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

arXiv: https://arxiv.org/abs/2404.03043 · HTML: https://mlsanity.com/paper/2404.03043/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 28 references that are in the map.
- First posted on arXiv 3 Apr 2024.

## Builds on (most cited first, 7 of 7)

- [Line Segment Detection Using Transformers without Edges](https://mlsanity.com/paper/2101.01909/) (2021)
- [DeepLSD: Line Segment Detection and Refinement with Deep Image Gradients](https://mlsanity.com/paper/2212.07766/) (2022)
- [SOLD2: Self-supervised Occlusion-aware Line Description and Detection](https://mlsanity.com/paper/2104.03362/) (2021)
- [Towards Light-weight and Real-time Line Segment Detection](https://mlsanity.com/paper/2106.00186/) (2021)
- [TP-LSD: Tri-Points Based Line Segment Detector](https://mlsanity.com/paper/2009.05505/) (2020)
- [LSDNet: Trainable Modification of LSD Algorithm for Real-Time Line Segment Detection](https://mlsanity.com/paper/2209.04642/) (2022)
- [A Comprehensive Review of Image Line Segment Detection and Description: Taxonomies, Comparisons, and Challenges](https://mlsanity.com/paper/2305.00264/) (2023)

## Abstract (arXiv)

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.