The analysis of thin curvilinear objects in 3D images is a complex and challenging task. In this article, we introduce a new, non-linear operator, called RORPO (Ranking the Orientation Responses of Path Operators). Inspired by the multidirectional paradigm currently used in linear filtering for thin structure analysis, RORPO is built upon the notion of path operator from mathematical morphology. This operator, unlike most operators commonly used for 3D curvilinear structure analysis, is discrete, non-linear and non-local. From this new operator, two main curvilinear structure characteristics can be estimated: an intensity feature, that can be assimilated to a quantitative measure of curvilinearity; and a directional feature, providing a quantitative measure of the structure's orientation. We provide a full description of the structural and algorithmic details for computing these two features from RORPO, and we discuss computational issues. We experimentally assess RORPO by comparison with three of the most popular curvilinear structure analysis filters, namely Frangi Vesselness, Optimally Oriented Flux, and Hybrid Diffusion with Continuous Switch. In particular, we show that our method provides up to 8 percent more true positive and 50 percent less false positives than the next best method, on synthetic and real 3D images.

中文翻译：

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通过对路径算子的取向响应进行排名对曲线结构进行分析

分析3D图像中的细曲线物体是一项复杂而艰巨的任务。在本文中，我们介绍了一种新的非线性运算符，称为RORPO（路径运算符的方向响应）。受到当前线性过滤中用于薄结构分析的多方向范例的启发，RORPO建立在数学形态学上路径运算符概念的基础上。与大多数通常用于3D曲线结构分析的大多数算子不同，该算子是离散的，非线性的和非局部的。从这个新的算子中，可以估算出两个主要的曲线结构特征：一个强度特征，可以与曲线的定量度量相提并论；和方向特征，可定量测量结构的方向。我们提供了有关从RORPO计算这两个功能的结构和算法细节的完整描述，并讨论了计算问题。我们通过与三种最流行的曲线结构分析过滤器（即Frangi Vesselness，最优定向通量和具有连续开关的混合扩散）进行比较，对RORPO进行实验评估。尤其是，我们证明，在合成和真实3D图像上，我们的方法比次佳方法提供的真实正值最多高8％，而误报率则低50％。