CN106778771A - 一种新型的二值sift描述子及其图像匹配方法 - Google Patents

一种新型的二值sift描述子及其图像匹配方法 Download PDF

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CN106778771A
CN106778771A CN201611044893.5A CN201611044893A CN106778771A CN 106778771 A CN106778771 A CN 106778771A CN 201611044893 A CN201611044893 A CN 201611044893A CN 106778771 A CN106778771 A CN 106778771A
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马燕
苏明哲
张相芬
李顺宝
张玉萍
徐晓钟
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Shanghai Normal University
University of Shanghai for Science and Technology
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Abstract

本发明公开了一种新型的二值SIFT描述子及其图像匹配方法，解决现有技术中存在的大容量图像匹配速度慢、SIFT方法或BSIFT方法对图像镜像翻转变化敏感的问题。包括步骤：S1：构建描述子步骤；S2：图像匹配步骤；其中，S1：构建描述子步骤包括：S11：分别提取待匹配图像对的SIFT特征点；S12：计算128维SIFT特征点描述子；S13：对128维SIFT特征点描述子进行重构，得到128维R‑SIFT描述子；S14：计算128维R‑SIFT描述子的相邻值之间的差值；S15：二值化R‑SIFT描述子，得到128位二值描述子BR‑SIFT；S16：构建翻转图的二值描述子MBR‑SIFT；S2：图像匹配步骤包括：S21：对于待匹配图像对中的SIFT特征点对计算相似距离；S22：根据最近邻匹配进行SIFT特征点对的相似性判断；S23：输出SIFT特征点匹配后的图像对。

Description

一种新型的二值SIFT描述子及其图像匹配方法
技术领域
本发明涉及计算机图形图像处理技术领域，尤其涉及一种新型的二值SIFT描述子及其图像匹配方法。
背景技术
局部特征点在图像检索、目标识别、手势识别、纹理识别、3-D重建、构造全景图、宽基线匹配等许多模式识别和计算机视觉任务中的应用是非常成功的。一个好的特征点描述子，应对亮度、色彩等光学变换具有鲁棒性，同时，对于旋转、尺度、视角、模糊、镜像翻转等几何变换也能保持良好的不变性。
目前大量的特征描述子已经被提出，其中，Lowe提出的尺度不变特征变换(SIFT)描述子是最成功也是最流行的局部图像特征描述子之一。SIFT描述子是结合尺度不变区域检测器和基于梯度分布的描述符所构建的。SIFT描述子被Mikolajczyk和Schmid证实是最好的局部不变特征描述子。
在利用SIFT特征进行图像匹配时，由于每幅图像约有上千个SIFT特征点，而且距离计算中牵涉到均方根运算，因此，对于大规模图像库而言，基于SIFT特征的图像检索将非常耗时。近几年出现了许多二值化SIFT方法，即将SIFT描述子转换为二值SIFT(BinarySIFT，简称BSIFT)描述子，在匹配比较时，利用汉明距离(Hamming Distance)计算两个BSIFT描述子间的距离，这样，利用位运算来替代原来的均方根和平方运算，从而使得匹配比较的计算量大大降低。
上述SIFT、BSIFT及其改进算法均未考虑水平或垂直镜像翻转问题，即在匹配图像对呈水平或垂直镜像关系时，利用上述SIFT、BSIFT描述子进行匹配时，错误匹配率就会明显上升。Guo在SIFT基础上，提出镜像翻转保持不变的描述子MIFT，但MIFT是针对SIFT描述子进行设计的，在进行图像匹配时，MIFT耗时与SIFT类似。
针对上述问题，本发明提出了一种新型的二值SIFT描述子及其图像匹配方法，该方法在二值化SIFT描述子的同时，兼顾水平或垂直镜像翻转问题。首先对SIFT特征点周围的16个小块进行重构并按方向重组，由此获得了128维R-SIFT描述子，接着对R-SIFT描述子进行二值化，获得128位二值描述子BR-SIFT，并以此为基础，构建水平或垂直翻转图的二值描述子MBR-SIFT。在匹配时，采用汉明距离进行相似性度量。在水平镜像翻转图像对、垂直镜像翻转图像对，以及具有旋转、尺度、视角、亮度和模糊变化的图像对的匹配实验结果表明，本发明提出的方法较好地解决了在图像匹配过程中，SIFT方法或BSIFT方法对图像镜像翻转变化敏感的问题，并且在保证匹配准确率的同时，达到了图像快速匹配目的。
发明内容
有鉴于现有技术的上述缺陷，本发明所要解决的技术问题是解决现有技术中存在的大容量图像匹配速度慢、SIFT方法或BSIFT方法对图像镜像翻转变化敏感的问题。
为实现上述目的，本发明提供了一种新型的二值SIFT描述子及其图像匹配方法，其特征在于，包括步骤：S1：构建描述子步骤；S2：图像匹配步骤；
其中，S1：构建描述子步骤包括：
S11：分别提取待匹配图像对的SIFT特征点；
S12：计算128维SIFT特征点描述子；
S13：对128维SIFT特征点描述子进行重构，得到128维R-SIFT描述子；
S14：计算128维R-SIFT描述子的相邻值之间的差值；
S15：二值化R-SIFT描述子，得到128位二值描述子BR-SIFT；
S16：构建翻转图的二值描述子MBR-SIFT；
S2：图像匹配步骤包括：
S21：对于待匹配图像对中的SIFT特征点对计算相似距离；
S22：根据最近邻匹配进行SIFT特征点对的相似性判断；
S23：输出SIFT特征点匹配后的图像对。
进一步地，提取待匹配图像对的SIFT特征点，其具体步骤为：对图像进行归一化预处理后，将图像放大并进行预滤波以剔除噪声；将可变尺度高斯卷积核和输入图像卷积得到图像的尺度空间，在高斯差分DOG尺度空间中检测局部极值以作为SIFT特征点，得到SIFT特征点后，去除其中对比度低和稳定性差的SIFT特征点。其中，可变尺度高斯卷积核G(x,y,σ)和输入图像I(x,y)卷积得到图像的尺度空间为：
L(x,y,σ)＝G(x,y,σ)*I(x,y)
式中，I(x,y)为输入图像，L(x,y,σ)为图像的尺度空间，G(x,y,σ)为可变尺度高斯卷积核，符号*表示卷积，(x,y)代表图像的像素位置，σ是尺度空间因子；DOG算子如下：
D(x,y,σ)＝(G(x,y,kσ)-G(x,y,σ))*I(x,y)＝L(x,y,kσ)-L(x,y,σ)
式中，k为常数因子。
进一步地，计算128维SIFT特征点描述子的获取方式包括：以SIFT特征点为中心，将其周围区域分为4×4个小块，计算每个小块中包含的8个方向的梯度直方图，每个方向给定一个数值，得到一个128维的向量，由此获得该SIFT特征点的128维描述子。
进一步地，对128维SIFT特征点描述子进行重构，得到128维R-SIFT描述子的具体方式包括：把SIFT特征点周围的4×4共16个小块中的第2列与第4列改为逆序输出；将16个小块再按8方向重组，由此得到重构后的128维R-SIFT描述子。
进一步地，使用计算128维R-SIFT描述子相邻值之间的差值；其中，(D0,D1,...,D127)表示重构后的128维R-SIFT特征点描述子，mod()表示取模运算，ADi(i＝0,1,...,127)表示128维R-SIFT描述子相邻值之间的差值。
进一步地，二值化R-SIFT描述子包括使用得到128位二值描述子BR-SIFT；其中，bi表示第i个差值对应的编码值，即，当ADi大于或等于0时，其编码值为1，当ADi小于0时，其编码值为0，由此将R-SIFT描述子二值化为128位二值描述子BR-SIFT。
进一步地，构建翻转图的二值描述子MBR-SIFT，其具体步骤包括：先将二值描述子BR-SIFT的128位按位取反，然后对于各方向中的第0-15位，保持第15位位置不变，其余第0-14位按倒序输出；即输出次序为第14位，第13位，第12位，……，第2位，第1位，第0位，第15位；接着，将H方向与B方向对应的16个二值数值交换，完成G方向与C方向，以及F方向与D方向的数值交换，完成了二值描述子MBR-SIFT的构造。
进一步地，对于待匹配图像对中的SIFT特征点对计算相似距离的具体步骤包括：分别计算第一幅待匹配图像中第一SIFT特征点的二值描述子BR-SIFT与第二幅待匹配图像中第二SIFT特征点的二值描述子BR-SIFT和MBR-SIFT之间的汉明距离，取两者中的较小者作为SIFT特征点对间的相似距离R。其中，所述汉明距离为：两个二值串，对应位数值相同为0，不同则为1，然后计算1的个数即为两个二值串间汉明距离的大小。
进一步地，根据最近邻匹配进行SIFT特征点对的相似性判断，其具体步骤为：对于一幅待匹配图像中的SIFT特征点A，将SIFT特征点A分别与另一幅待匹配图像的所有SIFT特征点构成SIFT特征点对，计算所有SIFT特征点对之间的相似距离R，将R由小到大排序，再将最小值与次小值相比，若比值小于预先设定值distratio，则认为SIFT特征点A与另一幅待匹配图像中的相似距离R最小值所对应的SIFT特征点匹配。具体公式如下：
其中，vals(1)、vals(2)分别为按相似距离R由小到大排序后的最小值和次小值，distratio∈[0,1]为预设阈值。在本发明的一种优选实施方式中，distratio的值为0.65。
进一步地，比值大于预先设定值distratio，则认为SIFT特征点A与另一幅待匹配图像中的相似距离R最小值所对应的SIFT特征点不匹配。
技术效果
本发明提出的一种新型二值SIFT描述子及其图像匹配方法，它是将128维SIFT描述子进行重构，然后二值化重构后的描述子，并对二值化重构后的描述子进行逆序编码；然后直接利用汉明距离进行描述子间的距离度量，实现快速准确的大容量的图像匹配，解决了在图像匹配过程中，SIFT方法或BSIFT方法对图像镜像翻转变化敏感的问题，有利于在当前大容量图像数据库中的快速匹配，尤其具有镜像翻转变换的图像库中，可广泛应用于工业检测、卫星导航、安防监控等行业，具有较高的推广价值，市场前景广阔。
以下将结合附图对本发明的构思、具体结构及产生的技术效果作进一步说明，以充分地了解本发明的目的、特征和效果。
附图说明
图1为本发明一个较佳实施例的流程示意图。
图2为本发明一个较佳实施例的原始图像中SIFT特征点周围的16个小块及8个方向示意图。
图3为本发明一个较佳实施例的原始图像中128维SIFT描述子示意图。
图4为本发明一个较佳实施例的水平镜像图像中SIFT特征点周围的16个小块及8个方向示意图。
图5为本发明一个较佳实施例的水平镜像图像中128维SIFT描述子示意图。
图6为本发明一个较佳实施例的垂直镜像图像中SIFT特征点周围的16个小块及8个方向示意图。
图7为本发明一个较佳实施例的垂直镜像图像中128维SIFT描述子示意图。
图8为本发明一个较佳实施例的对原图16个小块按逆序重排示意图。
图9为本发明一个较佳实施例的原图16个小块的输出次序示意图。
图10为本发明一个较佳实施例的对水平或垂直翻转图16个小块按逆序重排示意图。
图11为本发明一个较佳实施例的水平或垂直翻转图16个小块的输出次序示意图。
图12为本发明一个较佳实施例的原图R-SIFT描述子示意图。
图13为本发明一个较佳实施例的水平或垂直翻转图R-SIFT描述子示意图。
图14为本发明一个较佳实施例的原图与水平或垂直翻转图R-SIFT描述子中A方向的差值编码示意图。
图15为本发明一个较佳实施例的本实施方式中SIFT特征点A周围的16个小块及8个方向示意图。
图16为本发明一个较佳实施例的SIFT特征点A周围的16个小块按逆序重排示意图。
图17为本发明一个较佳实施例的SIFT特征点A的R-SIFT描述子示意图。
图18为本发明一个较佳实施例的SIFT特征点A的R-SIFT描述子相邻值之间的差值示意图。
图19为本发明一个较佳实施例的SIFT特征点A的BR-SIFT描述子示意图。
图20为本发明一个较佳实施例的SIFT特征点A的MBR-SIFT描述子示意图。
具体实施方式
对本发明的方法，作总体的描述、说明和解释如下。首先，对本发明的方法作如下的总体描述。
SIFT方法首先在原始图像中寻找SIFT特征点，然后以SIFT特征点为中心，如图2所示，黑色三角形表示SIFT特征点，将其周围区域分为16个小块，每个小块包含8个方向，每个方向给定一个数值，由此获得128维的描述子，其数值构成次序如图3所示。当遇到待匹配图像对为水平或垂直镜像关系时，例如，对图像作水平翻转，如图4所示，由16个小块构成4列以及每小块中的8个方向均按垂直对称轴进行了翻转变换，由此得到了如图5中的128维SIFT描述子。同理，对图像作垂直翻转，如图6所示，由16个小块构成4列以及每小块中的8个方向均按水平对称轴进行了翻转变换，由此得到了如图7中的128维SIFT描述子。
