特征匹配
一、特征匹配与描述
在本小节中，我们将会了解到如何匹配不同图像间的特征，以及OpenCV中的蛮力匹配器和FLANN匹配器
1. 蛮力匹配器的基本概念
蛮力匹配器很简单。 它采用第一组中一个特征的描述符，并使用一些距离计算与第二组中的所有其他特征匹配。 并返回最接近的那个。
对于 BF 匹配器，首先我们必须使用 cv.BFMatcher() 创建 BFMatcher 对象。 它需要两个可选参数。
- 第一个是 normType。 它指定要使用的距离测量。 默认情况下，它是 cv.NORM_L2。 它 用于 SIFT、SURF 等（cv.NORM_L1同样适用）。 对于基于二进制字符串的描述符，如 ORB、BRIEF、BRISK 等，应使用 cv.NORM_HAMMING，它使用汉明距离作为度量。 如果 ORB 使用 WTA_K == 3 或 4，则应使用 cv.NORM_HAMMING2。
- 第二个参数是布尔变量 crossCheck，默认为 false。 如果为真，则 Matcher 仅返回值为 (i,j) 的匹配项，使得集合 A 中的第 i 个描述符具有集合 B 中的第 j 个描述符作为最佳匹配，反之亦然。 也就是说，两组中的两个特征应该相互匹配(也就是最佳匹配事一对一对应的，A中i对应B中的最佳匹配是j，那么B中j的最佳匹配也一定要为A中i才返回)。 它提供了一致的结果，是 D.Lowe 在 SIFT 论文中提出的比率测试的一个很好的替代方案。
创建后，两个重要的方法是 ：
- BFMatcher.match() ：返回最佳匹配
- BFMatcher.knnMatch()：返回 k 最佳匹配，其中 k 由用户指定。 当我们需要对此进行额外操作时，它可能很有用。
就像我们使用 cv.drawKeypoints() 来绘制关键点一样，
- cv.drawMatches() 帮助我们绘制匹配。 它水平堆叠两张图像，并从第一张图像到第二张图像绘制线条，显示最佳匹配。
- cv.drawMatchesKnn 绘制所有 k 个最佳匹配。 如果 k=2，它将为每个关键点绘制两条匹配线。 因此，如果我们想选择性地绘制它，我们必须传递一个遮罩mask。用法如下：
- cv.drawMatches( img1, keypoints1, img2, keypoints2, matches1to2, outImg[, matchColor[, singlePointColor[, matchesMask[, flags]]]] ) -> outImg
- cv.drawMatches( img1, keypoints1, img2, keypoints2, matches1to2, outImg, matchesThickness[, matchColor[, singlePointColor[, matchesMask[, flags]]]] ) -> outImg
- cv.drawMatchesKnn( img1, keypoints1, img2, keypoints2, matches1to2, outImg[, matchColor[, singlePointColor[, matchesMask[, flags]]]] ) -> out
让我们看一个 SIFT 和 ORB 的示例（两者都使用不同的距离测量）。
import cv2 as cv
import numpy as np
import matplotlib
import matplotlib.pyplot as plt
%matplotlib inline
def cv_show(name, img):
cv.imshow(name, img)
cv.waitKey(0)
cv.destroyAllWindows()
def compare(imgs):
# for i in range(len(imgs)):
# imgs[i][:,-3:-1,:] = [255,255,255]
res = np.hstack(imgs)
cv_show('Compare', res)
A. 使用ORB描述符的蛮力匹配
在这里，我们将看到一个关于如何在两张图像之间匹配特征的简单示例。 在这种情况下，我有一个 queryImage 和一个 trainImage。 我们将尝试使用特征匹配在 trainImage 中找到 queryImage。 （图像是 /samples/data/box.png 和 /samples/data/box_in_scene.png）
我们使用 ORB 描述符来匹配特征。 因此，让我们从加载图像、查找描述符等开始。
img = cv.imread('ipad.png',0)
others = cv.imread('others.png',0)
# 修改图像大小
img = cv.resize(img, (0,0), fx = 0.2, fy = 0.2)
others = cv.resize(others, (0,0), fx = 0.2, fy = 0.2)
# 初始化ORB检测器
orb = cv.ORB_create()
# 使用ORB检测关键点和描述符
kp1, des1 = orb.detectAndCompute(img,None)
kp2, des2 = orb.detectAndCompute(others,None)
接下来我们创建一个带有距离测量 cv.NORM_HAMMING 的 BFMatcher 对象（因为我们使用的是 ORB）并打开 crossCheck 以获得更好的结果。 然后我们使用 Matcher.match() 方法来获得两个图像中的最佳匹配。 我们按照距离的升序对它们进行排序，以便最佳匹配（距离低）排在前面。 然后我们只绘制前 10 个最佳匹配（只是为了可见性。您可以随意增加）
# 创建蛮力匹配器对象
bf = cv.BFMatcher(cv.NORM_HAMMING, crossCheck=True)
# 对描述符进行匹配
matches = bf.match(des1,des2)
# 根据海明距离对匹配结果集进行排序
matches = sorted(matches, key = lambda x:x.distance)
# 将匹配长度较高的前10对特征点绘出
res = cv.drawMatches(img,kp1,others,kp2,matches[:10],None,flags=cv.DrawMatchesFlags_NOT_DRAW_SINGLE_POINTS)
cv_show('result', res)
匹配器对象是什么？
matches = bf.match(des1,des2) 行的结果是 DMatch 对象的列表。 此 DMatch 对象具有以下属性：
- DMatch.distance - 描述符之间的距离。 越低越好。
- DMatch.trainIdx - 样本图像描述符中的描述符索引
- DMatch.queryIdx - 测试图像描述符中描述符的索引
- DMatch.imgIdx - 训练图像的索引。
B.使用SIFT描述符以及Ratio测试的蛮力匹配
这一次，我们将使用 BFMatcher.knnMatch() 来获得 k 个最佳匹配。 在这个例子中，我们将取 k=2，以便我们可以应用 D.Lowe 在他的论文中解释的比率测试。
img1 = cv.imread('ipad.png',cv.IMREAD_GRAYSCALE) # queryImage
img2 = cv.imread('others.png',cv.IMREAD_GRAYSCALE) # trainImage
img1 = cv.resize(img1, (0,0), fx = 0.2, fy = 0.2)
img2 = cv.resize(img2, (0,0), fx = 0.2, fy = 0.2)
# Initiate SIFT detector
sift = cv.SIFT_create()
# find the keypoints and descriptors with SIFT
kp1, des1 = sift.detectAndCompute(img1,None)
kp2, des2 = sift.detectAndCompute(img2,None)
# BFMatcher with default params
bf = cv.BFMatcher()
matches = bf.knnMatch(des1,des2,k=2)
# Apply ratio test
good = []
for m,n in matches:
if m.distance < 0.75*n.distance:
good.append([m])
