目标检测中的mAP是什么含义？
Metrics for object detection
The motivation of this project is the lack of consensus used by different works and implementations concerning the evaluation metrics of the object detection problem. Although on-line competitions use their own metrics to evaluate the task of object detection, just some of them offer reference code snippets to calculate the accuracy of the detected objects.
Researchers who want to evaluate their work using different datasets than those offered by the competitions, need to implement their own version of the metrics. Sometimes a wrong or different implementation can create different and biased results. Ideally, in order to have trustworthy benchmarking among different approaches, it is necessary to have a flexible implementation that can be used by everyone regardless the dataset used.
This project provides easy-to-use functions implementing the same metrics used by the the most popular competitions of object detection. Our implementation does not require modifications of your detection model to complicated input formats, avoiding conversions to XML or JSON files. We simplified the input data (ground truth bounding boxes and detected bounding boxes) and gathered in a single project the main metrics used by the academia and challenges. Our implementation was carefully compared against the official implementations and our results are exactly the same.
In the topics below you can find an overview of the most popular metrics used in different competitions and works, as well as samples showing how to use our code.
Table of contents
- Motivation
- Different competitions, different metrics
- Important definitions
- Metrics
- Precision x Recall curve
- Average Precision
- 11-point interpolation
- Interpolating all points
- How to use this project
- References
Different competitions, different metrics
-
PASCAL VOC Challenge offers a Matlab script in order to evaluate the quality of the detected objects. Participants of the competition can use the provided Matlab script to measure the accuracy of their detections before submitting their results. The official documentation explaining their criteria for object detection metrics can be accessed here. The current metrics used by the current PASCAL VOC object detection challenge are the Precision x Recall curve and Average Precision.
The PASCAL VOC Matlab evaluation code reads the ground truth bounding boxes from XML files, requiring changes in the code if you want to apply it to other datasets or to your speficic cases. Even though projects such as Faster-RCNNimplement PASCAL VOC evaluation metrics, it is also necessary to convert the detected bounding boxes into their specific format. Tensorflow framework also has their PASCAL VOC metrics implementation. -
COCO Detection Challenge uses different metrics to evaluate the accuracy of object detection of different algorithms. Here you can find a documentation explaining the 12 metrics used for characterizing the performance of an object detector on COCO. This competition offers Python and Matlab codes so users can verify their scores before submitting the results. It is also necessary to convert the results to a format required by the competition.
-
Google Open Images Dataset V4 Competition also uses mean Average Precision (mAP) over the 500 classes to evaluate the object detection task.
-
ImageNet Object Localization Challenge defines an error for each image considering the class and the overlapping region between ground truth and detected boxes. The total error is computed as the average of all min errors among all test dataset images. Here are more details about their evaluation method.
Important definitions
Intersection Over Union (IOU)
Intersection Over Union (IOU) is measure based on Jaccard Index that evaluates the overlap between two bounding boxes. It requires a ground truth bounding box 
and a predicted bounding box 
. By applying the IOU we can tell if a detection is valid (True Positive) or not (False Positive).
IOU is given by the overlapping area between the predicted bounding box and the ground truth bounding box divided by the area of union between them:
The image below illustrates the IOU between a ground truth bounding box (in green) and a detected bounding box (in red).
True Positive, False Positive, False Negative and True Negative
Some basic concepts used by the metrics:
- True Positive (TP): A correct detection. Detection with IOU ≥ threshold
- False Positive (FP): A wrong detection. Detection with IOU < threshold
- False Negative (FN): A ground truth not detected
- True Negative (TN): Does not apply. It would represent a corrected misdetection. In the object detection task there are many possible bounding boxes that should not be detected within an image. Thus, TN would be all possible bounding boxes that were corrrectly not detected (so many possible boxes within an image). That's why it is not used by the metrics.
threshold: depending on the metric, it is usually set to 50%, 75% or 95%.
Precision
Precision is the ability of a model to identify only the relevant objects. It is the percentage of correct positive predictions and is given by:
Recall
Recall is the ability of a model to find all the relevant cases (all ground truth bounding boxes). It is the percentage of true positive detected among all relevant ground truths and is given by:
Metrics
In the topics below there are some comments on the most popular metrics used for object detection.
Precision x Recall curve
The Precision x Recall curve is a good way to evaluate the performance of an object detector as the confidence is changed by plotting a curve for each object class. An object detector of a particular class is considered good if its precision stays high as recall increases, which means that if you vary the confidence threshold, the precision and recall will still be high. Another way to identify a good object detector is to look for a detector that can identify only relevant objects (0 False Positives = high precision), finding all ground truth objects (0 False Negatives = high recall).