下面我们对SIFT描述子重构。如图8所示，把图2中SIFT特征点周围的16个小块中的第2列与第4列改为逆序输出，由此得到如图9所示的SIFT描述子，16个小块的输出次序为“1,2,3,4,8,7,6,5,9,10,11,12,16,15,14,13”。对于水平或垂直翻转后的16个小块也同样做法，结果见图10和图11，可见水平或垂直翻转后的16个小块的输出次序均为“13,14,15,16,12,11,10,9,5,6,7,8,4,3,2,1”。对原图与水平或垂直翻转后SIFT特征点周围16个小块的输出次序作比较的话，可以发现，两者呈逆序关系。对于每一小块又包含8个方向，比如，对于第1小块，其8个方向的输出次序是“A1B1C1D1E1F1G1H1”，经水平或垂直翻转后，改为“A1H1G1F1E1D1C1B1”，两者无逆序关系。为保证16个小块间的逆序关系，我们进一步将上面得到的16个小块再按8方向重组，由此得到重组后的SIFT描述子(以下简称R-SIFT描述子)，如图12和图13所示。SIFT描述子是先按16个小块，再按每个小块8个方向的形式输出，本发明提出的R-SIFT描述子是先按8个方向，每个方向再按16个小块的形式输出，这样就保证了原图与水平或垂直翻转图对应方向的16个数值呈逆序关系。
这里我们把R-SIFT描述子用128维向量(D0,D1,...,D127)表示，按式(1)求得其差值ADi(i＝0,1,...,127)，并且保证差值是同一方向的数值间的差值。
在对差值ADi进行二值化时，我们采用一种二值化方法如式(2)所示，按ADi与0比较的大小分别表示为0或1，用1位二进制数值表示，由此将128维的R-SIFT描述子二值化为128位的BR-SIFT描述子，表示为{b0,b1,...,b127}。
上面对原图构造了BR-SIFT，接下来在这个二值描述子的基础上分别构造水平或垂直翻转图的二值描述子MBR-SIFT。从图14中可见，就A方向而言，由于原图与水平或垂直翻转图的R-SIFT描述子呈逆序关系，则原图的二值描述子BR-SIFT与翻转图的二值描述子MBR-SIFT之间也存在如下关系：除了b15改为～b15(这里的～表示取反，即0变成1，1变成0)，BR-SIFT与MBR-SIFT两者的描述子A方向的其余位呈逆序并取反的关系，即对于A方向的16位而言，要从BR-SIFT构造MBR-SIFT，只要先把所有的位取反，然后第15位位置不变，其余位按倒序输出。另外，由于原图的BR-SIFT描述子中的8个方向输出次序是“ABCDEFGH”，而水平或垂直翻转图的二值描述子MBR-SIFT的8个方向输出次序是“AHGFEDCB”，因此，要在BR-SIFT基础上构造MBR-SIFT，在按方向逆序输出后，还需要将BR-SIFT描述子中方向B与H、C与G、D与F对应的16个二值数值交换，这样就完成了二值描述子MBR-SIFT的构造。
假设待匹配图像对I1与I2，I1中SIFT特征点a1的二值描述子BR-SIFT记为B1＝{b1,0,b1,1,...,b1,127}，I2中SIFT特征点a2的二值描述子BR-SIFT记为B2＝{b2,0,b2,1,...,b2,127}和二值描述子MBR-SIFT记为M2＝{m2,0,m2,1,...,m2,127}，分别计算B1与B2、M2之间的汉明距离，取两者中的距离较小者作为SIFT特征点a1与a2的距离。
待匹配图像对I1与I2在进行匹配比较时，需要逐一提取I1中SIFT特征点，比如，取出SIFT特征点a1，计算其与I2中所有SIFT特征点间的距离，并将距离按升序重新排序，按式(3)确定匹配点对。
其中，vals(1)、vals(2)分别为按相似距离由小到大排序后的最小值和次小值，distratio∈[0,1]为预设阈值。在这里，我们设distratio为0.65。
实施例一
本实施例流程示意图如图1所示；读入具有水平镜像翻转变化的待匹配图像对，分别提取待匹配图像对的SIFT特征点；由于提取的SIFT特征点较多，为便于说明，在本实施例中，假设在匹配图像对的左图仅提取A SIFT特征点，右图仅提取a-j共10个SIFT特征点。上述SIFT特征点A的SIFT描述子构成示意图如图15所示，128维描述子如下：
A:(0.0138,0.0079,0.0020,0.0059,0,0,0,0.0079,0.0039,0.0020,0.0138,0.2222,0.0098,0,0.0020,0.0079,0.0747,0.0118,0.0393,0.2517,0.0118,0,0,0.1160,0.0983,0.0236,0.0138,0.0197,0.0059,0.0020,0.0059,0.1986,0.0020,0.0118,0.0177,0.0688,0.0472,0.0039,0,0,0.0531,0.0374,0.0767,0.2517,0.1809,0.0452,0.0098,0.0098,0.2517,0.1062,0.0669,0.1200,0.0059,0.0059,0.0059,0.1711,0.0846,0.0177,0.0275,0.1475,0.0079,0,0,0.1062,0,0.0865,0.0983,0.0157,0.0590,0.0334,0.0059,0,0.0374,0.0334,0.0374,0.0590,0.1750,0.2517,0.2045,0.0551,0.2517,0.0649,0.0177,0.0157,0.0138,0.0374,0.1514,0.2262,0.0393,0.0295,0.0610,0.2517,0.0924,0.0256,0.0039,0.0079,0,0.0590,0.0590,0,0,0.0767,0.1908,0,0,0.1003,0.0885,0,0,0.0787,0.1495,0.0059,0.0059,0.1062,0.0944,0.0020,0.0098,0.0216,0.0669,0.0413,0.0118,0.0354,0.0256,0.0216,0.0767,0.0964,0.0590,0.0236)；
从图15可见，SIFT特征点A的SIFT描述子中的前面8个数字，包括0.0138,0.0079,0.0020,0.0059,0,0,0,0.0079分别对应于图2中第1个小块的8个方向A1，B1，C1，D1，E1，F1，G1，H1，而SIFT特征点A的SIFT描述子中的第9至16个数字，包括0.0039,0.0020,0.0138,0.2222,0.0098,0,0.0020,0.0079分别对应于图2中第2个小块的8个方向A2，B2，C2，D2，E2，F2，G2，H2，以此类推，SIFT特征点A的SIFT描述子中的最后8个数字，包括0.0118,0.0354,0.0256,0.0216,0.0767,0.0964,0.0590,0.0236分别对应于图2中第16个小块的8个方向A16，B16，C16，D16，E16，F16，G16，H16。
对于a～j这10个SIFT特征点，其128维描述子如下：
a:(0,0,0.1987,0.0866,0,0,0.0512,0.0571,0,0.0039,0.1495,0.0866,0,0,0.0846,0.1004,0.0059,0.0413,0.0728,0.0256,0.0059,0.0020,0.0905,0.1141,0.0098,0.0177,0.0472,0.0905,0.0787,0.0236,0.0295,0.0394,0,0,0.0079,0.0216,0.0453,0.0118,0.1043,0.1023,0.0216,0.0374,0.1791,0.2499,0.1810,0.0571,0.0413,0.0374,0.2499,0.2381,0.1791,0.0551,0.0157,0.0138,0.0157,0.0571,0.0571,0.0118,0.0039,0.0197,0.0826,0.2322,0.0610,0.0295,0.0020,0,0,0.0020,0.0354,0.0492,0.0197,0.0118,0.0315,0.0079,0.0098,0.0492,0.1909,0.2499,0.0708,0.0275,0.2499,0.1574,0.0079,0.0098,0.0118,0.1594,0.0748,0.1102,0.1181,0.1338,0,0,0.0039,0.1200,0.0275,0.0197,0.0138,0.0059,0,0,0,0.0039,0.0020,0.0098,0.0039,0.0079,0.0020,0,0.0059,0.1948,0.0138,0.0020,0.0551,0.0925,0,0,0.0098,0.2499,0.0374,0.0138,0.1004,0.2184,0.0039,0.0020,0.0039,0.0236,0.0177,0.0256)；
b:(0.0197,0.0590,0.0433,0.0295,0.0098,0,0,0.0079,0.0157,0.0728,0.0236,0.0354,0.1141,0.0295,0,0.0118,0.0177,0.0334,0.0216,0.0826,0.1711,0.0885,0.0236,0.0197,0.1141,0.1770,0.0315,0.0354,0.0472,0.0059,0.0039,0.0236,0.0334,0.0806,0.0472,0.0846,0.2222,0.0197,0.0039,0.0079,0.2301,0.2026,0.0295,0.0197,0.0629,0.0492,0.0157,0.0295,0.0334,0.0138,0.0079,0.0570,0.2301,0.2301,0.0236,0.0197,0.2301,0.0728,0.0098,0.0177,0.0610,0.0551,0.0177,0.0885,0.0236,0.0039,0,0.0059,0.1750,0.1731,0.1003,0.0393,0.2301,0.0708,0.0098,0.0157,0.0472,0.0315,0.0551,0.1337,0.0315,0.0177,0.0059,0.0433,0.2301,0.1160,0.0118,0.0118,0.2262,0.0983,0.0138,0.0275,0.0787,0.0393,0.0138,0.0826,0,0.0079,0.0039,0.0020,0.0315,0.2144,0.0688,0.0020,0.0472,0.0767,0.0138,0.0098,0.0531,0.1318,0.0787,0.0334,0.0216,0.0275,0.0020,0.0177,0.1829,0.0944,0.0413,0.0295,0.1495,0.0157,0.0020,0.0138,0.0629,0.0452,0.0590,0.2301)；
c:(0.0354,0.0393,0.1200,0.2321,0.0256,0,0,0,0.0334,0.0393,0.0629,0.1554,0.0885,0.0275,0.0039,0,0.1416,0.0551,0.0374,0.0610,0.0275,0.0236,0.0138,0.0806,0.0629,0.0039,0.0079,0.0728,0.0590,0.0649,0.0138,0.0570,0.1751,0.0393,0.0236,0.1279,0.1180,0.0236,0.0216,0.0787,0.1377,0.0315,0.0118,0.1397,0.2321,0.0236,0.0059,0.0354,0.2321,0.1102,0.0236,0.0649,0.0787,0.0059,0.0039,0.0747,0.0728,0.0374,0.0236,0.2006,0.2321,0.0020,0,0.0295,0.0669,0.0295,0.0216,0.0197,0.0374,0.0649,0.0610,0.1456,0.0492,0.0059,0,0.0177,0.1908,0.2321,0.0669,0.0964,0.1397,0.0374,0.0079,0.0079,0.0393,0.0570,0.0669,0.2321,0.0295,0.0177,0.0059,0.0354,0.2321,0.1082,0.0256,0.0492,0.2183,0.0511,0.0374,0.0511,0.0256,0.0020,0,0.0590,0.0629,0.0197,0.0590,0.2085,0.0885,0.0511,0.0118,0.0315,0.1023,0.0826,0.0747,0.0315,0.0079,0.0138,0.0157,0.0964,0.0413,0.0098,0,0.0059,0.0452,0.1298,0.0570,0.0629)；
d:(0.0039,0.0039,0.0964,0.0708,0.0098,0,0.0138,0.2497,0,0.0079,0.0590,0.1593,0.1278,0.0216,0.0157,0.0315,0.0138,0.0334,0.0354,0.0393,0.1003,0.0197,0.0315,0.0472,0.0472,0.0039,0.0059,0.0452,0.1376,0.0059,0,0.0177,0.0157,0.1082,0.2497,0.2183,0,0,0,0.0177,0.0511,0.1023,0.2497,0.2379,0.0079,0,0,0.0020,0.2006,0.1141,0.0747,0.0393,0.0826,0.0118,0.0020,0.0256,0.0531,0,0,0.0079,0.1435,0.0708,0.0236,0.0570,0.0197,0.0334,0.0846,0.1966,0.0138,0.0098,0.0177,0.0216,0.2497,0.0649,0.1553,0.1357,0,0,0,0.0157,0.2497,0.0295,0.0079,0.0098,0.0905,0.0157,0.0020,0.0767,0.1652,0.0433,0,0.0059,0.0708,0.0236,0.0256,0.0531,0.0118,0.0059,0.0334,0.1927,0.0098,0.0020,0,0.0157,0.2497,0.0157,0.0157,0.0157,0,0,0,0.1357,0.2497,0.0177,0,0.0059,0.0492,0.0315,0.0079,0.0610,0.0944,0.0433,0,0.0039,0.0374,0.0354,0.0334,0.0393)；