# cv.drawMatchesKnn expects list of lists as matches.
img3 = cv.drawMatchesKnn(img1,kp1,img2,kp2,good,None,flags=cv.DrawMatchesFlags_NOT_DRAW_SINGLE_POINTS)
cv_show('res', img3)
补充：match和knnmatch的返回差别
# match返回值
bf = cv.BFMatcher_create()
matches = bf.match(des1, des2)
for matche in matches[:4]:
print(matche)
<DMatch 0000029466B12830>
<DMatch 0000029466B120D0>
<DMatch 0000029466B12770>
<DMatch 0000029466B123D0>
可以看出，match返回的都是单个Dmatch数据，那么这个这个DMatch数据结构究竟是什么呢？ 它包含三个非常重要的数据分别是queryIdx，trainIdx，distance 先说一下这三个分别是什么在演示其用途：
- queryIdx：测试图像的特征点描述符的下标（第几个特征点描述符），同时也是描述符对应特征点的下标。
- trainIdx：样本图像的特征点描述符下标,同时也是描述符对应特征点的下标。
- distance：代表这对匹配的特征点描述符的欧式距离，数值越小也就说明俩个特征点越相近。
bf = cv.BFMatcher_create()
matches = bf.match(des1, des2)
for matche in matches[:4]:
print(matche)
print(matche.queryIdx)
print(matche.trainIdx)
print(matche.distance)
<DMatch 0000029455804710>
0
1417
295.50634765625
<DMatch 0000029466B122B0>
1
1550
273.9197082519531
<DMatch 0000029465E90C30>
2
1874
215.26495361328125
<DMatch 0000029465E90950>
3
2061
143.17471313476562
每个特征点本身也具有以下属性：
- .pt:关键点坐标，
- .angle：表示关键点方向，
- .response表示响应强度，
- .size:表示该点的直径大小。
# Knnmatch返回值，k = 2 表明对一个关键点绘制两条匹配线(两个对应点)
matches = bf.knnMatch(des1, des2, k=2)
# matchesMask = [[0, 0] for i in range(len(matches))]
for i, matche in enumerate(matches):
print(matche)
(<DMatch 0000029466B122D0>, <DMatch 0000029466B124D0>)
(<DMatch 0000029466B12030>, <DMatch 0000029466B124B0>)
(<DMatch 0000029466B12190>, <DMatch 0000029466B12130>)
(<DMatch 0000029466B126F0>, <DMatch 0000029466B12310>)
(<DMatch 0000029466B125B0>, <DMatch 0000029466B12750>)
(<DMatch 0000029466B12270>, <DMatch 0000029466B12430>)
(<DMatch 0000029466B12650>, <DMatch 0000029466B12510>)
(<DMatch 0000029466B12050>, <DMatch 0000029466B12110>)
(<DMatch 0000029466B12150>, <DMatch 0000029466B122F0>)
(<DMatch 0000029466B127B0>, <DMatch 0000029466B121D0>)
(<DMatch 0000029466B126B0>, <DMatch 0000029466B126D0>)
(<DMatch 0000029466B12850>, <DMatch 0000029466B121B0>)
(<DMatch 0000029466B12490>, <DMatch 0000029466B12610>)
(<DMatch 0000029466B12890>, <DMatch 0000029466B12590>)
(<DMatch 0000029466B128F0>, <DMatch 0000029466B12910>)
(<DMatch 0000029466B12930>, <DMatch 0000029466B12950>)
(<DMatch 0000029466B12970>, <DMatch 0000029466B12990>)
(<DMatch 0000029466B129D0>, <DMatch 0000029466B129F0>)
(<DMatch 0000029466B12A10>, <DMatch 0000029466B12A30>)
(<DMatch 0000029466B12A50>, <DMatch 0000029466B12A70>)
(<DMatch 0000029466B12A90>, <DMatch 0000029466B12AB0>)
(<DMatch 0000029466B12AD0>, <DMatch 0000029466B12AF0>)
(<DMatch 0000029466B12B10>, <DMatch 0000029466B12B30>)
(<DMatch 0000029466B12B50>, <DMatch 0000029466B12B70>)
(<DMatch 0000029466B12B90>, <DMatch 0000029466B12BB0>)
(<DMatch 0000029466B12BD0>, <DMatch 0000029466B12BF0>)
(<DMatch 0000029466B12C10>, <DMatch 0000029466B12C30>)
(<DMatch 0000029466B12C50>, <DMatch 0000029466B12C70>)
(<DMatch 0000029466B12C90>, <DMatch 0000029466B12CB0>)
(<DMatch 0000029466B12CD0>, <DMatch 0000029466B12CF0>)
(<DMatch 0000029466B12D10>, <DMatch 0000029466B12D30>)
(<DMatch 0000029466B12D50>, <DMatch 0000029466B12D70>)
(<DMatch 0000029466B12D90>, <DMatch 0000029466B12DB0>)
(<DMatch 0000029466B12DD0>, <DMatch 0000029466B12DF0>)
(<DMatch 0000029466B12E10>, <DMatch 0000029466B12E30>)
(<DMatch 0000029466B12E50>, <DMatch 0000029466B12E70>)
(<DMatch 0000029466B12E90>, <DMatch 0000029466B12EB0>)
(<DMatch 0000029466B12ED0>, <DMatch 0000029466B12EF0>)
(<DMatch 0000029466B12F10>, <DMatch 0000029466B12F30>)
(<DMatch 0000029466B12F50>, <DMatch 0000029466B12F70>)
(<DMatch 0000029466B12F90>, <DMatch 0000029466B12FB0>)
(<DMatch 0000029466B12FD0>, <DMatch 000002945582FE10>)
(<DMatch 0000029465E90950>, <DMatch 0000029465E90ED0>)
(<DMatch 0000029465E90F70>, <DMatch 0000029465E90D10>)
(<DMatch 0000029465E90E10>, <DMatch 0000029465E906D0>)
(<DMatch 0000029465E90EF0>, <DMatch 0000029465E909B0>)
(<DMatch 0000029465E90C50>, <DMatch 0000029465E90990>)
(<DMatch 0000029465E90DB0>, <DMatch 0000029465E90EB0>)
(<DMatch 0000029465E90C10>, <DMatch 0000029465E90BB0>)
(<DMatch 0000029465E90610>, <DMatch 0000029466B10C50>)
(<DMatch 0000029466B10F50>, <DMatch 0000029466B10710>)
(<DMatch 0000029466B109B0>, <DMatch 0000029466B10FB0>)
(<DMatch 0000029466B10890>, <DMatch 0000029466B10FD0>)
(<DMatch 0000029466B10F30>, <DMatch 0000029466B10BB0>)
(<DMatch 0000029466B10470>, <DMatch 0000029466B10F90>)
(<DMatch 0000029466B102B0>, <DMatch 0000029466B10E10>)
(<DMatch 0000029466B10830>, <DMatch 0000029466B10E70>)
(<DMatch 0000029466B10E90>, <DMatch 0000029466B108D0>)
(<DMatch 0000029466B10CF0>, <DMatch 0000029466B106B0>)
(<DMatch 0000029466B10DB0>, <DMatch 0000029466B105D0>)
(<DMatch 0000029466B10150>, <DMatch 0000029466B10670>)
(<DMatch 0000029466B10510>, <DMatch 0000029466B10EB0>)
(<DMatch 0000029466B10C30>, <DMatch 0000029466B10D30>)
(<DMatch 0000029466B10CB0>, <DMatch 0000029466B10DF0>)
(<DMatch 0000029466B10EF0>, <DMatch 0000029466B10D90>)
(<DMatch 0000029466B10810>, <DMatch 0000029466B10C10>)
(<DMatch 0000029466B105F0>, <DMatch 0000029466B10AD0>)
(<DMatch 0000029466B104D0>, <DMatch 0000029466B10DD0>)
(<DMatch 0000029466B10970>, <DMatch 0000029466B1D7B0>)
(<DMatch 0000029466B1D3B0>, <DMatch 0000029466B1DA10>)
(<DMatch 0000029466B1D770>, <DMatch 0000029466B1D150>)
(<DMatch 0000029466B1D050>, <DMatch 0000029466B1D9D0>)
(<DMatch 0000029466B1D6B0>, <DMatch 0000029466B1DC70>)
(<DMatch 0000029466B1D970>, <DMatch 0000029466B1D850>)
(<DMatch 0000029466B1D070>, <DMatch 0000029466B1DB30>)
(<DMatch 0000029466B1D990>, <DMatch 0000029466B1DAD0>)
(<DMatch 0000029466B1DD90>, <DMatch 0000029466B1D6F0>)
(<DMatch 0000029466B1DAF0>, <DMatch 0000029466B1DA30>)
(<DMatch 0000029466B1D670>, <DMatch 0000029466B1D0B0>)
(<DMatch 0000029466B1D630>, <DMatch 0000029466B1D750>)
(<DMatch 0000029466B1D450>, <DMatch 0000029466B1DF70>)
(<DMatch 0000029466B1DD10>, <DMatch 0000029466B1DD50>)
(<DMatch 0000029466B1DB70>, <DMatch 0000029466B1DDB0>)
(<DMatch 0000029466B1DEB0>, <DMatch 0000029466B1DF30>)
(<DMatch 0000029466B1D390>, <DMatch 0000029466B1DC50>)
