Can Geometry Save Central Views for Sports Field Registration?

TL;DR

This work tackles single-frame sports field calibration for central-view images, where markings are sparsely distributed and traditional line/point-based cues may fail. It introduces a purely geometric bottom-up method that converts circle correspondences into robust point and line constraints using pole-polar geometry and ellipse projections, enabling homography or camera-parameter estimation. The approach covers three cases (line, point, unknown center) and can yield eight point correspondences plus eight lines, improving calibration in difficult central views and supporting more accurate image annotation. Experiments on SoccerNet and synthetic data show the method complements existing detectors, enabling calibration when central views challenge standard pipelines, though performance still depends on robust circle/ellipse detection and center localization.

Abstract

Single-frame sports field registration often serves as the foundation for extracting 3D information from broadcast videos, enabling applications related to sports analytics, refereeing, or fan engagement. As sports fields have rigorous specifications in terms of shape and dimensions of their line, circle and point components, sports field markings are commonly used as calibration targets for this task. However, because of the sparse and uneven distribution of field markings, close-up camera views around central areas of the field often depict only line and circle markings. On these views, sports field registration is challenging for the vast majority of existing methods, as they focus on leveraging line field markings and their intersections. It is indeed a challenge to include circle correspondences in a set of linear equations. In this work, we propose a novel method to derive a set of points and lines from circle correspondences, enabling the exploitation of circle correspondences for both sports field registration and image annotation. In our experiments, we illustrate the benefits of our bottom-up geometric method against top-performing detectors and show that our method successfully complements them, enabling sports field registration in difficult scenarios.

Figures (10)

• Figure 1: Single-frame camera calibration is challenging when only a limited amount of field markings are visible in the scene. For example, in this image, camera parameters cannot be derived from the line and point correspondences without incorporating priors about the camera. This is why current methods generate virtual keypoints (PnLCalib Gutierrez2024Pnlcalib-arxiv in yellow) which here, however, are not sufficient to allow for a registration of the sports field. Our geometric approach derives the pink points from the fitted ellipse and the detected center, which allow for the estimation of the homography (blue).
• Figure 2: Top-view of the soccer field layout, as decomposed into different semantic elements. These elements form a set of markings include points, lines, and circles that can be used to calibrate a camera.
• Figure 3: Visualization of the fitted ellipse (purple), its tangents from the great axis extremities (orange), or from the points extracted by our proposed method (green), that come from the line crossing the actual image of the circle center. The green tangents better capture the perspectivity as parallels should intersect at one point on the vanishing line of the supporting plane.
• Figure 4: Starting either from a line correspondence $\textbf{l}_1$ (left) or a point correspondence $\textbf{x}$ (right), we derive the dashed lines and the set of points $\textbf{a}$, $\textbf{b}$, $\textbf{d}$, and $\textbf{e}$.
• Figure 5: Distribution of Euclidean distances, in pixels, between the circle center and each line formed by opposed keypoints pairs. Compared to SoccerNet (SN), the out-of-distribution dataset (OOD) shows a significant number of unbounded errors.