e:(0.0118,0,0,0.0039,0.0157,0.1730,0.0511,0.0020,0.0020,0.0118,0.0236,0.0334,0.0236,0.2280,0.2280,0,0.0079,0.0609,0.0354,0,0,0.1887,0.2280,0.0039,0.0236,0.1690,0.0256,0,0,0.0688,0.1278,0.0020,0.0138,0.0334,0.0098,0.0197,0.1022,0.0256,0.0039,0.0020,0.0295,0.0904,0.1101,0.1474,0.2280,0.1258,0.0256,0.0079,0.2280,0.1926,0.0511,0.0118,0.0118,0.1042,0.1789,0.0570,0.0236,0.0039,0.0020,0.0039,0.0059,0.2162,0.2280,0.0138,0.0157,0.0295,0.0059,0,0.0315,0.0354,0.0393,0.0256,0.0275,0.0118,0.0020,0.0059,0.1710,0.2280,0.1514,0.0550,0.2280,0.0354,0.0216,0.0472,0.0197,0.0609,0.1337,0.2280,0.0334,0.0059,0.1081,0.1258,0.0177,0.0275,0.0197,0.0079,0,0.0020,0.0177,0.0059,0,0.0059,0.0216,0.0059,0.0079,0.0118,0.0098,0.0138,0.0079,0.0334,0.0629,0.0118,0.0059,0.0020,0.0118,0.1022,0.0983,0.0315,0.0531,0.0216,0,0.0059,0.0904,0.1907,0.0747,0.0098,0,0)；
f:(0,0,0.0138,0.0098,0.0217,0.0512,0.1772,0.0197,0,0.0197,0.0472,0.0630,0.0394,0.0197,0.1437,0.0118,0.0039,0.0650,0.0374,0.0157,0,0.0020,0.1063,0.0256,0.0039,0.0157,0.0118,0.0039,0,0,0.0256,0.0394,0,0.0197,0.1457,0.1791,0.2480,0.0374,0.0098,0,0.0295,0.0846,0.2480,0.2480,0.0768,0.0059,0.0098,0.0098,0.2480,0.2480,0.0827,0.0807,0.0059,0.0020,0.0118,0.0394,0.0433,0.0236,0.0118,0.0098,0.0039,0.0059,0.0236,0.0433,0,0.0039,0.0413,0.1890,0.2480,0.0650,0.1043,0.0276,0.0295,0.0079,0.0728,0.1004,0.0650,0.0551,0.2480,0.1535,0.2480,0.0276,0.0079,0.0236,0.0098,0.0059,0.1280,0.2480,0.0354,0.0177,0.0394,0.0256,0.0059,0,0.0118,0.0354,0,0,0,0.0079,0.0335,0.0945,0.1654,0.0571,0.0020,0,0,0,0.0413,0.0669,0.2362,0.0866,0.0413,0.0098,0.0020,0.0217,0.0630,0.0650,0.0846,0.0906,0.0295,0.0394,0.0315,0.0354,0.0472,0.0512,0.0394,0.0335)；
g:(0.0059,0.0157,0.0255,0.0039,0,0,0,0.0059,0.0098,0.0431,0.0196,0,0,0.0039,0.0510,0.0431,0.0078,0.1019,0.0392,0,0,0.0216,0.0392,0.0098,0.0412,0.2489,0.0235,0,0,0,0.0039,0.0294,0.0921,0.0353,0.0255,0.0196,0.0020,0,0,0.0196,0.2489,0.0451,0.0098,0.0059,0.0059,0.0451,0.1646,0.2332,0.0235,0.0078,0.0098,0.0314,.0862,0.2489,0.1783,0.0490,0.0510,0.0529,0.0274,0.0176,0.0176,0.0216,0.0137,0.0490,0.0941,0.0372,0.0078,0.0137,0.0078,0.0490,0.2489,0.0372,0.2489,0.2234,0.1803,0.0314,0.0157,0.0412,0.0666,0.0470,0.0098,0.0314,0.2410,0.2254,0.1078,0.0490,0.0078,0.0059,0.0235,0.0490,0.0333,0.0608,0.0235,0.0059,0,0,0.0020,0,0,0.0078,0.1176,0.1607,0.2489,0.1391,0.0078,0.0196,0.0568,0.0255,0.2489,0.2489,0.1078,0.0098,0.0137,0.0196,0.1039,0.0314,0.0176,0.0098,0.0078,0.0216,0.0353,0.0294,0.0078,0.0078,0,0,0,0.0059)；
h:(0.0020,0.0216,0.1159,0.0884,0.0216,0.0373,0.0373,0.0059,0.0138,0.0727,0.1218,0.0354,0.0334,0.0864,0.0923,0.0334,0.0138,0.0295,0.0530,0.0157,0.0138,0.0550,0.0530,0.0255,0.0039,0.0059,0.0059,0.0354,0.0432,0.0157,0.0098,0.0059,0,0.0707,0.1631,0.2259,0.1906,0.1611,0.0236,0,0.0255,0.2436,0.2436,0.1002,0.0138,0.0766,0.0314,0.0079,0.1886,0.2436,0.2240,0.0354,0.0039,0.0079,0.0079,0.0196,0.0138,0.0314,0.0354,0.0118,0.0334,0.0295,0.0079,0.0020,0,0.0157,0.0786,0.0295,0.0805,0.2436,0.0864,0,0.0393,0.0314,0.0805,0.0471,0.0255,0.2436,0.2436,0.0786,0.2436,0.0884,0.0452,0.0098,0.0020,0.0255,0.0904,0.2220,0.0334,0.0393,0.0196,0.0079,0.0079,0.0059,0.0177,0.0275,0.0020,0.0393,0.1454,0.0354,0.0039,0.0295,0.0805,0.0236,0,0.0098,0.1002,0.0550,0.0334,0.1375,0.1218,0.0354,0.0354,0.1356,0.1434,0.0275,0.0275,0.0452,0.0177,0.0255,0.0255,0.1002,0.0432,0.0059,0.0039,0,0,0.0020)；
i:(0,0.0492,0.1201,0.0158,0,0.0059,0.0059,0,0.0256,0.0473,0.1713,0.0591,0.0059,0.0315,0.0374,0.0256,0.0492,0.1122,0.0512,0.0177,0.0295,0.0295,0.0610,0.0670,0,0.0020,0.0118,0.0354,0.2127,0.2048,0.0532,0.0335,0.0866,0.1989,0.1063,0.2048,0.0217,0,0,0.0020,0.2284,0.1122,0.1457,0.1122,0.0079,0,0,0.1004,0.0965,0.0453,0.0847,0.0492,0.0059,0.0118,0.0256,0.1142,0.0039,0.0276,0.0414,0.0158,0.0197,0.0729,0.0866,0.0138,0.2028,0.2284,0.0492,0.0807,0.0335,0.0098,0.0098,0.0729,0.2284,0.1319,0.1556,0.0827,0.0138,0.0059,0.0020,0.0610,0.0630,0.2028,0.2284,0.1280,0,0,0,0.0059,0.0158,0.1595,0.2186,0.0473,0,0,0,0,0.1516,0.0670,0.0453,0,0,0.0059,0.0256,0.0591,0.0315,0.0571,0.2107,0.0374,0,0.0039,0.0256,0.0098,0.0473,0.1260,0.1575,0.0295,0,0,0.0098,0.0118,0.0236,0.1339,0.1142,0.0039,0,0,0.0020,0.0098)；
j:(0.0079,0.0177,0.1261,0.0611,0.0059,0.0039,0.0118,0.0414,0.0158,0.0591,0.1576,0.0177,0,0,0.0020,0.0197,0.0315,0.0177,0.0749,0.0414,0.0177,0.0118,0.0414,0.0512,0.0020,0,0,0.0039,0.0315,0.1399,0.1911,0.0217,0.0020,0.0079,0.2620,0.1044,0.0039,0.0039,0.0079,0.0197,0.0394,0.0867,0.2620,0.0414,0,0,0.0020,0.0374,0.2620,0.1852,0.0690,0.0059,0,0,0.0276,0.1064,0.0630,0.0217,0.0670,0.0887,0.0059,0.0355,0.1438,0.0433,0.0118,0.0099,0.1221,0.0650,0.0059,0.0020,0.0394,0.1596,0.0512,0.0335,0.0690,0,0,0,0.0946,0.2620,0.2088,0.0532,0.0276,0.0177,0.0039,0.0236,0.1005,0.2620,0.0256,0.0177,0.0926,0.1556,0.0335,0.0788,0.0394,0.0039,0.0020,0,0,0.0039,0.0039,0.0020,0.1005,0.2620,0.0256,0.0276,0.1103,0.0394,0.0039,0,0.0374,0.2620,0.0079,0.0591,0.2502,0.0118,0,0.0177,0.0374,0.0611,0.0020,0.0217,0.1103,0.0276,0.0276,0.0571,0.0355,0.0020)；
把图15中SIFT特征点A周围的16个小块中的第2列与第4列分别改为逆序输出，获得如图16所示结果，SIFT特征点A的128维描述子如下所示：
A:(0.0138,0.0079,0.0020,0.0059,0,0,0,0.0079,0.0039,0.0020,0.0138,0.2222,0.0098,0,0.0020,0.0079,0.0747,0.0118,0.0393,0.2517,0.0118,0,0,0.1160,0.0983,0.0236,0.0138,0.0197,0.0059,0.0020,0.0059,0.1986,0.0846,0.0177,0.0275,0.1475,0.0079,0,0,0.1062,0.2517,0.1062,0.0669,0.1200,0.0059,0.0059,0.0059,0.1711,0.0531,0.0374,0.0767,0.2517,0.1809,0.0452,0.0098,0.0098,0.0020,0.0118,0.0177,0.0688,0.0472,0.0039,0,0,0,0.0865,0.0983,0.0157,0.0590,0.0334,0.0059,0,0.0374,0.0334,0.0374,0.0590,0.1750,0.2517,0.2045,0.0551,0.2517,0.0649,0.0177,0.0157,0.0138,0.0374,0.1514,0.2262,0.0393,0.0295,0.0610,0.2517,0.0924,0.0256,0.0039,0.0079,0.0118,0.0354,0.0256,0.0216,0.0767,0.0964,0.0590,0.0236,0.0059,0.1062,0.0944,0.0020,0.0098,0.0216,0.0669,0.0413,0,0.1003,0.0885,0,0,0.0787,0.1495,0.0059,0,0.0590,0.0590,0,0,0.0767,0.1908,0)；