(<DMatch 0000029466B1DCF0>, <DMatch 0000029466B1DDD0>)
(<DMatch 0000029466B1DE90>, <DMatch 0000029466B1DF50>)
(<DMatch 0000029466B1DC30>, <DMatch 0000029466B1D430>)
(<DMatch 0000029466B1D410>, <DMatch 0000029466B1D470>)
(<DMatch 0000029466B1DD30>, <DMatch 0000029466B1DE50>)
(<DMatch 0000029466B1DF90>, <DMatch 0000029466B1D9F0>)
(<DMatch 0000029466B1D510>, <DMatch 0000029466B1DFB0>)
(<DMatch 0000029466B1D030>, <DMatch 0000029466B1D650>)
(<DMatch 0000029466B1D5D0>, <DMatch 0000029466B1DC10>)
(<DMatch 0000029466B1DFD0>, <DMatch 0000029466B1DC90>)
(<DMatch 0000029466B1DDF0>, <DMatch 0000029466B1D3F0>)
(<DMatch 0000029466B1D8F0>, <DMatch 0000029466B1D950>)
(<DMatch 0000029466B1D6D0>, <DMatch 0000029466B1DD70>)
(<DMatch 0000029466B1D710>, <DMatch 0000029466B1DF10>)
(<DMatch 0000029466B1DBF0>, <DMatch 0000029466B1D610>)
(<DMatch 0000029466B1DA50>, <DMatch 0000029466B1D7D0>)
(<DMatch 0000029466B1DBD0>, <DMatch 0000029466B1D890>)
(<DMatch 0000029466B1D130>, <DMatch 0000029466B1D570>)
(<DMatch 0000029466B1D2B0>, <DMatch 0000029466B1D3D0>)
(<DMatch 0000029466B1D0F0>, <DMatch 0000029466B1D330>)
(<DMatch 0000029466B1D2F0>, <DMatch 0000029466B1DB50>)
(<DMatch 0000029466B1D9B0>, <DMatch 0000029466B1DA90>)
(<DMatch 0000029466B1D830>, <DMatch 0000029466B1D810>)
(<DMatch 0000029466B1DA70>, <DMatch 0000029466B1DB90>)
(<DMatch 0000029466B1D790>, <DMatch 0000029466B1D590>)
(<DMatch 0000029466B1D870>, <DMatch 0000029466B1D1D0>)
(<DMatch 0000029466B1D550>, <DMatch 0000029466B1D910>)
(<DMatch 0000029466B1DAB0>, <DMatch 0000029466B1D1B0>)
(<DMatch 0000029466B1D490>, <DMatch 0000029466B1D7F0>)
(<DMatch 0000029466B1D5B0>, <DMatch 0000029466B1DCD0>)
(<DMatch 0000029466B1D5F0>, <DMatch 0000029466B1D230>)
(<DMatch 0000029466B1D4B0>, <DMatch 0000029466B1DE70>)
(<DMatch 0000029466B1DE30>, <DMatch 0000029466B1D350>)
(<DMatch 0000029466B1D090>, <DMatch 0000029466B1D250>)
(<DMatch 0000029466B1D270>, <DMatch 0000029466B1D8D0>)
(<DMatch 0000029466B1D290>, <DMatch 0000029466B1DED0>)
(<DMatch 0000029466B1D530>, <DMatch 0000029466B1D190>)
(<DMatch 0000029465E45E70>, <DMatch 0000029403B2F530>)
(<DMatch 0000029403B2F510>, <DMatch 0000029403B2F030>)
(<DMatch 0000029403B2F050>, <DMatch 0000029403B2F070>)
(<DMatch 0000029403B2F090>, <DMatch 0000029403B2F0B0>)
(<DMatch 0000029403B2F0D0>, <DMatch 0000029403B2F0F0>)
(<DMatch 0000029403B2F110>, <DMatch 0000029403B2F130>)
(<DMatch 0000029403B2F150>, <DMatch 0000029403B2F170>)
(<DMatch 0000029403B2F190>, <DMatch 0000029403B2F1B0>)
(<DMatch 0000029403B2F1D0>, <DMatch 0000029403B2F1F0>)
(<DMatch 0000029403B2F210>, <DMatch 0000029403B2F230>)
(<DMatch 0000029403B2F250>, <DMatch 0000029403B2F270>)
(<DMatch 0000029403B2F290>, <DMatch 0000029403B2F2B0>)
(<DMatch 0000029403B2F2D0>, <DMatch 0000029403B2F2F0>)
(<DMatch 0000029403B2F310>, <DMatch 0000029403B2F330>)
(<DMatch 0000029403B2F350>, <DMatch 0000029403B2F370>)
(<DMatch 0000029403B2F390>, <DMatch 0000029403B2F3B0>)
(<DMatch 0000029403B2F3D0>, <DMatch 0000029403B2F3F0>)
(<DMatch 0000029403B2F410>, <DMatch 0000029403B2F430>)
(<DMatch 0000029403B2F450>, <DMatch 0000029403B2F470>)
(<DMatch 0000029403B2F490>, <DMatch 0000029403B2F4B0>)
(<DMatch 0000029403B2F4D0>, <DMatch 0000029403B2F4F0>)
(<DMatch 0000029403B6D510>, <DMatch 0000029403B6D530>)
(<DMatch 0000029403B6D550>, <DMatch 0000029403B6D570>)
(<DMatch 0000029403B6D590>, <DMatch 0000029403B6D5B0>)
(<DMatch 0000029403B6D5D0>, <DMatch 0000029403B6D5F0>)
(<DMatch 0000029403B6D610>, <DMatch 0000029403B6D630>)
(<DMatch 0000029403B6D650>, <DMatch 0000029403B6D670>)
(<DMatch 0000029403B6D690>, <DMatch 0000029403B6D6B0>)
(<DMatch 0000029403B6D6D0>, <DMatch 0000029403B6D6F0>)
(<DMatch 0000029403B6D710>, <DMatch 0000029403B6D730>)
(<DMatch 0000029403B6D750>, <DMatch 0000029403B6D770>)
(<DMatch 0000029403B6D790>, <DMatch 0000029403B6D7B0>)
(<DMatch 0000029403B6D7D0>, <DMatch 0000029403B6D7F0>)
(<DMatch 0000029403B6D810>, <DMatch 0000029403B6D830>)
(<DMatch 0000029403B6D850>, <DMatch 0000029403B6D870>)
(<DMatch 0000029403B6D890>, <DMatch 0000029403B6D8B0>)
(<DMatch 0000029403B6D8D0>, <DMatch 0000029403B6D8F0>)
(<DMatch 0000029403B6D930>, <DMatch 0000029403B6D950>)
(<DMatch 0000029403B6D970>, <DMatch 0000029403B6D990>)
(<DMatch 0000029403B6D9B0>, <DMatch 0000029403B6D9D0>)
(<DMatch 0000029403B6D9F0>, <DMatch 0000029403B6DA10>)
(<DMatch 0000029403B6DA30>, <DMatch 0000029403B6DA50>)
(<DMatch 0000029403B6DA70>, <DMatch 0000029403B6DA90>)
(<DMatch 0000029403B6DAB0>, <DMatch 0000029403B6DAD0>)
(<DMatch 0000029403B6DAF0>, <DMatch 0000029403B6DB10>)
(<DMatch 0000029403B6DB30>, <DMatch 0000029403B6DB50>)
(<DMatch 0000029403B6DB70>, <DMatch 0000029403B6DB90>)
(<DMatch 0000029403B6DBB0>, <DMatch 0000029403B6DBD0>)
(<DMatch 0000029403B6DBF0>, <DMatch 0000029403B6DC10>)
(<DMatch 0000029403B6DC30>, <DMatch 0000029403B6DC50>)
(<DMatch 0000029403B6DC70>, <DMatch 0000029403B6DC90>)
(<DMatch 0000029403B6DCB0>, <DMatch 0000029403B6DCD0>)
(<DMatch 0000029403B6DCF0>, <DMatch 0000029403B6DD10>)
(<DMatch 0000029403B6DD30>, <DMatch 0000029403B6DD50>)
(<DMatch 0000029403B6DD70>, <DMatch 0000029403B6DD90>)
(<DMatch 0000029403B6DDB0>, <DMatch 0000029403B6DDD0>)
(<DMatch 0000029403B6DDF0>, <DMatch 0000029403B6DE10>)
(<DMatch 0000029403B6DE30>, <DMatch 0000029403B6DE50>)
(<DMatch 0000029403B6DE70>, <DMatch 0000029403B6DE90>)
(<DMatch 0000029403B6DEB0>, <DMatch 0000029403B6DED0>)
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(<DMatch 0000029466B2FEB0>, <DMatch 0000029466B2FED0>)
(<DMatch 0000029466B2FEF0>, <DMatch 0000029466B2FF10>)
(<DMatch 0000029466B2FF30>, <DMatch 0000029466B2FF50>)
(<DMatch 0000029466B2FF70>, <DMatch 0000029466B2FF90>)
(<DMatch 0000029466B2FFB0>, <DMatch 0000029466B2FFD0>)
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(<DMatch 0000029403B03070>, <DMatch 0000029403B03090>)
(<DMatch 0000029403B030B0>, <DMatch 0000029403B030D0>)
(<DMatch 0000029403B030F0>, <DMatch 0000029403B03110>)
(<DMatch 0000029403B03130>, <DMatch 0000029403B03150>)
