Accurate detection of the centerline of a thick linear structure and good estimation of its thickness are challenging topics in many real-world applications such X-ray imaging, remote sensing and lane marking detection in road traffic. Model-based approaches using Hough and Radon transforms are often used but, are not recommended for thick line detection, whereas methods based on image derivatives need further step-by-step processing making their efficiency dependent on each step outcome. In this paper, a novel paradigm to better detect thick linear objects is presented, where the 3D image gray level representation is considered as a finite mixture model of a statistical distribution, called linear anchored Gaussian distribution and parametrized by a scale factor to describe the structure thickness and radius and angle parameters to localize the structure centerline. Expectation-Maximization algorithm (Algo1) using the original image as input data is used to estimate the model parameters. To rid the data of irrelevant information brought by nonuniform and noisy background, a modified EM algorithm (Algo2) is detailed. In Experiments, the proposed algorithms show promising results on real-world images and synthetic images corrupted by blur and noise, where Algo2, using Hessian-based angle initialization, outperforms Algo1 and Algo2 with random angle initialization, in terms of running time and structure location and thickness computation accuracy.

翻译：厚线性结构中心线的精确检测及其厚度的准确估计，是X射线成像、遥感及道路交通车道标记检测等实际应用中的挑战性课题。基于霍夫变换和拉东变换的模型驱动方法虽常用，但并不适用于厚线检测；而基于图像导数的方法需逐步处理，其效率依赖各步骤的结果。本文提出一种新型范式以更优地检测厚线形物体，将三维图像灰度表征视为一种名为"线性锚定高斯分布"的统计分布的有限混合模型，该分布通过尺度因子参数化以描述结构厚度，并通过半径和角度参数定位结构中心线。采用以原始图像为输入数据的期望最大化算法（Algo1）估计模型参数。为剔除由非均匀噪声背景带来的无关信息，进一步详述了一种改进型EM算法（Algo2）。实验表明，所提算法在真实图像及受模糊与噪声污染的合成图像上展现出良好效果，其中基于Hessian矩阵角度初始化的Algo2在运行时间、结构定位及厚度计算精度方面均优于Algo1及随机角度初始化的Algo2。