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

An accurate detection of the centerlines of linear objects is a challenging topic in many sensitive 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 approaches based on image derivatives need further step-by-step processing, making their efficiency dependent on each step outcomes. In this paper, we aim to detect linear structures found in images by considering the 3D representation of the image gray levels as a finite mixture model of statistical distribution. The latter, which we named linear anchored Gaussian distribution could be parametrized by a scale value ${\sigma}$ describing the linear structure thickness and a line equation, parametrized, in turn, by a radius ${\rho}$ and an orientation angle ${\theta}$, describing the linear structure centerline location. Expectation-Maximization (EM) algorithm is used for the mixture model parameter estimation, where a new paradigm, using the background subtraction for the likelihood function computation, is proposed. For the EM algorithm, two ${\theta}$ parameter initialization schemes are used: the first one is based on a random choice of the first component of ${\theta}$ vector, whereas the second is based on the image Hessian with a simultaneous computation of the mixture model components number. Experiments on real world images and synthetic images corrupted by blur and additive noise show the good performance of the proposed methods, where the algorithm using background subtraction and Hessian-based ${\theta}$ initialization provides an outstanding accuracy of the linear structure detection despite irregular image background and presence of blur and noise.