从图16可见，第2列与第4列作了逆序输出。例如，图15中第8个小块8个方向的数字，包括0.0846,0.0177,0.0275,0.1475,0.0079,0,0,0.1062，经逆序后，其输出顺序是排在第4小块的后面。又如，图15中第7个小块8个方向的数字，包括0.2517,0.1062,0.0669,0.1200,0.0059,0.0059,0.0059,0.1711，经逆序后，其输出顺序是排在图15中第8个小块的后面。
SIFT特征点a～j这10个SIFT特征点周围的16个小块中的第2列与第4列同样改为逆序输出，其128维SIFT描述子如下所示：
a:(0,0,0.1987,0.0866,0,0,0.0512,0.0571,0,0.0039,0.1495,0.0866,0,0,0.0846,0.1004,0.0059,0.0413,0.0728,0.0256,0.0059,0.0020,0.0905,0.1141,0.0098,0.0177,0.0472,0.0905,0.0787,0.0236,0.0295,0.0394,0.0571,0.0118,0.0039,0.0197,0.0826,0.2322,0.0610,0.0295,0.2499,0.2381,0.1791,0.0551,0.0157,0.0138,0.0157,0.0571,0.0216,0.0374,0.1791,0.2499,0.1810,0.0571,0.0413,0.0374,0,0,0.0079,0.0216,0.0453,0.0118,0.1043,0.1023,0.0020,0,0,0.0020,0.0354,0.0492,0.0197,0.0118,0.0315,0.0079,0.0098,0.0492,0.1909,0.2499,0.0708,0.0275,0.2499,0.1574,0.0079,0.0098,0.0118,0.1594,0.0748,0.1102,0.1181,0.1338,0,0,0.0039,0.1200,0.0275,0.0197,0.1004,0.2184,0.0039,0.0020,0.0039,0.0236,0.0177,0.0256,0.0551,0.0925,0,0,0.0098,0.2499,0.0374,0.0138,0.0039,0.0079,0.0020,0,0.0059,0.1948,0.0138,0.0020,0.0138,0.0059,0,0,0,0.0039,0.0020,0.0098)；
b:(0.0197,0.0590,0.0433,0.0295,0.0098,0,0,0.0079,0.0157,0.0728,0.0236,0.0354,0.1141,0.0295,0,0.0118,0.0177,0.0334,0.0216,0.0826,0.1711,0.0885,0.0236,0.0197,0.1141,0.1770,0.0315,0.0354,0.0472,0.0059,0.0039,0.0236,0.2301,0.0728,0.0098,0.0177,0.0610,0.0551,0.0177,0.0885,0.0334,0.0138,0.0079,0.0570,0.2301,0.2301,0.0236,0.0197,0.2301,0.2026,0.0295,0.0197,0.0629,0.0492,0.0157,0.0295,0.0334,0.0806,0.0472,0.0846,0.2222,0.0197,0.0039,0.0079,0.0236,0.0039,0,0.0059,0.1750,0.1731,0.1003,0.0393,0.2301,0.0708,0.0098,0.0157,0.0472,0.0315,0.0551,0.1337,0.0315,0.0177,0.0059,0.0433,0.2301,0.1160,0.0118,0.0118,0.2262,0.0983,0.0138,0.0275,0.0787,0.0393,0.0138,0.0826,0.1495,0.0157,0.0020,0.0138,0.0629,0.0452,0.0590,0.2301,0.0216,0.0275,0.0020,0.0177,0.1829,0.0944,0.0413,0.0295,0.0472,0.0767,0.0138,0.0098,0.0531,0.1318,0.0787,0.0334,0,0.0079,0.0039,0.0020,0.0315,0.2144,0.0688,0.0020)；
c:(0.0354,0.0393,0.1200,0.2321,0.0256,0,0,0,0.0334,0.0393,0.0629,0.1554,0.0885,0.0275,0.0039,0,0.1416,0.0551,0.0374,0.0610,0.0275,0.0236,0.0138,0.0806,0.0629,0.0039,0.0079,0.0728,0.0590,0.0649,0.0138,0.0570,0.0728,0.0374,0.0236,0.2006,0.2321,0.0020,0,0.0295,0.2321,0.1102,0.0236,0.0649,0.0787,0.0059,0.0039,0.0747,0.1377,0.0315,0.0118,0.1397,0.2321,0.0236,0.0059,0.0354,0.1751,0.0393,0.0236,0.1279,0.1180,0.0236,0.0216,0.0787,0.0669,0.0295,0.0216,0.0197,0.0374,0.0649,0.0610,0.1456,0.0492,0.0059,0,0.0177,0.1908,0.2321,0.0669,0.0964,0.1397,0.0374,0.0079,0.0079,0.0393,0.0570,0.0669,0.2321,0.0295,0.0177,0.0059,0.0354,0.2321,0.1082,0.0256,0.0492,0.0413,0.0098,0,0.0059,0.0452,0.1298,0.0570,0.0629,0.1023,0.0826,0.0747,0.0315,0.0079,0.0138,0.0157,0.0964,0.0629,0.0197,0.0590,0.2085,0.0885,0.0511,0.0118,0.0315,0.2183,0.0511,0.0374,0.0511,0.0256,0.0020,0,0.0590)；
d:(0.0039,0.0039,0.0964,0.0708,0.0098,0,0.0138,0.2497,0,0.0079,0.0590,0.1593,0.1278,0.0216,0.0157,0.0315,0.0138,0.0334,0.0354,0.0393,0.1003,0.0197,0.0315,0.0472,0.0472,0.0039,0.0059,0.0452,0.1376,0.0059,0,0.0177,0.0531,0,0,0.0079,0.1435,0.0708,0.0236,0.0570,0.2006,0.1141,0.0747,0.0393,0.0826,0.0118,0.0020,0.0256,0.0511,0.1023,0.2497,0.2379,0.0079,0,0,0.0020,0.0157,0.1082,0.2497,0.2183,0,0,0,0.0177,0.0197,0.0334,0.0846,0.1966,0.0138,0.0098,0.0177,0.0216,0.2497,0.0649,0.1553,0.1357,0,0,0,0.0157,0.2497,0.0295,0.0079,0.0098,0.0905,0.0157,0.0020,0.0767,0.1652,0.0433,0,0.0059,0.0708,0.0236,0.0256,0.0531,0.0944,0.0433,0,0.0039,0.0374,0.0354,0.0334,0.0393,0.2497,0.0177,0,0.0059,0.0492,0.0315,0.0079,0.0610,0.2497,0.0157,0.0157,0.0157,0,0,0,0.1357,0.0118,0.0059,0.0334,0.1927,0.0098,0.0020,0,0.0157)；
e:(0.0118,0,0,0.0039,0.0157,0.1730,0.0511,0.0020,0.0020,0.0118,0.0236,0.0334,0.0236,0.2280,0.2280,0,0.0079,0.0609,0.0354,0,0,0.1887,0.2280,0.0039,0.0236,0.1690,0.0256,0,0,0.0688,0.1278,0.0020,0.0236,0.0039,0.0020,0.0039,0.0059,0.2162,0.2280,0.0138,0.2280,0.1926,0.0511,0.0118,0.0118,0.1042,0.1789,0.0570,0.0295,0.0904,0.1101,0.1474,0.2280,0.1258,0.0256,0.0079,0.0138,0.0334,0.0098,0.0197,0.1022,0.0256,0.0039,0.0020,0.0157,0.0295,0.0059,0,0.0315,0.0354,0.0393,0.0256,0.0275,0.0118,0.0020,0.0059,0.1710,0.2280,0.1514,0.0550,0.2280,0.0354,0.0216,0.0472,0.0197,0.0609,0.1337,0.2280,0.0334,0.0059,0.1081,0.1258,0.0177,0.0275,0.0197,0.0079,0,0.0059,0.0904,0.1907,0.0747,0.0098,0,0,0.0059,0.0020,0.0118,0.1022,0.0983,0.0315,0.0531,0.0216,0.0079,0.0118,0.0098,0.0138,0.0079,0.0334,0.0629,0.0118,0,0.0020,0.0177,0.0059,0,0.0059,0.0216,0.0059)；
f:(0,0,0.0138,0.0098,0.0217,0.0512,0.1772,0.0197,0,0.0197,0.0472,0.0630,0.0394,0.0197,0.1437,0.0118,0.0039,0.0650,0.0374,0.0157,0,0.0020,0.1063,0.0256,0.0039,0.0157,0.0118,0.0039,0,0,0.0256,0.0394,0.0433,0.0236,0.0118,0.0098,0.0039,0.0059,0.0236,0.0433,0.2480,0.2480,0.0827,0.0807,0.0059,0.0020,0.0118,0.0394,0.0295,0.0846,0.2480,0.2480,0.0768,0.0059,0.0098,0.0098,0,0.0197,0.1457,0.1791,0.2480,0.0374,0.0098,0,0,0.0039,0.0413,0.1890,0.2480,0.0650,0.1043,0.0276,0.0295,0.0079,0.0728,0.1004,0.0650,0.0551,0.2480,0.1535,0.2480,0.0276,0.0079,0.0236,0.0098,0.0059,0.1280,0.2480,0.0354,0.0177,0.0394,0.0256,0.0059,0,0.0118,0.0354,0.0295,0.0394,0.0315,0.0354,0.0472,0.0512,0.0394,0.0335,0.0413,0.0098,0.0020,0.0217,0.0630,0.0650,0.0846,0.0906,0.0020,0,0,0,0.0413,0.0669,0.2362,0.0866,0,0,0,0.0079,0.0335,0.0945,0.1654,0.0571)；
