Center for Medical Image Science and Visualization, Linköping University, Linköping, Sweden.
IEEE Trans Image Process. 2013 Feb;22(2):621-30. doi: 10.1109/TIP.2012.2220148. Epub 2012 Sep 21.
Level set methods are a popular way to solve the image segmentation problem. The solution contour is found by solving an optimization problem where a cost functional is minimized. Gradient descent methods are often used to solve this optimization problem since they are very easy to implement and applicable to general nonconvex functionals. They are, however, sensitive to local minima and often display slow convergence. Traditionally, cost functionals have been modified to avoid these problems. In this paper, we instead propose using two modified gradient descent methods, one using a momentum term and one based on resilient propagation. These methods are commonly used in the machine learning community. In a series of 2-D/3-D-experiments using real and synthetic data with ground truth, the modifications are shown to reduce the sensitivity for local optima and to increase the convergence rate. The parameter sensitivity is also investigated. The proposed methods are very simple modifications of the basic method, and are directly compatible with any type of level set implementation. Downloadable reference code with examples is available online.
水平集方法是解决图像分割问题的一种流行方法。通过求解最小化代价函数的优化问题来找到解轮廓。由于梯度下降方法非常易于实现并且适用于一般的非凸泛函，因此经常用于求解此优化问题。但是，它们对局部最小值很敏感，并且常常显示出缓慢的收敛速度。传统上，已经对代价泛函进行了修改以避免这些问题。在本文中，我们提出了使用两种改进的梯度下降方法，一种使用动量项，另一种基于弹性传播。这些方法在机器学习社区中很常用。在一系列使用具有真实和合成数据以及地面真值的 2D/3D 实验中，这些修改被证明可以降低对局部最优值的敏感性并提高收敛速度。还研究了参数敏感性。所提出的方法是对基本方法的非常简单的修改，并且与任何类型的水平集实现都直接兼容。可在线下载带有示例的参考代码。
