mAP for Object Detection

Background

Mean Average Precision (mAP) at IoU threshold $\tau$ is the standard object-detection eval. For each class, walk the predicted boxes in score order, match each to the highest-IoU unmatched ground-truth box if $\text{IoU} \ge \tau$, otherwise mark as a false positive. AP is the area under the resulting precision-recall curve; mAP is the average AP across classes.

Problem statement

Implement map_detection(detections, golds, iou_threshold=0.5):

1. Group detections and golds by class.
2. For each class:
   • Sort detections by score descending.
   • Walk through, computing IoU to each gold; if a match $\ge \tau$ and that gold is unmatched, count as TP and mark gold as matched; else FP.
   • Compute precision and recall after each row; AP = $\sum_i (R_i - R_{i-1}) P_i$.
3. Return the mean of class APs.

Input

• detections — list[tuple[class, score, box]]. box = (x1, y1, x2, y2).
• golds — list[tuple[class, box]].
• iou_threshold — float in $[0, 1]$ (default 0.5).

Output

Returns a Python float in $[0, 1]$.

Examples

Example 1 — perfect detection

Input:  one detection that exactly matches a single gold box
Output: 1.0

Example 2 — no detections

Input:  detections=[], gold present
Output: 0.0

Example 3 — IoU below threshold → no match

Input:  detection and gold of same class but disjoint boxes
Output: 0.0

Constraints

• A gold box can be matched at most once across all detections (greedy).
• If a class has no gold, its AP is 0.0.
• Returns Python float.

Notes

• mAP@0.5 vs mAP@[.5:.95]. COCO reports the average mAP across IoU thresholds from 0.5 to 0.95; this kernel implements one fixed threshold.
• Greedy matching. Strict bipartite matching would be optimal but slower; greedy is the standard approximation.