g:(0.0059,0.0157,0.0255,0.0039,0,0,0,0.0059,0.0098,0.0431,0.0196,0,0,0.0039,0.0510,0.0431,0.0078,0.1019,0.0392,0,0,0.0216,0.0392,0.0098,0.0412,0.2489,0.0235,0,0,0,0.0039,0.0294,0.0510,0.0529,0.0274,0.0176,0.0176,0.0216,0.0137,0.0490,0.0235,0.0078,0.0098,0.0314,0.0862,0.2489,0.1783,0.0490,0.2489,0.0451,0.0098,0.0059,0.0059,0.0451,0.1646,0.2332,0.0921,0.0353,0.0255,0.0196,0.0020,0,0,0.0196,0.0941,0.0372,0.0078,0.0137,0.0078,0.0490,0.2489,0.0372,0.2489,0.2234,0.1803,0.0314,0.0157,0.0412,0.0666,0.0470,0.0098,0.0314,0.2410,0.2254,0.1078,0.0490,0.0078,0.0059,0.0235,0.0490,0.0333,0.0608,0.0235,0.0059,0,0,0.0353,0.0294,0.0078,0.0078,0,0,0,0.0059,0.0137,0.0196,0.1039,0.0314,0.0176,0.0098,0.0078,0.0216,0.0078,0.0196,0.0568,0.0255,0.2489,0.2489,0.1078,0.0098,0.0020,0,0,0.0078,0.1176,0.1607,0.2489,0.1391)；
h:(0.0020,0.0216,0.1159,0.0884,0.0216,0.0373,0.0373,0.0059,0.0138,0.0727,0.1218,0.0354,0.0334,0.0864,0.0923,0.0334,0.0138,0.0295,0.0530,0.0157,0.0138,0.0550,0.0530,0.0255,0.0039,0.0059,0.0059,0.0354,0.0432,0.0157,0.0098,0.0059,0.0138,0.0314,0.0354,0.0118,0.0334,0.0295,0.0079,0.0020,0.1886,0.2436,0.2240,0.0354,0.0039,0.0079,0.0079,0.0196,0.0255,0.2436,0.2436,0.1002,0.0138,0.0766,0.0314,0.0079,0,0.0707,0.1631,0.2259,0.1906,0.1611,0.0236,0,0,0.0157,0.0786,0.0295,0.0805,0.2436,0.0864,0,0.0393,0.0314,0.0805,0.0471,0.0255,0.2436,0.2436,0.0786,0.2436,0.0884,0.0452,0.0098,0.0020,0.0255,0.0904,0.2220,0.0334,0.0393,0.0196,0.0079,0.0079,0.0059,0.0177,0.0275,0.0255,0.1002,0.0432,0.0059,0.0039,0,0,0.0020,0.0354,0.1356,0.1434,0.0275,0.0275,0.0452,0.0177,0.0255,0,0.0098,0.1002,0.0550,0.0334,0.1375,0.1218,0.0354,0.0020,0.0393,0.1454,0.0354,0.0039,0.0295,0.0805,0.0236)；
i:(0,0.0492,0.1201,0.0158,0,0.0059,0.0059,0,0.0256,0.0473,0.1713,0.0591,0.0059,0.0315,0.0374,0.0256,0.0492,0.1122,0.0512,0.0177,0.0295,0.0295,0.0610,0.0670,0,0.0020,0.0118,0.0354,0.2127,0.2048,0.0532,0.0335,0.0039,0.0276,0.0414,0.0158,0.0197,0.0729,0.0866,0.0138,0.0965,0.0453,0.0847,0.0492,0.0059,0.0118,0.0256,0.1142,0.2284,0.1122,0.1457,0.1122,0.0079,0,0,0.1004,0.0866,0.1989,0.1063,0.2048,0.0217,0,0,0.0020,0.2028,0.2284,0.0492,0.0807,0.0335,0.0098,0.0098,0.0729,0.2284,0.1319,0.1556,0.0827,0.0138,0.0059,0.0020,0.0610,0.0630,0.2028,0.2284,0.1280,0,0,0,0.0059,0.0158,0.1595,0.2186,0.0473,0,0,0,0,0.0236,0.1339,0.1142,0.0039,0,0,0.0020,0.0098,0.0473,0.1260,0.1575,0.0295,0,0,0.0098,0.0118,0.0315,0.0571,0.2107,0.0374,0,0.0039,0.0256,0.0098,0.1516,0.0670,0.0453,0,0,0.0059,0.0256,0.0591)；
j:(0.0079,0.0177,0.1261,0.0611,0.0059,0.0039,0.0118,0.0414,0.0158,0.0591,0.1576,0.0177,0,0,0.0020,0.0197,0.0315,0.0177,0.0749,0.0414,0.0177,0.0118,0.0414,0.0512,0.0020,0,0,0.0039,0.0315,0.1399,0.1911,0.0217,0.0630,0.0217,0.0670,0.0887,0.0059,0.0355,0.1438,0.0433,0.2620,0.1852,0.0690,0.0059,0,0,0.0276,0.1064,0.0394,0.0867,0.2620,0.0414,0,0,0.0020,0.0374,0.0020,0.0079,0.2620,0.1044,0.0039,0.0039,0.0079,0.0197,0.0118,0.0099,0.1221,0.0650,0.0059,0.0020,0.0394,0.1596,0.0512,0.0335,0.0690,0,0,0,0.0946,0.2620,0.2088,0.0532,0.0276,0.0177,0.0039,0.0236,0.1005,0.2620,0.0256,0.0177,0.0926,0.1556,0.0335,0.0788,0.0394,0.0039,0.0020,0.0217,0.1103,0.0276,0.0276,0.0571,0.0355,0.0020,0.0079,0.0591,0.2502,0.0118,0,0.0177,0.0374,0.0611,0.0256,0.0276,0.1103,0.0394,0.0039,0,0.0374,0.2620,0.0020,0,0,0.0039,0.0039,0.0020,0.1005,0.2620)；
对于SIFT特征点A，进一步将其经逆序后的128维SIFT描述子按8方向重组，如图17所示，由此得到128维R-SIFT描述子：
A:(0.0138,0.0039,0.0747,0.0983,0.0846,0.2517,0.0531,0.0020,0,0.0374,0.2517,0.0393,0.0118,0.0059,0,0,0.0079,0.0020,0.0118,0.0236,0.0177,0.1062,0.0374,0.0118,0.0865,0.0334,0.0649,0.0295,0.0354,0.1062,0.1003,0.0590,0.0020,0.0138,0.0393,0.0138,0.0175,0.0669,0.0767,0.0177,0.0983,0.0374,0.0177,0.0610,0.0256,0.0944,0.0885,0.0590,0.0059,0.2222,0.2517,0.0197,0.1475,0.1200,0.2517,0.0688,0.0157,0.0590,0.0157,0.2517,0.0216,0.0020,0,0,0,0.0098,0.0118,0.0059,0.0079,0.0059,0.1809,0.0472,0.0590,0.1750,0.0138,0.0924,0.0767,0.0098,0,0,0,0,0,0.0020,0,0.0059,0.0452,0.0039,0.0334,0.2517,0.0374,0.0256,0.0964,0.0216,0.0787,0.0767,0,0.0020,0,0.0059,0,0.0059,0.0098,0,0.0059,0.2045,0.1514,0.0039,0.0590,0.0669,0.1495,0.1908,0.0079,0.0079,0.1160,0.1986,0.1062,0.1711,0.0098,0,0,0.0551,0.2262,0.0079,0.0236,0.0413,0.0059,0)；
从图17可见，SIFT特征点A的R-SIFT描述子中的前16个数字，包括0.0138,0.0039,0.0747,0.0983,0.0846,0.2517,0.0531,0.0020,0,0.0374,0.2517,0.0393,0.0118,0.0059,0,0代表的是A方向，分别是将图16中16个小块中的A方向数字抽取出来后的结果。同样，SIFT特征点A的R-SIFT描述子中的第17至32个数字，包括0.0079,0.0020,0.0118,0.0236,0.0177,0.1062,0.0374,0.0118,0.0865,0.0334,0.0649,0.0295,0.0354,0.1062,0.1003,0.0590代表的是B方向，分别是将图16中16个小块中的B方向数字抽取出来后的结果。以此类推，SIFT特征点A的R-SIFT描述子中的最后16个数字，包括0.0079,0.0079,0.1160,0.1986,0.1062,0.1711,0.0098,0,0,0.0551,0.2262,0.0079,0.0236,0.0413,0.0059,0代表的是H方向，分别是将图16中16个小块中的H方向数字抽取出来后的结果。
对于SIFT特征点a～j，同样将其经逆序后的128维SIFT描述子按8方向重组，由此得到128维R-SIFT描述子：
a:(0,0,0.0059,0.0098,0.0571,0.2499,0.0216,0,0.0020,0.0315,0.2499,0.1181,0.1004,0.0551,0.0039,0.0138,0,0.0039,0.0413,0.0177,0.0118,0.2381,0.0374,0,0,0.0079,0.1574,0.1338,0.2184,0.0925,0.0079,0.0059,0.1987,0.1495,0.0728,0.0472,0.0039,0.1791,0.1791,0.0079,0,0.0098,0.0079,0,0.0039,0,0.0020,0,0.0866,0.0866,0.0256,0.0905,0.0197,0.0551,0.2499,0.0216,0.0020,0.0492,0.0098,0,0.0020,0,0,0,0,0,0.0059,0.0787,0.0826,0.0157,0.1810,0.0453,0.0354,0.1909,0.0118,0.0039,0.0039,0.0098,0.0059,0,0,0,0.0020,0.0236,0.2322,0.0138,0.0571,0.0118,0.0492,0.2499,0.1594,0.1200,0.0236,0.2499,0.1948,0.0039,0.0512,0.0846,0.0905,0.0295,0.0610,0.0157,0.0413,0.1043,0.0197,0.0708,0.0748,0.0275,0.0177,0.0374,0.0138,0.0020,0.0571,0.1004,0.1141,0.0394,0.0295,0.0571,0.0374,0.1023,0.0118,0.0275,0.1102,0.0197,0.0256,0.0138,0.0020,0.0098)；