(<DMatch 0000029403B03170>, <DMatch 0000029403B03190>)
(<DMatch 0000029403B031B0>, <DMatch 0000029403B031D0>)
(<DMatch 0000029403B031F0>, <DMatch 0000029403B03210>)
(<DMatch 0000029403B03230>, <DMatch 0000029403B03250>)
(<DMatch 0000029403B03270>, <DMatch 0000029403B03290>)
(<DMatch 0000029403B032B0>, <DMatch 0000029403B032D0>)
(<DMatch 0000029403B032F0>, <DMatch 0000029403B03310>)
(<DMatch 0000029403B03330>, <DMatch 0000029403B03350>)
(<DMatch 0000029403B03370>, <DMatch 0000029403B03390>)
(<DMatch 0000029403B033B0>, <DMatch 0000029403B033D0>)
(<DMatch 0000029403B033F0>, <DMatch 0000029403B03410>)
(<DMatch 0000029403B03430>, <DMatch 0000029403B03450>)
(<DMatch 0000029403B03470>, <DMatch 0000029403B03490>)
(<DMatch 0000029403B034B0>, <DMatch 0000029403B034D0>)
(<DMatch 0000029403B034F0>, <DMatch 0000029403B03510>)
(<DMatch 0000029403B03530>, <DMatch 0000029403B03550>)
(<DMatch 0000029403B03570>, <DMatch 0000029403B03590>)
(<DMatch 0000029403B035B0>, <DMatch 0000029403B035F0>)
(<DMatch 0000029403B03610>, <DMatch 0000029403B03630>)
(<DMatch 0000029403B03650>, <DMatch 0000029403B03670>)
(<DMatch 0000029403B03690>, <DMatch 0000029403B036B0>)
(<DMatch 0000029403B036D0>, <DMatch 0000029403B036F0>)
(<DMatch 0000029403B03710>, <DMatch 0000029403B03730>)
(<DMatch 0000029403B03750>, <DMatch 0000029403B03770>)
(<DMatch 0000029403B03790>, <DMatch 0000029403B037B0>)
(<DMatch 0000029403B037D0>, <DMatch 0000029403B037F0>)
(<DMatch 0000029403B03810>, <DMatch 0000029403B03830>)
(<DMatch 0000029403B03870>, <DMatch 0000029403B03890>)
(<DMatch 0000029403B038B0>, <DMatch 0000029403B038D0>)
(<DMatch 0000029403B038F0>, <DMatch 0000029403B03910>)
(<DMatch 0000029403B03930>, <DMatch 0000029403B03950>)
(<DMatch 0000029403B03970>, <DMatch 0000029403B03990>)
(<DMatch 0000029403B039B0>, <DMatch 0000029403B039F0>)
(<DMatch 0000029403B03A10>, <DMatch 0000029403B03A30>)
(<DMatch 0000029403B03A50>, <DMatch 0000029403B03A70>)
(<DMatch 0000029403B03A90>, <DMatch 0000029403B03AB0>)
(<DMatch 0000029403B03AF0>, <DMatch 0000029403B03B30>)
(<DMatch 0000029403B03B50>, <DMatch 0000029403B03B70>)
(<DMatch 0000029403B03B90>, <DMatch 0000029403B03BB0>)
(<DMatch 0000029403B03BD0>, <DMatch 0000029403B03BF0>)
(<DMatch 0000029403B03C10>, <DMatch 0000029403B03C30>)
(<DMatch 0000029403B03C50>, <DMatch 0000029403B03C70>)
(<DMatch 0000029403B03C90>, <DMatch 0000029403B03CB0>)
(<DMatch 0000029403B03CD0>, <DMatch 0000029403B03CF0>)
(<DMatch 0000029403B03D10>, <DMatch 0000029403B03D30>)
(<DMatch 0000029403B03D50>, <DMatch 0000029403B03D70>)
(<DMatch 0000029403B03D90>, <DMatch 0000029403B03DB0>)
(<DMatch 0000029403B03DD0>, <DMatch 0000029403B03DF0>)
(<DMatch 0000029403B03E10>, <DMatch 0000029403B03E30>)
(<DMatch 0000029403B03E50>, <DMatch 0000029403B03E70>)
(<DMatch 0000029403B03E90>, <DMatch 0000029403B03EB0>)
(<DMatch 0000029403B03ED0>, <DMatch 0000029403B03EF0>)
(<DMatch 0000029403B03F10>, <DMatch 0000029403B03F30>)
(<DMatch 0000029403B03F50>, <DMatch 0000029403B03F70>)
(<DMatch 0000029403B03F90>, <DMatch 0000029403B03FB0>)
(<DMatch 0000029403B03FD0>, <DMatch 0000029403B07030>)
(<DMatch 0000029403B07050>, <DMatch 0000029403B07070>)
(<DMatch 0000029403B07090>, <DMatch 0000029403B070B0>)
(<DMatch 0000029403B070D0>, <DMatch 0000029403B070F0>)
(<DMatch 0000029403B07110>, <DMatch 0000029403B07130>)
(<DMatch 0000029403B07150>, <DMatch 0000029403B07170>)
(<DMatch 0000029403B07190>, <DMatch 0000029403B071B0>)
(<DMatch 0000029403B071D0>, <DMatch 0000029403B071F0>)
(<DMatch 0000029403B07210>, <DMatch 0000029403B07230>)
(<DMatch 0000029403B07250>, <DMatch 0000029403B07270>)
(<DMatch 0000029403B072B0>, <DMatch 0000029403B072D0>)
(<DMatch 0000029403B072F0>, <DMatch 0000029403B07310>)
(<DMatch 0000029403B07330>, <DMatch 0000029403B07350>)
(<DMatch 0000029403B07370>, <DMatch 0000029403B07390>)
(<DMatch 0000029403B073B0>, <DMatch 0000029403B073D0>)
(<DMatch 0000029403B073F0>, <DMatch 0000029403B07410>)
(<DMatch 0000029403B07430>, <DMatch 0000029403B07450>)
(<DMatch 0000029403B07470>, <DMatch 0000029403B07490>)
(<DMatch 0000029403B074B0>, <DMatch 0000029403B074D0>)
(<DMatch 0000029403B074F0>, <DMatch 0000029403B07510>)
(<DMatch 0000029403B07530>, <DMatch 0000029403B07550>)
(<DMatch 0000029403B07570>, <DMatch 0000029403B07590>)
(<DMatch 0000029403B075B0>, <DMatch 0000029403B075D0>)
(<DMatch 0000029403B075F0>, <DMatch 0000029403B07610>)
(<DMatch 0000029403B07630>, <DMatch 0000029403B07650>)
(<DMatch 0000029403B07670>, <DMatch 0000029403B07690>)
(<DMatch 0000029403B076B0>, <DMatch 0000029403B076D0>)
(<DMatch 0000029403B076F0>, <DMatch 0000029403B07710>)
(<DMatch 0000029403B07730>, <DMatch 0000029403B07750>)
(<DMatch 0000029403B07770>, <DMatch 0000029403B07790>)
(<DMatch 0000029403B077B0>, <DMatch 0000029403B077D0>)
(<DMatch 0000029403B077F0>, <DMatch 0000029403B07810>)
(<DMatch 0000029403B07830>, <DMatch 0000029403B07850>)
(<DMatch 0000029403B07870>, <DMatch 0000029403B07890>)
(<DMatch 0000029403B078B0>, <DMatch 0000029403B078F0>)
(<DMatch 0000029403B07910>, <DMatch 0000029403B07930>)
(<DMatch 0000029403B07970>, <DMatch 0000029403B07990>)
(<DMatch 0000029403B079B0>, <DMatch 0000029403B079D0>)
(<DMatch 0000029403B079F0>, <DMatch 0000029403B07A10>)
(<DMatch 0000029403B07A30>, <DMatch 0000029403B07A50>)
(<DMatch 0000029403B07A70>, <DMatch 0000029403B07A90>)
(<DMatch 0000029403B07AB0>, <DMatch 0000029403B07AD0>)
(<DMatch 0000029403B07AF0>, <DMatch 0000029403B07B10>)
(<DMatch 0000029403B07B30>, <DMatch 0000029403B07B70>)
(<DMatch 0000029403B07B90>, <DMatch 0000029403B07BB0>)
(<DMatch 0000029403B07BD0>, <DMatch 0000029403B07BF0>)
(<DMatch 0000029403B07C10>, <DMatch 0000029403B07C30>)
(<DMatch 0000029403B07C70>, <DMatch 0000029403B07C90>)
(<DMatch 0000029403B07CB0>, <DMatch 0000029403B07CD0>)
(<DMatch 0000029403B07CF0>, <DMatch 0000029403B07D10>)
(<DMatch 0000029403B07D30>, <DMatch 0000029403B07D50>)
(<DMatch 0000029403B07D70>, <DMatch 0000029403B07D90>)
(<DMatch 0000029403B07DB0>, <DMatch 0000029403B07DD0>)
(<DMatch 0000029403B07DF0>, <DMatch 0000029403B07E10>)
