We propose a novel minimal path method for the segmentation of 2D and 3D line structures. Minimal path methods perform propagation of a wavefront emanating from a start point at a speed derived from image features, followed by path extraction using backtracing. Usually, the computation of the speed and the propagation of the wave are two separate steps, and point features are used to compute a static speed. We introduce a new continuous minimal path method which steers the wave propagation progressively using dynamic speed based on path features. We present three instances of our method, using an appearance feature of the path, a geometric feature based on the curvature of the path, and a joint appearance and geometric feature based on the tangent of the wavefront. These features have not been used in previous continuous minimal path methods. We compute the features dynamically during the wave propagation, and also efficiently using a fast numerical scheme and a low-dimensional parameter space. Our method does not suffer from discretization or metrication errors. We performed qualitative and quantitative evaluations using 2D and 3D images from different application areas.

中文翻译：

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用于2D和3D线结构分割的渐进最小路径方法

我们提出了一种用于2D和3D线结构分割的新颖的最小路径方法。最小路径方法以从图像特征中得出的速度执行从起点发出的波前传播，然后使用回溯进行路径提取。通常，速度的计算和波的传播是两个分离 步骤，以及 点特征 用于计算 静态的速度。我们介绍了一种新的连续最小路径方法，该方法可以控制波的传播逐步 使用 动态的 速度基于 路径特征。我们使用路径的外观特征，基于路径曲率的几何特征以及基于波前切线的联合外观和几何特征，展示了我们方法的三个实例。这些功能未在以前的连续最小路径方法中使用。我们计算特征动态地 在波传播过程中，以及 有效率的使用快速数值方案和低维参数空间。我们的方法没有离散化或度量错误。我们使用来自不同应用领域的2D和3D图像进行了定性和定量评估。