b:(0.0197,0.0157,0.0177,0.1141,0.2301,0.0334,0.2301,0.0334,0.0236,0.2301,0.0315,0.2262,0.1495,0.0216,0.0472,0,0.0590,0.0728,0.0334,0.1770,0.0728,0.0138,0.2026,0.0806,0.0039,0.0708,0.0177,0.0983,0.0157,0.0275,0.0767,0.0079,0.0433,0.0236,0.0216,0.0315,0.0098,0.0079,0.0295,0.0472,0,0.0098,0.0059,0.0138,0.0020,0.0020,0.0138,0.0039,0.0295,0.0354,0.0826,0.0354,0.0177,0.0570,0.0197,0.0846,0.0059,0.0157,0.0433,0.0275,0.0138,0.0177,0.0098,0.0020,0.0098,0.1141,0.1711,0.0472,0.0610,0.2301,0.0629,0.2222,0.1750,0.0472,0.2301,0.0787,0.0629,0.1829,0.0531,0.0315,0,0.0295,0.0885,0.0059,0.0551,0.2301,0.0492,0.0197,0.1731,0.0315,0.1160,0.0393,0.0452,0.0944,0.1318,0.2144,0,0,0.0236,0.0039,0.0177,0.0236,0.0157,0.0039,0.1003,0.0551,0.0118,0.0138,0.0590,0.0413,0.0787,0.0688,0.0079,0.0118,0.0197,0.0236,0.0885,0.0197,0.0295,0.0079,0.0393,0.1337,0.0118,0.0826,0.2301,0.0295,0.0334,0.0020)；
c:(0.0354,0.0334,0.1416,0.0629,0.0728,0.2321,0.1377,0.1751,0.0669,0.0492,0.1397,0.0295,0.0413,0.1023,0.0629,0.2183,0.0393,0.0393,0.0551,0.0039,0.0374,0.1102,0.0315,0.0393,0.0295,0.0059,0.0374,0.0177,0.0098,0.0826,0.0197,0.0511,0.1200,0.0629,0.0374,0.0079,0.0236,0.0236,0.0118,0.0236,0.0216,0,0.0079,0.0059,0,0.0747,0.0590,0.0374,0.2321,0.1554,0.0610,0.0728,0.2006,0.0649,0.1397,0.1279,0.0197,0.0177,0.0079,0.0354,0.0059,0.0315,0.2085,0.0511,0.0256,0.0885,0.0275,0.0590,0.2321,0.0787,0.2321,0.1180,0.0374,0.1908,0.0393,0.2321,0.0452,0.0079,0.0885,0.0256,0,0.0275,0.0236,0.0649,0.0020,0.0059,0.0236,0.0236,0.0649,0.2321,0.0570,0.1082,0.1298,0.0138,0.0511,0.0020,0,0.0039,0.0138,0.0138,0,0.0039,0.0059,0.0216,0.0610,0.0669,0.0669,0.0256,0.0570,0.0157,0.0118,0,0,0,0.0806,0.0570,0.0295,0.0747,0.0354,0.0787,0.1456,0.0964,0.2321,0.0492,0.0629,0.0964,0.0315,0.0590)；
d:(0.0039,0,0.0138,0.0472,0.0531,0.2006,0.0511,0.0157,0.0197,0.2497,0.2497,0.1652,0.0944,0.2497,0.2497,0.0118,0.0039,0.0079,0.0334,0.0039,0,0.1141,0.1023,0.1082,0.0334,0.0649,0.0295,0.0433,0.0433,0.0177,0.0157,0.0059,0.0964,0.0590,0.0354,0.0059,0,0.0747,0.2497,0.2497,0.0846,0.1553,0.0079,0,0,0,0.0157,0.0334,0.0708,0.1593,0.0393,0.0452,0.0079,0.0393,0.2379,0.2183,0.1966,0.1357,0.0098,0.0059,0.0039,0.0059,0.0157,0.1927,0.0098,0.1278,0.1003,0.1376,0.1435,0.0826,0.0079,0,0.0138,0,0.0905,0.0708,0.0374,0.0492,0,0.0098,0,0.0216,0.0197,0.0059,0.0708,0.0118,0,0,0.0098,0,0.0157,0.0236,0.0354,0.0315,0,0.0020,0.0138,0.0157,0.0315,0,0.0236,0.0020,0,0,0.0177,0,0.0020,0.0256,0.0334,0.0079,0,0,0.2497,0.0315,0.0472,0.0177,0.0570,0.0256,0.0020,0.0177,0.0216,0.0157,0.0767,0.0531,0.0393,0.0610,0.1357,0.0157)；
e:(0.0118,0.0020,0.0079,0.0236,0.0236,0.2280,0.0295,0.0138,0.0157,0.0275,0.2280,0.0334,0,0.0059,0.0079,0,0,0.0118,0.0609,0.1690,0.0039,0.1926,0.0904,0.0334,0.0295,0.0118,0.0354,0.0059,0.0059,0.0020,0.0118,0.0020,0,0.0236,0.0354,0.0256,0.0020,0.0511,0.1101,0.0098,0.0059,0.0020,0.0216,0.1081,0.0904,0.0118,0.0098,0.0177,0.0039,0.0334,0,0,0.0039,0.0118,0.1474,0.0197,0,0.0059,0.0472,0.1258,0.1907,0.1022,0.0138,0.0059,0.0157,0.0236,0,0,0.0059,0.0118,0.2280,0.1022,0.0315,0.1710,0.0197,0.0177,0.0747,0.0983,0.0079,0,0.1730,0.2280,0.1887,0.0688,0.2162,0.1042,0.1258,0.0256,0.0354,0.2280,0.0609,0.0275,0.0098,0.0315,0.0334,0.0059,0.0511,0.2280,0.2280,0.1278,0.2280,0.1789,0.0256,0.0039,0.0393,0.1514,0.1337,0.0197,0,0.0531,0.0629,0.0216,0.0020,0,0.0039,0.0020,0.0138,0.0570,0.0079,0.0020,0.0256,0.0550,0.2280,0.0079,0,0.0216,0.0118,0.0059)；
f:(0,0,0.0039,0.0039,0.0433,0.2480,0.0295,0,0,0.0295,0.2480,0.0354,0.0295,0.0413,0.0020,0,0,0.0197,0.0650,0.0157,0.0236,0.2480,0.0846,0.0197,0.0039,0.0079,0.0276,0.0177,0.0394,0.0098,0,0,0.0138,0.0472,0.0374,0.0118,0.0118,0.0827,0.2480,0.1457,0.0413,0.0728,0.0079,0.0394,0.0315,0.0020,0,0,0.0098,0.0630,0.0157,0.0039,0.0098,0.0807,0.2480,0.1791,0.1890,0.1004,0.0236,0.0256,0.0354,0.0217,0,0.0079,0.0217,0.0394,0,0,0.0039,0.0059,0.0768,0.2480,0.2480,0.0650,0.0098,0.0059,0.0472,0.0630,0.0413,0.0335,0.0512,0.0197,0.0020,0,0.0059,0.0020,0.0059,0.0374,0.0650,0.0551,0.0059,0,0.0512,0.0650,0.0669,0.0945,0.1772,0.1437,0.1063,0.0256,0.0236,0.0118,0.0098,0.0098,0.1043,0.2480,0.1280,0.0118,0.0394,0.0846,0.2362,0.1654,0.0197,0.0118,0.0256,0.0394,0.0433,0.0394,0.0098,0,0.0276,0.1535,0.2480,0.0354,0.0335,0.0906,0.0866,0.0571)；
g:(0.0059,0.0098,0.0078,0.0412,0.0510,0.0235,0.2489,0.0921,0.0941,0.2489,0.0098,0.0235,0.0353,0.0137,0.0078,0.0020,0.0157,0.0431,0.1019,0.2489,0.0529,0.0078,0.0451,0.0353,0.0372,0.2234,0.0314,0.0490,0.0294,0.0196,0.0196,0,0.0255,0.0196,0.0392,0.0235,0.0274,0.0098,0.0098,0.0255,0.0078,0.1803,0.2410,0.0333,0.0078,0.1039,0.0568,0,0.0039,0,0,0,0.0176,0.0314,0.0059,0.0196,0.0137,0.0314,0.2254,0.0608,0.0078,0.0314,0.0255,0.0078,0,0,0,0,0.0176,0.0862,0.0059,0.0020,0.0078,0.0157,0.1078,0.0235,0,0.0176,0.2489,0.1176,0,0.0039,0.0216,0,0.0216,0.2489,0.0451,0,0.0490,0.0412,0.0490,0.0059,0,0.0098,0.2489,0.1607,0,0.0510,0.0392,0.0039,0.0137,0.1783,0.1646,0,0.2489,0.0666,0.0078,0,0,0.0078,0.1078,0.2489,0.0059,0.0431,0.0098,0.0294,0.0490,0.0490,0.2332,0.0196,0.0372,0.0470,0.0059,0,0.0059,0.0216,0.0098,0.1391)；
h:(0.0020,0.0138,0.0138,0.0039,0.0138,0.1886,0.0255,0,0,0.0393,0.2436,0.0334,0.0255,0.0354,0,0.0020,0.0216,0.0727,0.0295,0.0059,0.0314,0.2436,0.2436,0.0707,0.0157,0.0314,0.0884,0.0393,0.1002,0.1356,0.0098,0.0393,0.1159,0.1218,0.0530,0.0059,0.0354,0.2240,0.2436,0.1631,0.0786,0.0805,0.0452,0.0196,0.0432,0.1434,0.1002,0.1454,0.0884,0.0354,0.0157,0.0354,0.0118,0.0354,0.1002,0.2259,0.0295,0.0471,0.0098,0.0079,0.0059,0.0275,0.0550,0.0354,0.0216,0.0334,0.0138,0.0432,0.0334,0.0039,0.0138,0.1906,0.0805,0.0255,0.0020,0.0079,0.0039,0.0275,0.0334,0.0039,0.0373,0.0864,0.0550,0.0157,0.0295,0.0079,0.0766,0.1611,0.2436,0.2436,0.0255,0.0059,0,0.0452,0.1375,0.0295,0.0236,0.0864,0.2436,0.0904,0.0177,0,0.0177,0.1218,0.0805,0.0059,0.0334,0.0255,0.0059,0.0020,0.0196,0.0079,0,0,0.0786,0.2220,0.0275,0.0020,0.0255,0.0354,0.0236)；
