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

TL;DR

The paper tackles thick line detection in noisy images by modeling the 3D grayscale relief as a finite mixture of Linear Anchored Gaussian distributions (LAGDs) and estimating their parameters with an Expectation-Maximization (EM) framework. It derives closed-form updates for the mixture components' proportions, radii, thickness-related scale, and orientation, and introduces a dynamic background subtraction step to reduce background interference. A Hessian-based initialization enhances convergence and accuracy, particularly under blur and noise, and experiments on synthetic and real data demonstrate improved centerline localization and thickness estimation. The approach offers a simple yet effective tool for thick line detection in domains like remote sensing, X-ray imaging, and road-marking analysis, with robust performance under challenging imaging conditions.

Abstract

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.

Figures (13)

• Figure 1: Linear anchored Gaussian function with $\sigma=5.8$ for the parameterized line $(\Delta)$ with $\rho=166$ and $\theta=\pi/6$
• Figure 2: An example of unitary volume illustration in the image relief related to the realizations of $\bm{v}$
• Figure 3: An example of a mixture of linear anchored Gaussian distributions
• Figure 4: (a) and (c) Original input images representing one and two bar(s), respectively. (b) and (d) Illustration of initial, intermediate and final results, represented, respectively, by solid, dashed and bold lines in case of Algorithm 1 where, the initial angle(s) is(are) taken perpendicular to the object(s) centerline(s).
• Figure 5: Radius and orientation angle parameters for an input synthetic image representing 3 thick lines.