  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.