i:(0,0.0256,0.0492,0,0.0039,0.0965,0.2284,0.0866,0.2028,0.2284,0.0630,0.0158,0.0236,0.0473,0.0315,0.1516,0.0492,0.0473,0.1122,0.0020,0.0276,0.0453,0.1122,0.1989,0.2284,0.1319,0.2028,0.1595,0.1339,0.1260,0.0571,0.0670,0.1201,0.1713,0.0512,0.0118,0.0414,0.0847,0.1457,0.1063,0.0492,0.1556,0.2284,0.2186,0.1142,0.1575,0.2107,0.0453,0.0158,0.0591,0.0177,0.0354,0.0158,0.0492,0.1122,0.2048,0.0807,0.0827,0.1280,0.0473,0.0039,0.0295,0.0374,0,0,0.0059,0.0295,0.2127,0.0197,0.0059,0.0079,0.0217,0.0335,0.0138,0,0,0,0,0,0,0.0059,0.0315,0.0295,0.2048,0.0729,0.0118,0,0,0.0098,0.0059,0,0,0,0,0.0039,0.0059,0.0059,0.0374,0.0610,0.0532,0.0866,0.0256,0,0,0.0098,0.0020,0,0,0.0020,0.0098,0.0256,0.0256,0,0.0256,0.0670,0.0335,0.0138,0.1142,0.1004,0.0020,0.0729,0.0610,0.0059,0,0.0098,0.0118,0.0098,0.0591)；
j:(0.0079,0.0158,0.0315,0.0020,0.0630,0.2620,0.0394,0.0020,0.0118,0.0512,0.2088,0.0256,0.0020,0.0079,0.0256,0.0020,0.0177,0.0591,0.0177,0,0.0217,0.1852,0.0867,0.0079,0.0099,0.0335,0.0532,0.0177,0.0217,0.0591,0.0276,0,0.1261,0.1576,0.0749,0,0.0670,0.0690,0.2620,0.2620,0.1221,0.0690,0.0276,0.0926,0.1103,0.2502,0.1103,0,0.0611,0.0177,0.0414,0.0039,0.0887,0.0059,0.0414,0.1044,0.0650,0,0.0177,0.1556,0.0276,0.0118,0.0394,0.0039,0.0059,0,0.0177,0.0315,0.0059,0,0,0.0039,0.0059,0,0.0039,0.0335,0.0276,0,0.0039,0.0039,0.0039,0,0.0118,0.1399,0.0355,0,0,0.0039,0.0020,0,0.0236,0.0788,0.0571,0.0177,0,0.0020,0.0118,0.0020,0.0414,0.1911,0.1438,0.0276,0.0020,0.0079,0.0394,0.0946,0.1005,0.0394,0.0355,0.0374,0.0374,0.1005,0.0414,0.0197,0.0512,0.0217,0.0433,0.1064,0.0374,0.0197,0.1596,0.2620,0.2620,0.0039,0.0020,0.0611,0.2620,0.2620)；
下一步，按下式计算SIFT特征点A的128维R-SIFT描述子相邻值之间的差值，见图18：
计算差值的结果如下所示：
A:(-0.0099,0.0708,0.0236,-0.0138,0.1672,-0.1986,-0.0511,-0.0020,0.0374,0.2144,-0.2124,-0.0275,-0.0059,-0.0059,0,0.0138,-0.0059,0.0098,0.0118,-0.0059,0.0885,-0.0688,-0.0256,0.0747,-0.0531,0.0315,-0.0354,0.0059,0.0708,-0.0059,-0.0413,-0.0511,0.0118,0.0256,-0.0256,0.0138,0.0393,0.0098,-0.0590,0.0806,-0.0610,-0.0197,0.0433,-0.0354,0.0688,-0.0059,-0.0295,-0.0570,0.2163,0.0295,-0.2321,0.1278,-0.0275,0.1318,-0.1829,-0.0531,0.0433,-0.0433,0.2360,-0.2301,-0.0197,-0.0020,0,0.0059,0.0098,0.0020,-0.0059,0.0020,-0.0020,0.1750,-0.1337,0.0118,0.1160,-0.1613,0.0787,-0.0157,-0.0669,-0.0098,0,0,0,0,0.0020,-0.0020,0.0059,0.0393,-0.0413,0.0295,0.2183,-0.2144,-0.0118,0.0708,-0.0747,0.0570,-0.0020,-0.0767,0.0020,-0.0020,0.0059,-0.0059,0.0059,0.0039,-0.0098,0.0059,0.1986,-0.0531,-0.1475,0.0551,0.0079,0.0826,0.0413,-0.1908,0,0.1082,0.0826,-0.0924,0.0649,-0.1613,-0.0098,0,0.0551,0.1711,-0.2183,0.0157,0.0177,-0.0354,-0.0059,0.0079)；
这里，举例说明图18中上述A SIFT特征点的求差结果中代表A方向的前16个数字，包括-0.0099,0.0708,0.0236,-0.0138,0.1672,-0.1986,-0.0511,-0.0020,0.0374,0.2144,-0.2124,-0.0275,-0.0059,0.0059,0,0.0138是如何计算得到的。按图17中A方向的16个数字，分别是0.0138,0.0039,0.0747,0.0983,0.0846,0.2517,0.0531,0.0020,0,0.0374,0.2517,0.0393,0.0118,0.0059,0,0。根据求差值公式：
这个求差值公式说明，前15个差值都是将后面数字减去前面数字所得的结果，第16个差值是将第1个数字减去第16个数字的结果。例如，将0.0039减去0.0138，得到-0.0099，再将0.0747减去0.0039，得到0.0708，以此类推，最后将0.0138减去0，得到0.0138。
同理，对于其余的B、C、D、E、F、G、H方向都分别按上述方法完成差值运算。
对于SIFT特征点a～j，同样分别计算128维R-SIFT描述子相邻值之间的差值，由此得到以下结果：
a:(0,0.0059,0.0039,0.0472,0.1928,-0.2283,-0.0216,0.0020,0.0295,0.2184,-0.1318,-0.0177,-0.0453,-0.0512,0.0098,-0.0138,0.0039,0.0374,-0.0236,-0.0059,0.2263,-0.2007,-0.0374,0,0.0079,0.1495,-0.0236,0.0846,-0.1259,-0.0846,-0.0020,-0.0059,-0.0492,-0.0767,-0.0256,-0.0433,0.1751,0,-0.1712,-0.0079,0.0098,-0.0020,-0.0079,0.0039,-0.0039,0.0020,-0.0020,0.1987,0,-0.0610,0.0649,-0.0708,0.0354,0.1948,-0.2283,-0.0197,0.0472,-0.0394,-0.0098,0.0020,-0.0020,0,0,0.0866,0,0.0059,0.0728,0.0039,-0.0669,0.1653,-0.1358,-0.0098,0.1555,-0.1791,-0.0079,0,0.0059,-0.0039,-0.0059,0,0,0.0020,0.0216,0.2086,-0.2184,0.0433,-0.0453,0.0374,0.2007,-0.0905,-0.0394,-0.0964,0.2263,-0.0551,-0.1909,-0.0039,0.0335,0.0059,-0.0610,0.0315,-0.0453,0.0256,0.0630,-0.0846,0.0512,0.0039,-0.0472,-0.0098,0.0197,-0.0236,-0.0118,0.0492,0.0433,0.0138,-0.0748,-0.0098,0.0275,-0.0197,0.0649,-0.0905,0.0157,0.0826,-0.0905,0.0059,-0.0118,-0.0118,0.0079,0.0472)；
b:(-0.0039,0.0020,0.0964,0.1160,-0.1967,0.1967,-0.1967,-0.0098,0.2065,-0.1986,0.1947,-0.0767,-0.1278,0.0256,-0.0472,0.0197,0.0138,-0.0393,0.1436,-0.1042,-0.0590,0.1888,-0.1219,-0.0767,0.0669,-0.0531,0.0806,-0.0826,0.0118,0.0492,-0.0688,0.0511,-0.0197,-0.0020,0.0098,-0.0216,-0.0020,0.0216,0.0177,-0.0472,0.0098,-0.0039,0.0079,-0.0118,0,0.0118,-0.0098,0.0393,0.0059,0.0472,-0.0472,-0.0177,0.0393,-0.0374,0.0649,-0.0787,0.0098,0.0275,-0.0157,-0.0138,0.0039,-0.0079,-0.0079,`0.0275,0.1042,0.0570,-0.1239,0.0138,0.1691,-0.1672,0.1593,-0.0472,-0.1278,0.1829,-0.1514,-0.0157,0.1200,-0.1298,-0.0216,-0.0216,0.0295,0.0590,-0.0826,0.0492,0.1750,-0.1809,-0.0295,0.1534,-0.1416,0.0846,-0.0767,0.0059,0.0492,0.0374,0.0826,-0.2144,0,0.0236,-0.0197,0.0138,0.0059,-0.0079,-0.0118,0.0964,-0.0452,-0.0433,0.0020,0.0452,-0.0177,0.0374,-0.0098,-0.0688,0.0039,0.0079,0.0039,0.0649,-0.0688,0.0098,-0.0216,0.0315,0.0944,-0.1219,0.0708,0.1475,-0.2006,0.0039,-0.0315,0.0059)；
c:(-0.0020,0.1082,-0.0787,0.0098,0.1593,-0.0944,0.0374,-0.1082,-0.0177,0.0905,-0.1102,0.0118,0.0610,-0.0393,0.1554,-0.1829,0,0.0157,-0.0511,0.0334,0.0728,-0.0787,0.0079,-0.0098,-0.0236,0.0315,-0.0197,-0.0079,0.0728,-0.0629,0.0315,-0.0118,-0.0570,-0.0256,-0.0295,0.0157,0,-0.0118,0.0118,-0.0020,-0.0216,0.0079,-0.0020,-0.0059,0.0747,-0.0157,-0.0216,0.0826,-0.0767,-0.0944,0.0118,0.1279,-0.1357,0.0747,-0.0118,-0.1082,-0.0020,-0.0098,0.0275,-0.0295,0.0256,0.1770,-0.1574,0.1810,0.0629,-0.0610,0.0315,0.1731,-0.1534,0.1534,-0.1141,-0.0806,0.1534,-0.1515,0.1928,-0.1869,-0.0374,0.0806,-0.0629,0,0.0275,-0.0039,0.0413,-0.0629,0.0039,0.0177,0,0.0413,0.1672,-0.1751,0.0511,0.0216,-0.1161,0.0374,-0.0492,-0.0020,0.0039,0.0098,0,-0.0138,0.0039,0.0020,0.0157,0.0393,0.0059,0,-0.0413,0.0315,-0.0413,-0.0039,-0.0118,0,0,0.0806,-0.0236,-0.0275,0.0452,-0.0393,0.0433,0.0669,-0.0492,0.1357,-0.1829,0.0138,0.0334,-0.0649,0.0275,-0.0590)；
