目标检测评价指标 AP、mAP

目标检测中的TP、FP、FN 

所有检测框都认为是Predicted Positive

所有真实框都是Ground-truth Positive

若一个检测框与一个真实框的IOU>阈值并对正确分类，则认为该检测框是一个True Positive

若一个检测框不与任何真实框IOU>阈值 或 当检测框与真实框IOU>阈值却没有正确分类时，则认为该检测框是一个False Positive

若一个真实框不与任何一个检测框匹配（即IOU>阈值且类别一致），则认为该真实框是一个False Negative

目标检测中没有True Negative的概念，因为True Negative有无数个

有了TP、FP、FN，就可以计算precision和recall

AP

对与单类目标检测（如人脸检测），如上图，绿色框为真实框（共有15个），红色框为检测框（共有24个，A,...,Y），判断TP、FP、FN的IOU阈值设为0.3。每个检测框都有一个置信度，将所有检测框按置信度从高到低排序，可得到下表：

其中acc TP表示从头到该位置累计TP数量，acc FP表示从头到该位置累计FP数量，precision表示从头到该位置的precision，recall表示从头到该位置的recall

下图表示从头到尾依次加入新样本时，P和R的变化情况（P-R线）：

AP有两种：

①AP_11（更常用）：在上图中，将recall分别取[0, 0.1, 0.2, ..., 1]11个值，对应precision为该recall值右侧P-R线的最高值，如下图所示，红色点表示这11个(recall, precision)：

AP_11就是11个红点precision的均值

②AP_all：如下图所示，红色虚线的纵坐标从1开始单调递减，每次减小到右侧P-R线的最高值

AP_all就是红色虚线下方的面积，即：

mAP

对目标检测中的每个类计算AP，再求每个类AP的平均值，如下图所示：

在COCO竞赛中，AP就是指mAP

 代码：

# --------------------------------------------------------
# Fast/er R-CNN
# Licensed under The MIT License [see LICENSE for details]
# Written by Bharath Hariharan
# --------------------------------------------------------

import xml.etree.ElementTree as ET
import os
import cPickle
import numpy as np

def parse_rec(filename):
    """ Parse a PASCAL VOC xml file """
    tree = ET.parse(filename)
    objects = []
    for obj in tree.findall('object'):
        obj_struct = {}
        obj_struct['name'] = obj.find('name').text
        obj_struct['pose'] = obj.find('pose').text
        obj_struct['truncated'] = int(obj.find('truncated').text)
        obj_struct['difficult'] = int(obj.find('difficult').text)
        bbox = obj.find('bndbox')
        obj_struct['bbox'] = [int(bbox.find('xmin').text),
                              int(bbox.find('ymin').text),
                              int(bbox.find('xmax').text),
                              int(bbox.find('ymax').text)]
        objects.append(obj_struct)

    return objects

def voc_ap(rec, prec, use_07_metric=False):
    """ ap = voc_ap(rec, prec, [use_07_metric])
    Compute VOC AP given precision and recall.
    If use_07_metric is true, uses the
    VOC 07 11 point method (default:False).
    """
    if use_07_metric:
        # 11 point metric
        ap = 0.
        for t in np.arange(0., 1.1, 0.1):
            if np.sum(rec >= t) == 0:
                p = 0
            else:
                p = np.max(prec[rec >= t])
            ap = ap + p / 11.
    else:
        # correct AP calculation
        # first append sentinel values at the end
        mrec = np.concatenate(([0.], rec, [1.]))
        mpre = np.concatenate(([0.], prec, [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

def voc_eval(detpath,
             annopath,
             imagesetfile,
             classname,
             cachedir,
             ovthresh=0.5,
             use_07_metric=False):
    """rec, prec, ap = voc_eval(detpath,
                                annopath,
                                imagesetfile,
                                classname,
                                [ovthresh],
                                [use_07_metric])

    Top level function that does the PASCAL VOC evaluation.

    detpath: Path to detections
        detpath.format(classname) should produce the detection results file.
    annopath: Path to annotations
        annopath.format(imagename) should be the xml annotations file.
    imagesetfile: Text file containing the list of images, one image per line.
    classname: Category name (duh)
    cachedir: Directory for caching the annotations
    [ovthresh]: Overlap threshold (default = 0.5)
    [use_07_metric]: Whether to use VOC07's 11 point AP computation
        (default False)
    """
    # assumes detections are in detpath.format(classname)
    # assumes annotations are in annopath.format(imagename)
    # assumes imagesetfile is a text file with each line an image name
    # cachedir caches the annotations in a pickle file

