Precision-Recall Curve Points

mediumPROObject DetectionDetectionCV: Recognition

You are given detection results (whether each detection matched a ground truth object) and need to compute precision and recall at each detection to construct a PR curve.

Detections should be processed in order of decreasing confidence (highest first).

For each detection processed:

Precision = True Positives / Total Detections So Far
Recall = True Positives / Total Ground Truth Objects

$Precision = \frac{TP}{TP + FP} \quad\quad Recall = \frac{TP}{TP + FN} = \frac{TP}{\text{num\_gt}}$

Where:

TP = detections that matched a ground truth
FP = detections that didn't match (false alarms)
num_gt = total ground truth objects

Round precision and recall to 4 decimal places.

Example

Input

matches = [True, False, True]
num_gt = 3

Output

[(1.0, 0.3333), (0.5, 0.3333), (0.6667, 0.6667)]

Reasoning

Inputs: matches lists the three detections from most to least confident: a hit, a false alarm, then another hit. num_gt = 3 means three real objects exist in the image, whether or not anything found them.
After detection 1 (hit): TP $= 1$ out of $1$ detection, so precision $= \frac{1}{1} = 1.0$ and recall $= \frac{1}{3} \approx 0.3333$ .
After detection 2 (false alarm): TP stays $1$ , but $2$ detections have now been made, so precision falls to $\frac{1}{2} = 0.5$ . Recall is still $\frac{1}{3} = 0.3333$ , because a false alarm finds no new object.
After detection 3 (hit): TP $= 2$ out of $3$ detections, so precision $= \frac{2}{3} \approx 0.6667$ and recall $= \frac{2}{3} \approx 0.6667$ .
Output: one (precision, recall) pair per detection, rounded to 4 decimal places: [(1.0, 0.3333), (0.5, 0.3333), (0.6667, 0.6667)].
Notice that recall can only rise or stay flat as you go down the list, while precision can drop and recover. That is why PR curves zigzag. Recall here never reaches $1$ : one object was never detected.

Constraints

matches: list of booleans, True if detection matched ground truth, False otherwise
Detections are already sorted by confidence (highest first)
num_gt: total number of ground truth objects
Return list of (precision, recall) tuples

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Concept primerPREVIEW

You are building the per-detection points of a precision–recall (PR) curve, given an ordered list of detections and whether each one is a true positive or false positive.

1. Background Knowledge

In object detection, a model outputs many candidate detections, each with a confidence score. To evaluate the model, each detection is matched (or not) to a ground-truth object. A detection that correctly matches a ground truth is a true positive (TP); one that doesn’t match any ground truth (or matches something already claimed by another detection) is a false positive (FP). The number of ground-truth objects is fixed and known as num_gt.

The precision–recall curve summarizes performance as you move down the list of detections from high confidence to low confidence. At each prefix of the list (first 1 detection, first 2 detections, etc.), you can compute:

Precision: fraction of processed detections that are correct.
Recall: fraction of ground-truth objects that have been correctly detected.

Formally:

$Precision = \frac{TP}{TP + FP}$
$Recall =$ \frac{TP}{TP + FN} $= \frac{TP}{$ \text{num_gt} $}$

Plotting precision vs recall for all prefixes gives the PR curve. In this problem, you just need to output the precision and recall values for each prefix, rounded to 4 decimal places.

2. Algorithm / General Approach

This is a classic running-prefix statistics problem:

You are given:
A list of detections already sorted by decreasing confidence.
For each detection, a boolean/flag: is this detection a TP or FP?
A total num_gt (number of ground-truth objects).
You process the detections in order, keeping cumulative counts of TPs and FPs.
After processing each detection, compute:
$precision_i = \frac{$ \text{cumulative_TP} $}{$ \text{detections_processed_so_far} $}$
$recall_i = \frac{$ \text{cumulative_TP} $}{$ \text{num_gt} $}$
Store or print these values for each step.

This pattern appears often in evaluation tasks: you walk over sorted predictions and maintain running statistics.

3. Step-by-Step Strategy

Understand the inputs

matches: an array where each element indicates whether the i-th detection is a TP (1 / true) or FP (0 / false).
num_gt: total number of ground-truth objects (positive instances).

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solution.py

Python 3.13

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