(<DMatch 0000029403B07E30>, <DMatch 0000029403B07E50>)
(<DMatch 0000029403B07E70>, <DMatch 0000029403B07E90>)
(<DMatch 0000029403B07EB0>, <DMatch 0000029403B07ED0>)
(<DMatch 0000029403B07EF0>, <DMatch 0000029403B07F10>)
(<DMatch 0000029403B07F30>, <DMatch 0000029403B07F50>)
(<DMatch 0000029403B07F70>, <DMatch 0000029403B07F90>)
(<DMatch 0000029403B07FB0>, <DMatch 0000029403B07FD0>)
(<DMatch 0000029403B09030>, <DMatch 0000029403B09050>)
(<DMatch 0000029403B09070>, <DMatch 0000029403B09090>)
(<DMatch 0000029403B090B0>, <DMatch 0000029403B090D0>)
(<DMatch 0000029403B090F0>, <DMatch 0000029403B09110>)
(<DMatch 0000029403B09130>, <DMatch 0000029403B09150>)
(<DMatch 0000029403B09170>, <DMatch 0000029403B091B0>)
(<DMatch 0000029403B091D0>, <DMatch 0000029403B091F0>)
(<DMatch 0000029403B09210>, <DMatch 0000029403B09230>)
(<DMatch 0000029403B09250>, <DMatch 0000029403B09270>)
(<DMatch 0000029403B09290>, <DMatch 0000029403B092B0>)
(<DMatch 0000029403B092D0>, <DMatch 0000029403B092F0>)
(<DMatch 0000029403B09310>, <DMatch 0000029403B09330>)
(<DMatch 0000029403B09350>, <DMatch 0000029403B09370>)
(<DMatch 0000029403B09390>, <DMatch 0000029403B093B0>)
(<DMatch 0000029403B093D0>, <DMatch 0000029403B093F0>)
(<DMatch 0000029403B09410>, <DMatch 0000029403B09430>)
(<DMatch 0000029403B09450>, <DMatch 0000029403B09470>)
(<DMatch 0000029403B09490>, <DMatch 0000029403B094B0>)
(<DMatch 0000029403B094D0>, <DMatch 0000029403B094F0>)
(<DMatch 0000029403B09510>, <DMatch 0000029403B09530>)
(<DMatch 0000029403B09550>, <DMatch 0000029403B09570>)
(<DMatch 0000029403B09590>, <DMatch 0000029403B095B0>)
(<DMatch 0000029403B095D0>, <DMatch 0000029403B095F0>)
(<DMatch 0000029403B09630>, <DMatch 0000029403B09650>)
(<DMatch 0000029403B09670>, <DMatch 0000029403B09690>)
(<DMatch 0000029403B096B0>, <DMatch 0000029403B096D0>)
(<DMatch 0000029403B096F0>, <DMatch 0000029403B09710>)
(<DMatch 0000029403B09730>, <DMatch 0000029403B09750>)
(<DMatch 0000029403B09770>, <DMatch 0000029403B09790>)
(<DMatch 0000029403B097B0>, <DMatch 0000029403B097D0>)
(<DMatch 0000029403B097F0>, <DMatch 0000029403B09810>)
(<DMatch 0000029403B09830>, <DMatch 0000029403B09850>)
(<DMatch 0000029403B09870>, <DMatch 0000029403B09890>)
(<DMatch 0000029403B098B0>, <DMatch 0000029403B098D0>)
(<DMatch 0000029403B098F0>, <DMatch 0000029403B09910>)
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(<DMatch 0000029403B099B0>, <DMatch 0000029403B099D0>)
(<DMatch 0000029403B099F0>, <DMatch 0000029403B09A10>)
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(<DMatch 0000029403B09A70>, <DMatch 0000029403B09A90>)
(<DMatch 0000029403B09AB0>, <DMatch 0000029403B1F4D0>)
(<DMatch 0000029403B1F4F0>, <DMatch 0000029403B1F510>)
(<DMatch 0000029403B1F530>, <DMatch 0000029403B1F550>)
(<DMatch 0000029403B1F570>, <DMatch 0000029403B1F5B0>)
(<DMatch 0000029403B1F5D0>, <DMatch 0000029403B1F5F0>)
(<DMatch 0000029403B1F610>, <DMatch 0000029403B1F630>)
(<DMatch 0000029403B1F650>, <DMatch 0000029403B1F670>)
(<DMatch 0000029403B1F690>, <DMatch 0000029403B1F6B0>)
(<DMatch 0000029403B1F6D0>, <DMatch 0000029403B1F6F0>)
(<DMatch 0000029403B1F710>, <DMatch 0000029403B1F730>)
(<DMatch 0000029403B1F750>, <DMatch 0000029403B1F770>)
(<DMatch 0000029403B1F790>, <DMatch 0000029403B1F7B0>)
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(<DMatch 0000029403B1F850>, <DMatch 0000029403B1F870>)
(<DMatch 0000029403B1F890>, <DMatch 0000029403B1F8B0>)
(<DMatch 0000029403B1F8D0>, <DMatch 0000029403B1F8F0>)
(<DMatch 0000029403B1F910>, <DMatch 0000029403B1F930>)
(<DMatch 0000029403B1F950>, <DMatch 0000029403B1F970>)
(<DMatch 0000029403B1F990>, <DMatch 0000029403B1F9B0>)
(<DMatch 0000029403B1F9D0>, <DMatch 0000029403B1F9F0>)
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(<DMatch 0000029403B67030>, <DMatch 0000029403B67050>)
(<DMatch 0000029403B67070>, <DMatch 0000029403B67090>)
(<DMatch 0000029403B670B0>, <DMatch 0000029403B670D0>)
(<DMatch 0000029403B670F0>, <DMatch 0000029403B67110>)
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(<DMatch 0000029403B67170>, <DMatch 0000029403B67190>)
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(<DMatch 0000029403B55350>, <DMatch 0000029403B55370>)
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(<DMatch 0000029403B553D0>, <DMatch 0000029403B553F0>)
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(<DMatch 0000029403B55610>, <DMatch 0000029403B55630>)
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(<DMatch 0000029403B55F90>, <DMatch 0000029403B55FB0>)
(<DMatch 0000029403B55FD0>, <DMatch 0000029403B50030>)
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(<DMatch 0000029403B50090>, <DMatch 0000029403B500B0>)
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(<DMatch 0000029403B501D0>, <DMatch 0000029403B501F0>)
(<DMatch 0000029403B50210>, <DMatch 0000029403B50230>)
(<DMatch 0000029403B50250>, <DMatch 0000029403B50270>)
(<DMatch 0000029403B50290>, <DMatch 0000029403B502B0>)
(<DMatch 0000029403B502D0>, <DMatch 0000029403B502F0>)
(<DMatch 0000029403B50310>, <DMatch 0000029403B50330>)
(<DMatch 0000029403B50350>, <DMatch 0000029403B50370>)
(<DMatch 0000029403B50390>, <DMatch 0000029403B503B0>)
(<DMatch 0000029403B503D0>, <DMatch 0000029403B503F0>)
(<DMatch 0000029403B50410>, <DMatch 0000029403B50430>)
(<DMatch 0000029403B50450>, <DMatch 0000029403B50470>)
(<DMatch 0000029403B50490>, <DMatch 0000029403B504B0>)
(<DMatch 0000029403B504D0>, <DMatch 0000029403B504F0>)
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(<DMatch 0000029403B50590>, <DMatch 0000029403B505B0>)
(<DMatch 0000029403B505D0>, <DMatch 0000029403B505F0>)
(<DMatch 0000029403B50610>, <DMatch 0000029403B50630>)
(<DMatch 0000029403B50650>, <DMatch 0000029403B50670>)
(<DMatch 0000029403B50690>, <DMatch 0000029403B506B0>)
(<DMatch 0000029403B506D0>, <DMatch 0000029403B506F0>)
(<DMatch 0000029403B50710>, <DMatch 0000029403B50730>)
(<DMatch 0000029403B50750>, <DMatch 0000029403B50770>)
(<DMatch 0000029403B50790>, <DMatch 0000029403B507B0>)
