Live Coding: NMS & IoU Matrix

Live Coding Non-Maximum Suppression (NMS) & Intersection over Union (IoU) represents the quintessential computer vision coding problem testing bounding-box coordinate geometry and greedy filtering algorithms; it comprises 2 stages: 1) Vectorized IoU Calculation: given boxes $A, B \in \mathbb{R}^{M \times 4}$ ($[x_1, y_1, x_2, y_2]$), leveraging numpy broadcasting to compute pairwise intersection coordinates ($x_{\text{inter1}} = \max(A_{x1}, B_{x1})$), yielding $\text{IoU} = \frac{\text{Area}(\text{Intersection})}{\text{Area}(A) + \text{Area}(B) - \text{Area}(\text{Intersection})}$; 2) Greedy NMS Filtering: sorting boxes by confidence descending, iteratively appending the top box to the keep-list and discarding all remaining candidates with $\text{IoU} > \text{threshold}$.

Object detection post-processing (YOLO, Faster R-CNN), OCR text-box deduplication, and autonomous driving point-cloud 3D box filtering.

Dense anchor-based and anchor-free object detectors emit dozens of redundant overlapping proposals around a single physical object; NMS eliminates duplicates to yield crisp, non-overlapping detections.

Write the complete Pure Numpy implementation of vectorized IoU and greedy NMS from scratch?

Explain why pixel width calculations add 1 ($w = x_2 - x_1 + 1$) for discrete raster grids vs continuous float coordinates?

Explain how Soft-NMS uses continuous Gaussian score decay to retain heavily occluded neighboring objects that hard NMS erroneously deletes?

Explain the coordinate-offset trick enabling multi-class batched NMS execution in a single vector operation?

How does DETR's bipartite Hungarian matching loss eliminate the need for heuristic NMS post-processing entirely?