对于二分类的情况，我们可以使用以下公式计算其精确度(precision)和召回率(recall)。

精确率和召回率的计算公式

例子

对于一幅图片，若person类别在图片中有7个，即7个ground truth box。而我们的模型一共检测出了10个bounding box，并且按照pred_conf进行排序，若bounding box与greound truth box的iou值大于IOU_thresh阈值（一般设为0.5））的话，GT为1。

检测情况

各阶段的精确率和召回率的计算

不同recall下，最大的precision值

代码实现

以下代码截取于YOLOv3的模型评估函数
计算单个类别的ap

# 计算每个类的ap 具体算法：
def ap_per_class(tp, conf, pred_cls, target_cls):
    """ Compute the average precision, given the recall and precision curves.
    Source: https://github.com/rafaelpadilla/Object-Detection-Metrics.
    # Arguments
        tp:    True positives (list).
        conf:  Objectness value from 0-1 (list).
        pred_cls: Predicted object classes (list).
        target_cls: True object classes (list).
    # Returns
        The average precision as computed in py-faster-rcnn.
    """

    # 1、按照pred_conf进行排序
    i = np.argsort(-conf)
    tp, conf, pred_cls = tp[i], conf[i], pred_cls[i]
    # 2、目标框中的不同类别(Person,Car...)
    unique_classes = np.unique(target_cls)
    # Create Precision-Recall curve and compute AP for each class
    ap, p, r = [], [], []
    # 3、遍历类别，计算每个类别的precison和recall
    for c in tqdm.tqdm(unique_classes, desc="Computing AP"):
        i = pred_cls == c
        n_gt = (target_cls == c).sum()  # 真实框中该类别数目
        n_p = i.sum()  # 预测框中该类别数目

        if n_p == 0 and n_gt == 0:
            continue
        elif n_p == 0 or n_gt == 0:
            ap.append(0)
            r.append(0)
            p.append(0)
        else:
            # Accumulate FPs and TPs
            fpc = (1 - tp[i]).cumsum()  # cumsum一维数组返回累计和
            tpc = (tp[i]).cumsum()

            # Recall
            recall_curve = tpc / (n_gt + 1e-16)
            r.append(recall_curve[-1])

            # Precision
            precision_curve = tpc / (tpc + fpc)
            p.append(precision_curve[-1])

            # AP from recall-precision curve
            ap.append(compute_ap(recall_curve, precision_curve))

    # Compute F1 score (harmonic mean of precision and recall)
    p, r, ap = np.array(p), np.array(r), np.array(ap)
    f1 = 2 * p * r / (p + r + 1e-16)

    return p, r, ap, f1, unique_classes.astype("int32")

对于上述例子，person类别的tp[i]为[1,1,0,0,0,1,0,0,1,1]，tpc即将tp进行累加得到每个rank的分子，为[1,2,2,2,2,3,3,3,4,5]。tpc+fpc即为当前rank的预测框数目，为[1,2,3,4,5,6,7,8,9,10]。
根据precision和recall计算ap

def compute_ap(recall, precision):
    """ Compute the average precision, given the recall and precision curves.
    Code originally from https://github.com/rbgirshick/py-faster-rcnn.

    # Arguments
        recall:    The recall curve (list).
        precision: The precision curve (list).
    # Returns
        The average precision as computed in py-faster-rcnn.
    """
    # correct AP calculation
    # first append sentinel values at the end
    mrec = np.concatenate(([0.0], recall, [1.0]))
    mpre = np.concatenate(([0.0], precision, [0.0]))

    # compute the precision envelope
    for i in range(mpre.size - 1, 0, -1):
        mpre[i - 1] = np.maximum(mpre[i - 1], mpre[i])

    # to calculate area under PR curve, look for points
    # where X axis (recall) changes value
    i = np.where(mrec[1:] != mrec[:-1])[0]

    # and sum (\Delta recall) * prec
    ap = np.sum((mrec[i + 1] - mrec[i]) * mpre[i + 1])
    return ap

参考

https://www.zhihu.com/question/53405779