(<DMatch 0000029403B507D0>, <DMatch 0000029403B507F0>)
(<DMatch 0000029403B50810>, <DMatch 0000029403B50830>)
(<DMatch 0000029403B50850>, <DMatch 0000029403B50870>)
(<DMatch 0000029403B50890>, <DMatch 0000029403B508B0>)
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(<DMatch 0000029403B50B90>, <DMatch 0000029403B50BB0>)
(<DMatch 0000029403B50BD0>, <DMatch 0000029403B50BF0>)
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(<DMatch 0000029403B65890>, <DMatch 0000029403B658B0>)
(<DMatch 0000029403B658D0>, <DMatch 0000029403B658F0>)
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(<DMatch 0000029403B65950>, <DMatch 0000029403B65970>)
(<DMatch 0000029403B65990>, <DMatch 0000029403B659B0>)
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(<DMatch 0000029403B65A90>, <DMatch 0000029403B65AB0>)
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(<DMatch 0000029403B65B50>, <DMatch 0000029403B65B70>)
(<DMatch 0000029403B65B90>, <DMatch 0000029403B65BB0>)
(<DMatch 0000029403B65BD0>, <DMatch 0000029403B65BF0>)
(<DMatch 0000029403B65C10>, <DMatch 0000029403B65C30>)
(<DMatch 0000029403B65C50>, <DMatch 0000029403B65C70>)
(<DMatch 0000029403B65C90>, <DMatch 0000029403B65CB0>)
(<DMatch 0000029403B65CD0>, <DMatch 0000029403B65CF0>)
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(<DMatch 0000029403B65E10>, <DMatch 0000029403B65E30>)
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(<DMatch 0000029403B65E90>, <DMatch 0000029403B65EB0>)
(<DMatch 0000029403B65ED0>, <DMatch 0000029403B65EF0>)
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(<DMatch 0000029403B65F90>, <DMatch 0000029403B65FB0>)
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(<DMatch 0000029403B61050>, <DMatch 0000029403B61070>)
(<DMatch 0000029403B61090>, <DMatch 0000029403B610B0>)
(<DMatch 0000029403B610D0>, <DMatch 0000029403B610F0>)
(<DMatch 0000029403B61110>, <DMatch 0000029403B61130>)
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(<DMatch 0000029403B61190>, <DMatch 0000029403B611B0>)
(<DMatch 0000029403B611D0>, <DMatch 0000029403B611F0>)
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(<DMatch 0000029403B61250>, <DMatch 0000029403B61270>)
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(<DMatch 0000029403B59910>, <DMatch 0000029403B59930>)
(<DMatch 0000029403B59950>, <DMatch 0000029403B59970>)
(<DMatch 0000029403B59990>, <DMatch 0000029403B599B0>)
(<DMatch 0000029403B599D0>, <DMatch 0000029403B599F0>)
(<DMatch 0000029403B59A10>, <DMatch 0000029403B59A30>)
(<DMatch 0000029403B59A50>, <DMatch 0000029403B59A70>)
(<DMatch 0000029403B59A90>, <DMatch 0000029403B59AB0>)
(<DMatch 0000029403B59AD0>, <DMatch 0000029403B59AF0>)
(<DMatch 0000029403B59B10>, <DMatch 0000029403B59B30>)
(<DMatch 0000029403B59B50>, <DMatch 0000029403B59B70>)
(<DMatch 0000029403B59B90>, <DMatch 0000029403B59BB0>)
(<DMatch 0000029403B59BD0>, <DMatch 0000029403B59BF0>)
(<DMatch 0000029403B59C10>, <DMatch 0000029403B59C30>)
(<DMatch 0000029403B59C50>, <DMatch 0000029403B59C70>)
(<DMatch 0000029403B59C90>, <DMatch 0000029403B59CB0>)
(<DMatch 0000029403B59CD0>, <DMatch 0000029403B59CF0>)
(<DMatch 0000029403B59D10>, <DMatch 0000029403B59D30>)
(<DMatch 0000029403B59D50>, <DMatch 0000029403B59D70>)
(<DMatch 0000029403B59D90>, <DMatch 0000029403B59DB0>)
(<DMatch 0000029403B59DD0>, <DMatch 0000029403B59DF0>)
(<DMatch 0000029403B59E10>, <DMatch 0000029403B59E30>)
(<DMatch 0000029403B59E50>, <DMatch 0000029403B59E70>)
(<DMatch 0000029403B59E90>, <DMatch 0000029403B59EB0>)
(<DMatch 0000029403B59ED0>, <DMatch 0000029403B59EF0>)
(<DMatch 0000029403B59F10>, <DMatch 0000029403B59F30>)
(<DMatch 0000029403B59F50>, <DMatch 0000029403B59F70>)
(<DMatch 0000029403B59F90>, <DMatch 0000029403B59FB0>)
(<DMatch 0000029403B59FD0>, <DMatch 0000029403B00030>)
(<DMatch 0000029403B00050>, <DMatch 0000029403B00070>)
(<DMatch 0000029403B00090>, <DMatch 0000029403B000B0>)
(<DMatch 0000029403B000D0>, <DMatch 0000029403B000F0>)
(<DMatch 0000029403B00110>, <DMatch 0000029403B00130>)
(<DMatch 0000029403B00150>, <DMatch 0000029403B00170>)
(<DMatch 0000029403B00190>, <DMatch 0000029403B001B0>)
(<DMatch 0000029403B001D0>, <DMatch 0000029403B001F0>)
(<DMatch 0000029403B00210>, <DMatch 0000029403B00230>)
(<DMatch 0000029403B00250>, <DMatch 0000029403B00270>)
(<DMatch 0000029403B00290>, <DMatch 0000029403B002B0>)
(<DMatch 0000029403B002D0>, <DMatch 0000029403B002F0>)
(<DMatch 0000029403B00310>, <DMatch 0000029403B00330>)
(<DMatch 0000029403B00350>, <DMatch 0000029403B00370>)
(<DMatch 0000029403B00390>, <DMatch 0000029403B003B0>)
(<DMatch 0000029403B003D0>, <DMatch 0000029403B003F0>)
(<DMatch 0000029403B00410>, <DMatch 0000029403B00430>)
(<DMatch 0000029403B00450>, <DMatch 0000029403B00470>)
(<DMatch 0000029403B00490>, <DMatch 0000029403B004B0>)
(<DMatch 0000029403B004D0>, <DMatch 0000029403B004F0>)
(<DMatch 0000029403B00510>, <DMatch 0000029403B00530>)
(<DMatch 0000029403B00550>, <DMatch 0000029403B00570>)
(<DMatch 0000029403B00590>, <DMatch 0000029403B005B0>)
(<DMatch 0000029403B005D0>, <DMatch 0000029403B005F0>)
(<DMatch 0000029403B00610>, <DMatch 0000029403B00630>)
(<DMatch 0000029403B00650>, <DMatch 0000029403B00670>)
(<DMatch 0000029403B00690>, <DMatch 0000029403B006B0>)
(<DMatch 0000029403B006D0>, <DMatch 0000029403B006F0>)
(<DMatch 0000029403B00710>, <DMatch 0000029403B00730>)
(<DMatch 0000029403B00750>, <DMatch 0000029403B00770>)
(<DMatch 0000029403B00790>, <DMatch 0000029403B007B0>)
(<DMatch 0000029403B007D0>, <DMatch 0000029403B007F0>)
(<DMatch 0000029403B00810>, <DMatch 0000029403B00830>)
(<DMatch 0000029403B00850>, <DMatch 0000029403B00870>)
(<DMatch 0000029403B00890>, <DMatch 0000029403B008B0>)
(<DMatch 0000029403B008D0>, <DMatch 0000029403B008F0>)
(<DMatch 0000029403B00910>, <DMatch 0000029403B00930>)
(<DMatch 0000029403B00950>, <DMatch 0000029403B00970>)
(<DMatch 0000029403B00990>, <DMatch 0000029403B009B0>)
(<DMatch 0000029403B009D0>, <DMatch 0000029403B009F0>)
(<DMatch 0000029403B00A10>, <DMatch 0000029403B00A30>)
