Tennis video arbitration

How accurately can two phones on tripods decide whether a ball landed in or out?

Result

19 mm mean error, 20/20 correct calls over twenty serves, against a tape measure · Hawk-Eye: 2.6–3.6 mm with ten high-speed cameras

When

Sep 2024 – Jul 2025, supervised research project (TIPE)

Code

github.com/NnicolasN/tennis-video-arbitration — MIT · numpy, OpenCV · 39 tests · CI

Method

1. 2D detection by background subtraction: median reference frame, threshold, morphology, remove the player, keep ball-sized blobs, choose by trajectory continuity.
2. Six landmarks with known world coordinates: four corners plus the two net-post tops (six coplanar points cannot fix a projection matrix).
3. DLT calibration: one 3×4 matrix P = K[R|t] per phone, Hartley-normalized, solved by SVD; reprojection RMSE as the sanity check.
4. Triangulation: two rays, A·X = 0 by SVD.
5. Bounce: a parabola fitted around the lowest sample recovers the contact instant between frames; signed distance to the nearest line gives the call.

Numbers

• The geometry is not the limit: on synthetic data it reproduces ground truth to twelve decimals
• Frame rate dominates: halving it more than doubles the error
• Outdoors, moving shadows break background subtraction — a limit of the method