Table tennis hawk-eye out-of-bounds simulation: a method based on 3D trajectory reconstruction

This paper introduces a lightweight framework for reconstructing 3D trajectories of table tennis balls using computer vision, specifically designed to simulate Hawk-Eye for out-of-bounds judgments in matches. Driven by the demand for precise real-time adjudication in high-speed sports like table tennis, where balls travel over 100 km/h and manual errors occur frequently at boundaries, our methodology combines YOLOv8 for 2D detection, a multilayer perceptron for depth estimation, and Kalman filtering for trajectory refinement. The framework projects 3D paths from single or multiple video views, facilitating accurate out-of-bounds simulations via trajectory-table boundary intersections. Evaluations on a blended Kaggle dataset for table tennis ball detection and simulated paths reveal superior reconstruction precision, with average Euclidean errors under 0.15 units and detection accuracies over 93%. Motion blur mitigation is included to bolster performance in authentic conditions. Comparisons indicate our approach surpasses baselines in computational speed, achieving under 30 ms inference on commodity hardware. This contribution fosters cost-effective Hawk-Eye substitutes in table tennis, minimizing disputes and aiding virtual simulations. Potential expansions encompass spin inference and multi-object tracking for enhanced sports insights.