NMS in a Crowded Scene: Why a Person Disappears

A pedestrian detector works well on sparse street scenes but misses people in dense crowds at a station entrance. Debugging one frame, the detector emits four boxes before NMS (boxes are x_1, y_1, x_2, y_2):

Ground truth: P1 and P2 are two different people standing close together, P3 is a third person, and P1b is a duplicate detection of P1. NMS uses an IoU threshold of 0.5.

1. Compute the pairwise IoUs that matter and run greedy NMS. What survives, and what is the effect on recall?
2. Run NMS again at threshold 0.65. What changes, and what is the price of raising the threshold further?
3. Apply Gaussian Soft-NMS with \sigma = 0.5 (score multiplied by \exp(-\mathrm{IoU}^2/\sigma)). What are the new scores?
4. List two other ways to fix this, and explain how this failure shows up in the mAP metric.