Measure Object Detection¶
Precision, Recall, and F1¶
\[ \begin{align}\begin{aligned}\begin{split}\begin{split}
&Precision &= \dfrac{TP}{\text{total detection}}&= \dfrac{TP}{TP+FP}\\
&Recall &= \dfrac{TP}{\text{total positive}} &= \dfrac{TP}{TP+FN}\\
&F1&=\dfrac{precision\cdot recall}{precision+recall}\\\end{split}\\\begin{split}&TP=\text{True Positive}\\
&TN=\text{True Negative}\\
&FP=\text{False Positive}\\
&FN=\text{False Negative}\\
\end{split}\end{split}\end{aligned}\end{align} \]
Intersection over union, IoU¶
consider area of Ground Truth and area of Prediction
\[IoU = \dfrac{\text{area of overlap}}{\text{area of union}}\]
It is used to define Positive or negative
Non-Maximum Suppression, NMS¶
To filter overlapped object
mean Average Precisiion, mAP¶
When The confident level threshold increase, the precision decrease and recall increase.
Average Precision is the area under the precision-recall curve, with a confident or IoU threshold
\[AP = \int_0^1p(r)dr\]
In Pascal VOC, an average for the 11-point interpolated AP is calculated. [0, 0.1, 0.2, 0.3, …1.0]
COCO AP¶
| Average Precision (AP) | - |
|---|---|
$AP$ |
% AP at IoU=.50:.05:.95 (primary challenge metric) |
$AP^{IoU=.50}$ |
% AP at IoU=.50 (PASCAL VOC metric) |
$AP^{IoU=.75}$ |
% AP at IoU=.75 (strict metric) |
| AP Across Scales | - |
|---|---|
$AP^{small}$ |
% AP for small objects: area < 322 |
$AP^{medium}$ |
% AP for medium objects: 322 < area < 962 |
$AP^{large}$ |
% AP for large objects: area > 962 |
| Average Recall (AR) | - |
|---|---|
$AR^{max=1}$ |
% AR given 1 detection per image |
$AR^{max=10}$ |
% AR given 10 detections per image |
$AR^{max=100}$ |
% AR given 100 detections per image |
| AR Across Scales | - |
|---|---|
$AR^{small}$ |
% AR for small objects: area < 322 |
$AR^{medium}$ |
% AR for medium objects: 322 < area < 962 |
$AR^{large}$ |
% AR for large objects: area > 962 |