When Does Non-Maximum Suppression Remove Touching Objects? A Geometric Analysis of Snooker Ball Detection with Implications for Real-Time Detector Design and Evaluation

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A frequent claim in real-time object detection is that non-maximum suppression (NMS) removes true objects when they touch, so that NMS-free detectors are needed in crowded scenes. We test this claim in snooker, where the geometry is known exactly: spheres of diameter 52.5 mm on a table of known size, including fifteen identical reds packed together. Under an orthographic camera at elevation θ, we derive the box IoU of two touching balls aligned in depth: (1 − sin θ)/(1 + sin θ) for whole-ball (amodal) boxes, and exactly half of that for visible-extent (modal) boxes. Hence, with the common visible-extent convention, such a pair can never be suppressed at the widely used threshold τ = 0.7. Simulating greedy NMS on the full rack, no red is suppressed for θ ≥ 10° with modal boxes, whereas amodal boxes lose on average 3.45 of 15 reds at 10°. With box noise of up to 10% of the diameter, any red is lost in at most 2.2% of trials for θ ≥ 15°. A ray-cast pinhole model agrees for θ ≥ 10°. We also show that a full-table view at a 640-pixel input renders a ball at 9.4 px, about one stride-8 feature cell, and that a stride-4 level matches the cells-per-ball of doubling the input at 29% of the compute for YOLO26n. Finally, the default Ultralytics augmentation rescales saturation by factors of 0.3–1.7, a hazard when colour defines the class. We derive four falsifiable predictions and reporting requirements for empirical studies. No trained detectors are evaluated; every number is produced by analysis scripts available from the author.