方法，通过水平集函数隐式表示轮廓。然而，LSM 存在高计算负担和数值不稳定性，需要额外的正则化项或重新初始化技术。在本文中，我们使用特征函数隐式表示轮廓，提出测地线活动轮廓的新表示，并推导出一种称为迭代卷积阈值方法（ICTM）的有效算法。与 LSM 相比，ICTM 更简单也更高效。此外，ICTM 享有基于水平集的方法最需要的特征。广泛的实验，二维 (2D) 合成，2D 超声，