(<DMatch 0000029403B00A50>, <DMatch 0000029403B00A70>)
(<DMatch 0000029403B00A90>, <DMatch 0000029403B00AB0>)
(<DMatch 0000029403B00AD0>, <DMatch 0000029403B00AF0>)
(<DMatch 0000029403B00B10>, <DMatch 0000029403B00B30>)
(<DMatch 0000029403B00B50>, <DMatch 0000029403B00B70>)
(<DMatch 0000029403B00B90>, <DMatch 0000029403B00BB0>)
(<DMatch 0000029403B00BD0>, <DMatch 0000029403B00BF0>)
(<DMatch 0000029403B00C10>, <DMatch 0000029403B00C30>)
(<DMatch 0000029403B00C50>, <DMatch 0000029403B00C70>)
(<DMatch 0000029403B00C90>, <DMatch 0000029403B00CB0>)
(<DMatch 0000029403B00CD0>, <DMatch 0000029403B00CF0>)
(<DMatch 0000029403B00D10>, <DMatch 0000029403B00D30>)
(<DMatch 0000029403B00D50>, <DMatch 0000029403B00D70>)
(<DMatch 0000029403B00D90>, <DMatch 0000029403B00DB0>)
(<DMatch 0000029403B00DD0>, <DMatch 0000029403B00DF0>)
(<DMatch 0000029403B00E10>, <DMatch 0000029403B00E30>)
(<DMatch 0000029403B00E50>, <DMatch 0000029403B00E70>)
(<DMatch 0000029403B00E90>, <DMatch 0000029403B00EB0>)
(<DMatch 0000029403B00ED0>, <DMatch 0000029403B00EF0>)
(<DMatch 0000029403B00F10>, <DMatch 0000029403B00F30>)
(<DMatch 0000029403B00F50>, <DMatch 0000029403B00F70>)
(<DMatch 0000029403B00F90>, <DMatch 0000029403B00FB0>)
(<DMatch 0000029403B00FD0>, <DMatch 0000029403B08030>)
(<DMatch 0000029403B08050>, <DMatch 0000029403B08070>)
(<DMatch 0000029403B08090>, <DMatch 0000029403B080B0>)
(<DMatch 0000029403B080D0>, <DMatch 0000029403B080F0>)
(<DMatch 0000029403B08110>, <DMatch 0000029403B08130>)
(<DMatch 0000029403B08150>, <DMatch 0000029403B08170>)
(<DMatch 0000029403B08190>, <DMatch 0000029403B081B0>)
(<DMatch 0000029403B081D0>, <DMatch 0000029403B081F0>)
(<DMatch 0000029403B08210>, <DMatch 0000029403B08230>)
(<DMatch 0000029403B08250>, <DMatch 0000029403B08270>)
(<DMatch 0000029403B08290>, <DMatch 0000029403B082B0>)
(<DMatch 0000029403B082D0>, <DMatch 0000029403B082F0>)
(<DMatch 0000029403B08310>, <DMatch 0000029403B08330>)
(<DMatch 0000029403B08350>, <DMatch 0000029403B08370>)
(<DMatch 0000029403B08390>, <DMatch 0000029403B083B0>)
(<DMatch 0000029403B083D0>, <DMatch 0000029403B083F0>)
(<DMatch 0000029403B08410>, <DMatch 0000029403B08430>)
(<DMatch 0000029403B08450>, <DMatch 0000029403B08470>)
(<DMatch 0000029403B08490>, <DMatch 0000029403B084B0>)
(<DMatch 0000029403B084D0>, <DMatch 0000029403B084F0>)
(<DMatch 0000029403B08510>, <DMatch 0000029403B08530>)
(<DMatch 0000029403B08550>, <DMatch 0000029403B08570>)
(<DMatch 0000029403B08590>, <DMatch 0000029403B085B0>)
(<DMatch 0000029403B085D0>, <DMatch 0000029403B085F0>)
(<DMatch 0000029403B08610>, <DMatch 0000029403B08630>)
(<DMatch 0000029403B08650>, <DMatch 0000029403B08670>)
(<DMatch 0000029403B08690>, <DMatch 0000029403B086B0>)
(<DMatch 0000029403B086D0>, <DMatch 0000029403B086F0>)
(<DMatch 0000029403B08710>, <DMatch 0000029403B08730>)
(<DMatch 0000029403B08750>, <DMatch 0000029403B08770>)
(<DMatch 0000029403B08790>, <DMatch 0000029403B087B0>)
(<DMatch 0000029403B087D0>, <DMatch 0000029403B087F0>)
(<DMatch 0000029403B08810>, <DMatch 0000029403B08830>)
(<DMatch 0000029403B08850>, <DMatch 0000029403B08870>)
(<DMatch 0000029403B08890>, <DMatch 0000029403B088B0>)
(<DMatch 0000029403B088D0>, <DMatch 0000029403B088F0>)
(<DMatch 0000029403B08910>, <DMatch 0000029403B08930>)
(<DMatch 0000029403B08950>, <DMatch 0000029403B08970>)
(<DMatch 0000029403B08990>, <DMatch 0000029403B089B0>)
(<DMatch 0000029403B089D0>, <DMatch 0000029403B089F0>)
(<DMatch 0000029403B08A10>, <DMatch 0000029403B08A30>)
(<DMatch 0000029403B08A50>, <DMatch 0000029403B08A70>)
(<DMatch 0000029403B08A90>, <DMatch 0000029403B08AB0>)
(<DMatch 0000029403B08AD0>, <DMatch 0000029403B08AF0>)
(<DMatch 0000029403B08B10>, <DMatch 0000029403B08B30>)
(<DMatch 0000029403B08B50>, <DMatch 0000029403B08B70>)
(<DMatch 0000029403B08B90>, <DMatch 0000029403B08BB0>)
(<DMatch 0000029403B08BD0>, <DMatch 0000029403B08BF0>)
(<DMatch 0000029403B08C10>, <DMatch 0000029403B08C30>)
(<DMatch 0000029403B08C50>, <DMatch 0000029403B08C70>)
(<DMatch 0000029403B08C90>, <DMatch 0000029403B08CB0>)
(<DMatch 0000029403B08CD0>, <DMatch 0000029403B08CF0>)
(<DMatch 0000029403B08D10>, <DMatch 0000029403B08D30>)
(<DMatch 0000029403B08D50>, <DMatch 0000029403B08D70>)
(<DMatch 0000029403B08D90>, <DMatch 0000029403B08DB0>)
(<DMatch 0000029403B08DD0>, <DMatch 0000029403B08DF0>)
(<DMatch 0000029403B08E10>, <DMatch 0000029403B08E30>)
(<DMatch 0000029403B08E50>, <DMatch 0000029403B08E70>)
(<DMatch 0000029403B08E90>, <DMatch 0000029403B08EB0>)
(<DMatch 0000029403B08ED0>, <DMatch 0000029403B08EF0>)
(<DMatch 0000029403B08F10>, <DMatch 0000029403B08F30>)
(<DMatch 0000029403B08F50>, <DMatch 0000029403B08F70>)
(<DMatch 0000029403B08F90>, <DMatch 0000029403B08FB0>)
(<DMatch 0000029403B08FD0>, <DMatch 0000029403B0A030>)
(<DMatch 0000029403B0A050>, <DMatch 0000029403B0A070>)
(<DMatch 0000029403B0A090>, <DMatch 0000029403B0A0B0>)
(<DMatch 0000029403B0A0D0>, <DMatch 0000029403B0A0F0>)
(<DMatch 0000029403B0A110>, <DMatch 0000029403B0A130>)
(<DMatch 0000029403B0A150>, <DMatch 0000029403B0A170>)
(<DMatch 0000029403B0A190>, <DMatch 0000029403B0A1B0>)
(<DMatch 0000029403B0A1D0>, <DMatch 0000029403B0A1F0>)
(<DMatch 0000029403B0A210>, <DMatch 0000029403B0A230>)
(<DMatch 0000029403B0A250>, <DMatch 0000029403B0A270>)
(<DMatch 0000029403B0A290>, <DMatch 0000029403B0A2B0>)
(<DMatch 0000029403B0A2D0>, <DMatch 0000029403B0A2F0>)
(<DMatch 0000029403B0A310>, <DMatch 0000029403B0A330>)
(<DMatch 0000029403B0A350>, <DMatch 0000029403B0A370>)
(<DMatch 0000029403B0A390>, <DMatch 0000029403B0A3B0>)
(<DMatch 0000029403B0A3D0>, <DMatch 0000029403B0A3F0>)
(<DMatch 0000029403B0A410>, <DMatch 0000029403B0A430>)
(<DMatch 0000029403B0A450>, <DMatch 0000029403B0A470>)
(<DMatch 0000029403B0A490>, <DMatch 0000029403B0A4B0>)
(<DMatch 0000029403B0A4D0>, <DMatch 0000029403B0A4F0>)
(<DMatch 0000029403B0A510>, <DMatch 0000029403B0A530>)
(<DMatch 0000029403B0A550>, <DMatch 0000029403B0A570>)
(<DMatch 0000029403B0A590>, <DMatch 0000029403B0A5B0>)
