Intelligent Sampling Consensus for Homography Estimation in Football Videos Using Featureless Unpaired Points

Estimating the homography matrix between images captured under radically different camera poses and zoom factors is a complex challenge. Traditional methods rely on the Random Sample Consensus (RANSAC) algorithm, which requires pairs of homologous points, pre-matched based on local image feature vectors. Sampling consensus is a core step in many Artificial Intelligence (AI) algorithms that enable computer systems to recognize patterns in data. In this paper, we propose <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i>-RANSAC, an algorithm for homography estimation that eliminates the need for feature vectors or explicit point pairing, while it optionally supports point labeling into two classes. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i>-RANSAC introduces a novel geometric (cheiral) criterion that intelligently rejects implausible point configurations at the beginning of each iteration, while leveraging concave quadrilaterals typically discarded by similar algorithms. A post-hoc criterion at the end of each iteration improves accuracy further. Analytical derivations of the expected maximum iterations are provided, considering success probabilities and outlier rates, enabling adaptive performance tuning. The algorithm is validated on a demanding task: estimating homography between video frames of football matches captured by 12 cameras with highly divergent viewpoints. Results show that <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i>-RANSAC significantly outperforms state-of-the-art classical methods, combined with deep learning-based salient point detection, in terms of average reprojection error and success rates. The relevant implementation is available in https://github.com/gnousias/H-RANSAC.