A poor object detector needs to increase the number of detected objects (increasing False Positives = lower precision) in order to retrieve all ground truth objects (high recall). That's why the Precision x Recall curve usually starts with high precision values, decreasing as recall increases. You can see an example of the Prevision x Recall curve in the next topic (Average Precision). This kind of curve is used by the PASCAL VOC 2012 challenge and is available in our implementation.
Average Precision
Another way to compare the performance of object detectors is to calculate the area under the curve (AUC) of the Precision x Recall curve. As AP curves are often zigzag curves going up and down, comparing different curves (different detectors) in the same plot usually is not an easy task - because the curves tend to cross each other much frequently. That's why Average Precision (AP), a numerical metric, can also help us compare different detectors. In practice AP is the precision averaged across all recall values between 0 and 1.
From 2010 on, the method of computing AP by the PASCAL VOC challenge has changed. Currently, the interpolation performed by PASCAL VOC challenge uses all data points, rather than interpolating only 11 equally spaced points as stated in their paper. As we want to reproduce their default implementation, our default code (as seen further) follows their most recent application (interpolating all data points). However, we also offer the 11-point interpolation approach.
11-point interpolation
The 11-point interpolation tries to summarize the shape of the Precision x Recall curve by averaging the precision at a set of eleven equally spaced recall levels [0, 0.1, 0.2, ... , 1]:
with
where 
is the measured precision at recall 
.
Instead of using the precision observed at each point, the AP is obtained by interpolating the precision only at the 11 levels 
taking the maximum precision whose recall value is greater than .
Interpolating all points
Instead of interpolating only in the 11 equally spaced points, you could interpolate through all points in such way that:
with
where is the measured precision at recall .
In this case, instead of using the precision observed at only few points, the AP is now obtained by interpolating the precision at each level, taking the maximum precision whose recall value is greater or equal than 
. This way we calculate the estimated area under the curve.
To make things more clear, we provided an example comparing both interpolations.
An ilustrated example
An example helps us understand better the concept of the interpolated average precision. Consider the detections below:
There are 7 images with 15 ground truth objects representented by the green bounding boxes and 24 detected objects represented by the red bounding boxes. Each detected object has a confidence level and is identified by a letter (A,B,...,Y).
The following table shows the bounding boxes with their corresponding confidences. The last column identifies the detections as TP or FP. In this example a TP is considered if IOU 
30%, otherwise it is a FP. By looking at the images above we can roughly tell if the detections are TP or FP.
In some images there are more than one detection overlapping a ground truth (Images 2, 3, 4, 5, 6 and 7). For those cases the detection with the highest IOU is considered TP and the others are considered FP. This rule is applied by the PASCAL VOC 2012 metric: "e.g. 5 detections (TP) of a single object is counted as 1 correct detection and 4 false detections”.
The Precision x Recall curve is plotted by calculating the precision and recall values of the accumulated TP or FP detections. For this, first we need to order the detections by their confidences, then we calculate the precision and recall for each accumulated detection as shown in the table below:
Plotting the precision and recall values we have the following Precision x Recall curve:
As mentioned before, there are two different ways to measure the interpolted average precision: 11-point interpolation and interpolating all points. Below we make a comparisson between them:
Calculating the 11-point interpolation
The idea of the 11-point interpolated average precision is to average the precisions at a set of 11 recall levels (0,0.1,...,1). The interpolated precision values are obtained by taking the maximum precision whose recall value is greater than its current recall value as follows:
By applying the 11-point interpolation, we have:
Calculating the interpolation performed in all points
By interpolating all points, the Average Precision (AP) can be interpreted as an approximated AUC of the Precision x Recall curve. The intention is to reduce the impact of the wiggles in the curve. By applying the equations presented before, we can obtain the areas as it will be demostrated here. We could also visually have the interpolated precision points by looking at the recalls starting from the highest (0.4666) to 0 (looking at the plot from right to left) and, as we decrease the recall, we collect the precision values that are the highest as shown in the image below:
Looking at the plot above, we can divide the AUC into 4 areas (A1, A2, A3 and A4):
Calculating the total area, we have the AP:
The results between the two different interpolation methods are a little different: 24.56% and 26.84% by the every point interpolation and the 11-point interpolation respectively.
Our default implementation is the same as VOC PASCAL: every point interpolation. If you want to use the 11-point interpolation, change the functions that use the argument method=MethodAveragePrecision.EveryPointInterpolation to method=MethodAveragePrecision.ElevenPointInterpolation.
If you want to reproduce these results, see the Sample 2.