Bayesian–Geometric Fusion: A Probabilistic Framework for Robust Line Feature Matching

Line feature matching is a fundamental and extensively studied subject in the fields of photogrammetry and computer vision. Traditional methods, which rely on handcrafted descriptors and distance-based filtering outliers, frequently encounter challenges related to robustness and a high incidence of outliers. While some approaches leverage point features to assist line feature matching by establishing the invariant geometric constraints between points and lines, this typically results in a considerable computational load. In order to overcome these limitations, we introduce a novel Bayesian posterior probability framework for line matching that incorporates three geometric constraints: the distance between line feature endpoints, midpoint distance, and angular consistency. Our approach initially characterizes inter-image geometric relationships using Fourier representation. Subsequently, we formulate the posterior probability distributions for the distance constraint and the uniform distribution based on the constraint of angular consistency. By calculating the joint probability distribution under three geometric constraints, robust line feature matches are iteratively optimized through the Expectation–Maximization (EM) algorithm. Comprehensive experiments confirm the effectiveness of our approach: (i) it outperforms state-of-the-art (including deep learning-based) algorithms in match count and accuracy across common scenarios; (ii) it exhibits superior robustness to rotation, illumination variation, and motion blur compared to descriptor-based methods; and (iii) it notably reduces computational overhead in comparison to algorithms that involve point-assisted line matching.