Linear Anchored Gaussian Mixture Model for Location and Width Computations of Objects in Thick Line Shape

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.