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深度学习目标检测——AP以及MAP

时间:2022-11-01 18:37:13浏览次数:83  
标签:11 MAP obj AP tp ap 深度 np


AP计算概述

深度学习目标检测——AP以及MAP_python

知道了​​AP​​​ 的定义,下一步就是理解​​AP​​​计算的实现,理论上可以通过积分来计算​​AP​​​,公式如下:
深度学习目标检测——AP以及MAP_python_02
但通常情况下都是使用近似或者插值的方法来计算 AP。

近似计算AP

深度学习目标检测——AP以及MAP_python_03

  • 近似计算 AP(​​approximated average precision​​),这种计算方式是 approximated 形式的;
  • 很显然位于一条竖直线上的点对计算AP没有贡献;
  • 这里 ​​N​​​ 为数据总量,​​k​​​ 为每个样本点的索引, 深度学习目标检测——AP以及MAP_python_04

近似计算​AP​​​和绘制​​PR​​曲线代码如下:

import numpy as np
import matplotlib.pyplot as plt

class_names = ["car", "pedestrians", "bicycle"]

def draw_PR_curve(predict_scores, eval_labels, name, cls_idx=1):
"""calculate AP and draw PR curve, there are 3 types
Parameters:
@all_scores: single test dataset predict scores array, (-1, 3)
@all_labels: single test dataset predict label array, (-1, 3)
@cls_idx: the serial number of the AP to be calculated, example: 0,1,2,3...
"""
# print('sklearn Macro-F1-Score:', f1_score(predict_scores, eval_labels, average='macro'))
global class_names
fig, ax = plt.subplots(nrows=1, ncols=1, figsize=(15, 10))
# Rank the predicted scores from large to small, extract their corresponding index(index number), and generate an array
idx = predict_scores[:, cls_idx].argsort()[::-1]
eval_labels_descend = eval_labels[idx]
pos_gt_num = np.sum(eval_labels == cls_idx) # number of all gt

predict_results = np.ones_like(eval_labels)
tp_arr = np.logical_and(predict_results == cls_idx, eval_labels_descend == cls_idx) # ndarray
fp_arr = np.logical_and(predict_results == cls_idx, eval_labels_descend != cls_idx)

tp_cum = np.cumsum(tp_arr).astype(float) # ndarray, Cumulative sum of array elements.
fp_cum = np.cumsum(fp_arr).astype(float)

precision_arr = tp_cum / (tp_cum + fp_cum) # ndarray
recall_arr = tp_cum / pos_gt_num
ap = 0.0
prev_recall = 0
for p, r in zip(precision_arr, recall_arr):
ap += p * (r - prev_recall)
# pdb.set_trace()
prev_recall = r
print("------%s, ap: %f-----" % (name, ap))

fig_label = '[%s, %s] ap=%f' % (name, class_names[cls_idx], ap)
ax.plot(recall_arr, precision_arr, label=fig_label)

ax.legend(loc="lower left")
ax.set_title("PR curve about class: %s" % (class_names[cls_idx]))
ax.set(xticks=np.arange(0., 1, 0.05), yticks=np.arange(0., 1, 0.05))
ax.set(xlabel="recall", ylabel="precision", xlim=[0, 1], ylim=[0, 1])

fig.savefig("./pr-curve-%s.png" % class_names[cls_idx])
plt.close(fig)

插值计算AP

插值计算(​​Interpolated average precision​​​) AP 的公式的演变过程这里不做讨论,详情可以参考这篇​​文章​​​,我这里的公式和图也是参考此文章的。​​11点插值计算方式计算AP公式​​​如下:
深度学习目标检测——AP以及MAP_目标检测_05

  • 这是通常意义上的 11 points_Interpolated 形式的 AP,选取固定的 {0,0.1,0.2,…,1.0} 11个阈值,这个在PASCAL2007中有使用
  • 这里因为参与计算的只有11个点,所以 K=11,称为11points_Interpolated,k为阈值索引
  • 深度学习目标检测——AP以及MAP_上传_06

[外链图片转存失败,源站可能有防盗链机制,建议将图片保存下来直接上传(img-KaGONv2a-1662646748371)(…/…/images/插值计算AP的PR曲线图.png)]

从曲线上看,真实 ​​AP< approximated AP < Interpolated AP​​​,​​11-points Interpolated AP​​​ 可能大也可能小,当数据量很多的时候会接近于 ​​Interpolated AP​​​,与 ​​Interpolated AP​​​ 不同,前面的公式中计算 ​​AP​​​ 时都是对 ​​PR​​​ 曲线的面积估计,PASCAL的论文里给出的公式就更加简单粗暴了,直接计算​​11​​​ 个阈值处的 ​​precision​​​ 的平均值。​​PASCAL​​​ 论文给出的 ​​11​​​ 点计算 ​​AP​​ 的公式如下。

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三,AP计算实现

1, 在给定 ​​recal​​​ 和 ​​precision​​​ 的条件下计算 ​​AP​​:

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

2,给定目标检测结果文件和测试集标签文件 ​​xml​​​ 等计算 ​​AP​​:

def parse_rec(filename):
""" Parse a PASCAL VOC xml file
Return : list, element is dict.
"""
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_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 result file
detpath.format(classname) should produce the detection results file.
annopath: Path to annotations file
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, '%s_annots.pkl' % imagesetfile)
# 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 annotations
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, 'wb') as f:
pickle.dump(recs, f)
else:
# load
with open(cachefile, 'rb') as f:
try:
recs = pickle.load(f)
except:
recs = pickle.load(f, encoding='bytes')

# 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])

nd = len(image_ids)
tp = np.zeros(nd)
fp = np.zeros(nd)

if BB.shape[0] > 0:
# 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
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

四,map计算方法

因为 mAP 值的计算是对数据集中所有类别的 AP 值求平均,所以我们要计算 mAP,首先得知道某一类别的 AP 值怎么求。不同数据集的某类别的 AP 计算方法大同小异,主要分为三种:

(1)在 ​​VOC2007​​​,只需要选取当Recall >= 0, 0.1, 0.2, …, 1共11个点时的Precision最大值,然后AP就是这11个Precision的平均值,map就是所有类别AP值的平均。​​VOC​​​ 数据集中计算 ​​AP​​​ 的代码(用的是插值计算方法,代码出自​​py-faster-rcnn仓库​​)

(2)在 ​​VOC2010​​​ 及以后,需要针对每一个不同的 ​​Recall​​​ 值(包括0和1),选取其大于等于这些 ​​Recall​​​ 值时的 ​​Precision​​ 最大值,然后计算PR曲线下面积作为 AP 值,map 就是所有类别 AP 值的平均。

(3)​​COCO​​ 数据集,设定多个 IOU 阈值(0.5-0.95,0.05为步长),在每一个IOU阈值下都有某一类别的 AP 值,然后求不同 IOU 阈值下的 AP 平均,就是所求的最终的某类别的AP值。


标签:11,MAP,obj,AP,tp,ap,深度,np
From: https://blog.51cto.com/u_13859040/5814673

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