    # first load gt
    if not os.path.isdir(cachedir):
        os.mkdir(cachedir)
    cachefile = os.path.join(cachedir, 'annots.pkl')
    # read list of images
    with open(imagesetfile, 'r') as f:
        lines = f.readlines()
    imagenames = [x.strip() for x in lines]

    if not os.path.isfile(cachefile):
        # load annots
        recs = {}
        for i, imagename in enumerate(imagenames):
            recs[imagename] = parse_rec(annopath.format(imagename))
            if i % 100 == 0:
                print 'Reading annotation for {:d}/{:d}'.format(
                    i + 1, len(imagenames))
        # save
        print 'Saving cached annotations to {:s}'.format(cachefile)
        with open(cachefile, 'w') as f:
            cPickle.dump(recs, f)
    else:
        # load
        with open(cachefile, 'r') as f:
            recs = cPickle.load(f)

    # extract gt objects for this class
    class_recs = {}
    npos = 0
    for imagename in imagenames:
        R = [obj for obj in recs[imagename] if obj['name'] == classname]
        bbox = np.array([x['bbox'] for x in R])
        difficult = np.array([x['difficult'] for x in R]).astype(np.bool)
        det = [False] * len(R)
        npos = npos + sum(~difficult)
        class_recs[imagename] = {'bbox': bbox,
                                 'difficult': difficult,
                                 'det': det}

    # read dets
    detfile = detpath.format(classname)
    with open(detfile, 'r') as f:
        lines = f.readlines()

    splitlines = [x.strip().split(' ') for x in lines]
    image_ids = [x[0] for x in splitlines]
    confidence = np.array([float(x[1]) for x in splitlines])
    BB = np.array([[float(z) for z in x[2:]] for x in splitlines])

    # sort by confidence
    sorted_ind = np.argsort(-confidence)
    sorted_scores = np.sort(-confidence)
    BB = BB[sorted_ind, :]
    image_ids = [image_ids[x] for x in sorted_ind]

    # go down dets and mark TPs and FPs
    nd = len(image_ids)
    tp = np.zeros(nd)
    fp = np.zeros(nd)
    for d in range(nd):
        R = class_recs[image_ids[d]]
        bb = BB[d, :].astype(float)
        ovmax = -np.inf
        BBGT = R['bbox'].astype(float)

        if BBGT.size > 0:
            # compute overlaps
            # intersection
            ixmin = np.maximum(BBGT[:, 0], bb[0])
            iymin = np.maximum(BBGT[:, 1], bb[1])
            ixmax = np.minimum(BBGT[:, 2], bb[2])
            iymax = np.minimum(BBGT[:, 3], bb[3])
            iw = np.maximum(ixmax - ixmin + 1., 0.)
            ih = np.maximum(iymax - iymin + 1., 0.)
            inters = iw * ih

            # union
            uni = ((bb[2] - bb[0] + 1.) * (bb[3] - bb[1] + 1.) +
                   (BBGT[:, 2] - BBGT[:, 0] + 1.) *
                   (BBGT[:, 3] - BBGT[:, 1] + 1.) - inters)

            overlaps = inters / uni
            ovmax = np.max(overlaps)
            jmax = np.argmax(overlaps)

        if ovmax > ovthresh:
            if not R['difficult'][jmax]:
                if not R['det'][jmax]:
                    tp[d] = 1.
                    R['det'][jmax] = 1
                else:
                    fp[d] = 1.
        else:
            fp[d] = 1.

    # compute precision recall
    fp = np.cumsum(fp)
    tp = np.cumsum(tp)
    rec = tp / float(npos)
    # avoid divide by zero in case the first detection matches a difficult
    # ground truth
    prec = tp / np.maximum(tp + fp, np.finfo(np.float64).eps)
    ap = voc_ap(rec, prec, use_07_metric)

    return rec, prec, ap

参考：

目标检测01：常用评价指标（AP、AP50、AP@50:5:95、mAP） - 黎明程序员 - 博客园

【目标检测】一、目标检测中常见的评价指标_满船清梦压星河HK的博客-CSDN博客

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AP，mAP计算详解（代码全解） - 知乎