(<DMatch 0000029403B0A5D0>, <DMatch 0000029403B0A5F0>)
(<DMatch 0000029403B0A610>, <DMatch 0000029403B0A630>)
(<DMatch 0000029403B0A650>, <DMatch 0000029403B0A670>)
(<DMatch 0000029403B0A690>, <DMatch 0000029403B0A6B0>)
(<DMatch 0000029403B0A6D0>, <DMatch 0000029403B0A6F0>)
(<DMatch 0000029403B0A710>, <DMatch 0000029403B0A730>)
(<DMatch 0000029403B0A750>, <DMatch 0000029403B0A770>)
(<DMatch 0000029403B0A790>, <DMatch 0000029403B0A7B0>)
(<DMatch 0000029403B0A7D0>, <DMatch 0000029403B0A7F0>)
(<DMatch 0000029403B0A810>, <DMatch 0000029403B0A830>)
(<DMatch 0000029403B0A850>, <DMatch 0000029403B0A870>)
(<DMatch 0000029403B0A890>, <DMatch 0000029403B0A8B0>)
(<DMatch 0000029403B0A8D0>, <DMatch 0000029403B0A8F0>)
(<DMatch 0000029403B0A910>, <DMatch 0000029403B0A930>)
(<DMatch 0000029403B0A950>, <DMatch 0000029403B0A970>)
(<DMatch 0000029403B0A990>, <DMatch 0000029403B0A9B0>)
(<DMatch 0000029403B0A9D0>, <DMatch 0000029403B0A9F0>)
(<DMatch 0000029403B0AA10>, <DMatch 0000029403B0AA30>)
(<DMatch 0000029403B0AA50>, <DMatch 0000029403B0AA70>)
(<DMatch 0000029403B0AA90>, <DMatch 0000029403B0AAB0>)
可以看出，Knnmatch与match的返回值类型一样，只不过一组返回的俩个DMatch类型，这两个DMatch数据类型是两个与原图像特征点最接近的两个特征点（match返回的是最匹配的）只有这两个特征点的欧式距离小于一定值的时候才会认为匹配成功。例如：原图像特征点与两个绿色苹果相匹配，那么就会认为这个特征点是绿苹果，但若与原图像最接近的匹配分别是一个绿苹果和一个红苹果，那么就会认为匹配是失败的，即没有相匹配的特征点。
2. 基于 FLANN 的匹配器
FLANN 代表 Fast Library for Approximate Nearest Neighbors。 它包含一组针对大型数据集中的快速最近邻搜索和高维特征优化的算法。 对于大型数据集，它比 BFMatcher 工作得更快。 我们将看到基于 FLANN 的匹配器的第二个示例。 对于基于 FLANN 的匹配器，我们需要传递两个字典，指定要使用的算法、相关参数等。第一个是IndexParams。 对于各种算法，要传递的信息在 FLANN 文档中进行了解释。 总而言之，对于 SIFT、SURF 等算法，您可以通过以下方法：
FLANN_INDEX_KDTREE = 1
index_params = dict(algorithm = FLANN_INDEX_KDTREE, trees = 5)
使用 ORB 时，您可以传递以下内容。 根据文档建议使用注释值(不一定适用于所有情况)。 其他值工作正常：
FLANN_INDEX_LSH = 6
index_params= dict(algorithm = FLANN_INDEX_LSH,
table_number = 6, # 12
key_size = 12, # 20
multi_probe_level = 1) #2
第二个字典是 SearchParams。 它指定应该递归遍历索引中的树的次数。 值越高，精度越高，但也需要更多时间。 如果要更改值，请通过 search_params = dict(checks=100)。 有了这些信息，我们就可以开始了。
img1 = cv.imread('ipad.png',cv.IMREAD_GRAYSCALE) # queryImage
img2 = cv.imread('others.png',cv.IMREAD_GRAYSCALE) # trainImage
# Initiate SIFT detector
sift = cv.SIFT_create()
# find the keypoints and descriptors with SIFT
kp1, des1 = sift.detectAndCompute(img1,None)
kp2, des2 = sift.detectAndCompute(img2,None)
# FLANN parameters
FLANN_INDEX_KDTREE = 1
index_params = dict(algorithm = FLANN_INDEX_KDTREE, trees = 5)
search_params = dict(checks=50) # or pass empty dictionary
flann = cv.FlannBasedMatcher(index_params,search_params)
matches = flann.knnMatch(des1,des2,k=2)
# Need to draw only good matches, so create a mask
matchesMask = [[0,0] for i in range(len(matches))]
# ratio test as per Lowe's paper
for i,(m,n) in enumerate(matches):
if m.distance < 0.7*n.distance:
matchesMask[i]=[1,0]
draw_params = dict(matchColor = (0,255,0),
singlePointColor = (255,0,0),
matchesMask = matchesMask,
flags = cv.DrawMatchesFlags_DEFAULT)
img3 = cv.drawMatchesKnn(img1,kp1,img2,kp2,matches,None,**draw_params)
fig = plt.figure(figsize = (20,8))
plt.imshow(img3,)
plt.xticks([]),plt.yticks([])
plt.show()
二、特征匹配 & 单应性查找对象
本小节中，我们将结合 calib3d 模块中的特征匹配和 findHomography用以在复杂图像中查找已知对象。
1. 概念
那么我们在上一小节上做了什么？我们使用了一个 queryImage，在其中找到了一些特征点，我们使用了另一个 trainImage，也找到了该图像中的特征，并在其中找到了最佳匹配。简而言之，我们在另一个杂乱的图像中找到了对象某些部分的位置。这些信息足以准确地在 trainImage 上找到对象。为此，我们可以使用来自 calib3d 模块的函数，即 cv.findHomography()。如果我们从两个图像中传递一组点，它将找到该对象的透视变换。然后我们可以使用 cv.perspectiveTransform() 来查找对象。至少需要四个正确的点才能找到转换。我们已经看到，匹配时可能会出现一些可能影响结果的错误。为了解决这个问题，算法使用 RANSAC 或 LEAST_MEDIAN（可以由标志决定）。因此，提供正确估计的良好匹配称为内点，其余的称为异常点。 cv.findHomography() 返回一个指定内点和异常点的掩码。
各函数用法如下：
- cv.findHomography：
- cv.findHomography( srcPoints, dstPoints[, method[, ransacReprojThreshold[, mask[, maxIters[, confidence]]]]] ) -> retval, mask
- cv.findHomography( srcPoints, dstPoints, params[, mask] ) -> retval, mask
- cv.perspectiveTransform( src, m[, dst] ) -> dst
- cv.findHomography() ：
- cv.findHomography( srcPoints, dstPoints[, method[, ransacReprojThreshold[, mask[, maxIters[, confidence]]]]] ) -> retval, mask
- cv.findHomography( srcPoints, dstPoints, params[, mask] ) -> retval, mask
2. 运用
MIN_MATCH_COUNT = 10
img1 = cv.imread('ipad.png',0) # queryImage
img2 = cv.imread('others.png',0) # trainImage
# Initiate SIFT detector
sift = cv.SIFT_create()
# find the keypoints and descriptors with SIFT
kp1, des1 = sift.detectAndCompute(img1,None)
kp2, des2 = sift.detectAndCompute(img2,None)
FLANN_INDEX_KDTREE = 1
index_params = dict(algorithm = FLANN_INDEX_KDTREE, trees = 5)
search_params = dict(checks = 50)
flann = cv.FlannBasedMatcher(index_params, search_params)
matches = flann.knnMatch(des1,des2,k=2)
# store all the good matches as per Lowe's ratio test.
good = []
for m,n in matches:
if m.distance < 0.7*n.distance:
good.append(m)
现在我们设置一个条件，即至少有 10 个匹配项（由 MIN_MATCH_COUNT 定义）在那里找到对象。 否则，只需显示一条消息，说明没有足够的匹配项。 如果找到足够的匹配项，我们将提取两个图像中匹配关键点的位置。 它们被传递以找到透视变换。 一旦我们得到这个 3x3 的变换矩阵，我们就用它把 queryImage 的角点变换到 trainImage 中的对应点。 然后我们画出来。
if len(good)>MIN_MATCH_COUNT:
# 分离样本图像和查询图像中的匹配点坐标
src_pts = np.float32([ kp1[m.queryIdx].pt for m in good ]).reshape(-1,1,2)
dst_pts = np.float32([ kp2[m.trainIdx].pt for m in good ]).reshape(-1,1,2)
# 获取掩码以及变换矩阵
M, mask = cv.findHomography(src_pts, dst_pts, cv.RANSAC,5.0)
matchesMask = mask.ravel().tolist()
h,w = img1.shape
# 获取样本图像的角点坐标
pts = np.float32([ [0,0],[0,h-1],[w-1,h-1],[w-1,0] ]).reshape(-1,1,2)
# 对个角点坐标进行透视变换映射到查询图像中
dst = cv.perspectiveTransform(pts,M)
img2 = cv.polylines(img2,[np.int32(dst)],True,255,10, cv.LINE_AA)
else:
print( "Not enough matches are found - {}/{}".format(len(good), MIN_MATCH_COUNT) )
matchesMask = None
最后，我们绘制我们的内点（如果成功找到对象）或匹配关键点（如果失败）。
draw_params = dict(matchColor = (0,255,0), # draw matches in green color
singlePointColor = None,
matchesMask = matchesMask, # draw only inliers
flags = 2)
img3 = cv.drawMatches(img1,kp1,img2,kp2,good,None,**draw_params)
fig = plt.figure(figsize = (20,8))
plt.imshow(img3,)
plt.xticks([]),plt.yticks([])
plt.show()
可以看出： 在杂乱的图像中，对象以白色边框标出