d:(-0.0039,0.0138,0.0334,0.0059,0.1475,-0.1494,-0.0354,0.0039,0.2301,0,-0.0846,-0.0708,0.1553,0,-0.2379,-0.0079,0.0039,0.0256,-0.0295,-0.0039,0.1141,-0.0118,0.0059,-0.0747,0.0315,-0.0354,0.0138,0,-0.0256,-0.0020,-0.0098,-0.0020,-0.0374,-0.0236,-0.0295,-0.0059,0.0747,0.1750,0,-0.1652,0.0708,-0.1475,-0.0079,0,0,0.0157,0.0177,0.0629,0.0885,-0.1200,0.0059,-0.0374,0.0315,0.1986,-0.0197,-0.0216,-0.0610,-0.1259,-0.0039,-0.0020,0.0020,0.0098,0.1770,-0.1219,0.1180,-0.0275,0.0374,0.0059,-0.0610,-0.0747,-0.0079,0.0138,-0.0138,0.0905,-0.0197,-0.0334,0.0118,-0.0492,0.0098,0,0.0216,-0.0020,-0.0138,0.0649,-0.0590,-0.0118,0,0.0098,-0.0098,0.0157,0.0079,0.0118,-0.0039,-0.0315,0.0020,-0.0020,0.0020,0.0157,-0.0315,0.0236,-0.0216,-0.0020,0,0.0177,-0.0177,0.0020,0.0236,0.0079,-0.0256,-0.0079,0,0.0138,-0.2183,0.0157,-0.0295,0.0393,-0.0315,-0.0236,0.0157,0.0039,-0.0059,0.0610,-0.0236,-0.0138,0.0216,0.0747,-0.1200,0.2340)；
e:(-0.0098,0.0059,0.0157,0,0.2044,-0.1985,-0.0157,0.0020,0.0118,0.2005,-0.1946,-0.0334,0.0059,0.0020,-0.0079,0.0118,0.0118,0.0491,0.1081,-0.1651,0.1887,-0.1022,-0.0570,-0.0039,-0.0177,0.0236,-0.0295,0,-0.0039,0.0098,-0.0098,-0.0020,0.0236,0.0118,-0.0098,-0.0236,0.0491,0.0590,-0.1002,-0.0039,-0.0039,0.0197,0.0865,-0.0177,-0.0786,-0.0020,0.0079,-0.0177,0.0295,-0.0334,0,0.0039,0.0079,0.1356,-0.1278,-0.0197,0.0059,0.0413,0.0786,0.0649,-0.0885,-0.0885,-0.0079,-0.0020,0.0079,-0.0236,0,0.0059,0.0059,0.2162,-0.1258,-0.0708,0.1396,-0.1514,-0.0020,0.0570,0.0236,-0.0904,-0.0079,0.0157,0.0550,-0.0393,-0.1199,0.1474,-0.1120,0.0216,-0.1002,0.0098,0.1926,-0.1671,-0.0334,-0.0177,0.0216,0.0020,-0.0275,0.1671,0.1769,0,-0.1002,0.1002,-0.0491,-0.1533,-0.0216,0.0354,0.1120,-0.0177,-0.1140,-0.0197,0.0531,0.0098,-0.0413,0.0295,-0.0020,0.0039,-0.0020,0.0118,0.0432,-0.0491,-0.0059,0.0236,0.0295,0.1730,-0.2202,-0.0079,0.0216,-0.0098,-0.0059,-0.0039)；
f:(0,0.0039,0,0.0394,0.2047,-0.2185,-0.0295,0,0.0295,0.2185,-0.2126,-0.0059,0.0118,-0.0394,-0.0020,0,0.0197,0.0453,-0.0492,0.0079,0.2244,-0.1634,-0.0650,-0.0157,0.0039,0.0197,-0.0098,0.0217,-0.0295,-0.0098,0,0,0.0335,-0.0098,-0.0256,0,0.0709,0.1654,-0.1024,-0.1043,0.0315,-0.0650,0.0315,-0.0079,-0.0295,-0.0020,0,0.0138,0.0532,-0.0472,-0.0118,0.0059,0.0709,0.1673,-0.0689,0.0098,-0.0886,-0.0768,0.0020,0.0098,-0.0138,-0.0217,0.0079,0.0020,0.0177,-0.0394,0,0.0039,0.0020,0.0709,0.1713,0,-0.1831,-0.0551,-0.0039,0.0413,0.0157,-0.0217,-0.0079,-0.0118,-0.0315,-0.0177,-0.0020,0.0059,-0.0039,0.0039,0.0315,0.0276,-0.0098,-0.0492,-0.0059,0.0512,0.0138,0.0020,0.0276,-0.0433,-0.0335,-0.0374,-0.0807,-0.0020,-0.0118,-0.0020,0,0.0945,0.1437,-0.1201,-0.1161,0.0276,0.0453,0.1516,-0.0709,0.0118,-0.0079,0.0138,0.0138,0.0039,-0.0039,-0.0295,-0.0098,0.0276,0.1260,0.0945,-0.2126,-0.0020,0.0571,-0.0039,-0.0295,-0.0374)；
g:(0.0039,-0.0020,0.0333,0.0098,-0.0274,0.2254,-0.1568,0.0020,0.1548,-0.2391,0.0137,0.0118,-0.0216,-0.0059,-0.0059,0.0039,0.0274,0.0588,0.1470,-0.1960,-0.0451,0.0372,-0.0098,0.0020,0.1862,-0.1921,0.0176,-0.0196,-0.0098,0,-0.0196,0.0157,-0.0059,0.0196,-0.0157,0.0039,-0.0176,0,0.0157,-0.0176,0.1725,0.0608,-0.2077,-0.0255,0.0960,-0.0470,-0.0568,0.0255,-0.0039,0,0,0.0176,0.0137,-0.0255,0.0137,-0.0059,0.0176,0.1940,-0.1646,-0.0529,0.0235,-0.0059,-0.0176,-0.0039,0,0,0,0.0176,0.0686,-0.0803,-0.0039,0.0059,0.0078,0.0921,-0.0843,-0.0235,0.0176,0.2313,-0.1313,-0.1176,0.0039,0.0176,-0.0216,0.0216,0.2273,-0.2038,-0.0451,0.0490,-0.0078,0.0078,-0.0431,-0.0059,0.0098,0.2391,-0.0882,-0.1607,0.0510,-0.0118,-0.0353,0.0098,0.1646,-0.0137,-0.1646,0.2489,-0.1823,-0.0588,-0.0078,0,0.0078,0.0999,0.1411,-0.2489,0.0372,-0.0333,0.0196,0.0196,0,0.1842,-0.2136,0.0176,0.0098,-0.0412,-0.0059,0.0059,0.0157,-0.0118,0.1293,-0.1333)；
h:(0.0118,0,-0.0098,0.0098,0.1748,-0.1631,-0.0255,0,0.0393,0.2043,-0.2102,-0.0079,0.0098,-0.0354,0.0020,0,0.0511,-0.0432,-0.0236,0.0255,0.2122,0,-0.1729,-0.0550,0.0157,0.0570,-0.0491,0.0609,0.0354,-0.1257,0.0295,-0.0177,0.0059,-0.0688,-0.0471,0.0295,0.1886,0.0196,-0.0805,-0.0845,0.0020,-0.0354,-0.0255,0.0236,0.1002,-0.0432,0.0452,-0.0295,-0.0530,-0.0196,0.0196,-0.0236,0.0236,0.0648,0.1257,-0.1964,0.0177,-0.0373,-0.0020,-0.0020,0.0216,0.0275,-0.0196,0.0530,0.0118,-0.0196,0.0295,-0.0098,-0.0295,0.0098,0.1768,-0.1100,-0.0550,-0.0236,0.0059,-0.0039,0.0236,0.0059,-0.0295,0.0177,0.0491,-0.0314,-0.0393,0.0138,-0.0216,0.0688,0.0845,0.0825,0,-0.2181,-0.0196,-0.0059,0.0452,0.0923,-0.1080,0.0079,0.0550,-0.0393,-0.0432,-0.0020,0,0.0236,-0.0079,0.0629,0.1572,-0.1532,-0.0727,-0.0177,0.0177,0.1041,-0.0413,-0.0432,0.0275,-0.0079,-0.0196,-0.0039,0.0177,-0.0118,-0.0079,0,0.0786,0.1434,-0.1945,-0.0255,0.0236,0.0098,-0.0118,-0.0177)；
i:(0.0256,0.0236,-0.0492,0.0039,0.0926,0.1319,-0.1418,0.1162,0.0256,-0.1654,-0.0473,0.0079,0.0236,-0.0158,0.1201,-0.1516,-0.0020,0.0650,-0.1103,0.0256,0.0177,0.0670,0.0866,0.0295,-0.0965,0.0709,-0.0433,-0.0256,-0.0079,-0.0689,0.0098,-0.0177,0.0512,-0.1201,-0.0394,0.0295,0.0433,0.0610,-0.0394,-0.0571,0.1063,0.0729,-0.0098,-0.1044,0.0433,0.0532,-0.1654,0.0748,0.0433,-0.0414,0.0177,-0.0197,0.0335,0.0630,0.0926,-0.1241,0.0020,0.0453,-0.0807,-0.0433,0.0256,0.0079,-0.0374,0.0158,0.0059,0.0236,0.1831,-0.1930,-0.0138,0.0020,0.0138,0.0118,-0.0197,-0.0138,0,0,0,0,0,0,0.0256,-0.0020,0.1753,-0.1319,-0.0610,-0.0118,0,0.0098,-0.0039,-0.0059,0,0,0,0.0039,0.0020,0,0.0315,0.0236,-0.0079,0.0335,-0.0610,-0.0256,0,0.0098,-0.0079,-0.0020,0,0.0020,0.0079,0.0158,0,-0.0197,0.0256,0.0414,-0.0335,-0.0197,0.1004,-0.0138,-0.0985,0.0709,-0.0118,-0.0551,-0.0059,0.0098,0.0020,-0.0020,0.0492,-0.0591)；
j:(0.0079,0.0158,-0.0296,0.0611,0.1990,-0.2226,-0.0374,0.0099,0.0394,0.1576,-0.1832,-0.0236,0.0059,0.0177,-0.0236,0.0059,0.0414,-0.0414,-0.0177,0.0217,0.1635,-0.0985,-0.0788,0.0020,0.0236,0.0197,-0.0355,0.0039,0.0374,-0.0315,-0.0276,0.0177,0.0315,-0.0827,-0.0749,0.0670,0.0020,0.1931,0,-0.1399,-0.0532,-0.0414,0.0650,0.0177,0.1399,-0.1399,-0.1103,0.1261,-0.0433,0.0236,-0.0374,0.0847,-0.0827,0.0355,0.0630,-0.0394,-0.0650,0.0177,0.1379,-0.1281,-0.0158,0.0276,-0.0355,0.0571,-0.0059,0.0177,0.0138,-0.0256,-0.0059,0,0.0039,0.0020,-0.0059,0.0039,0.0296,-0.0059,-0.0276,0.0039,0,0.0020,-0.0039,0.0118,0.1281,-0.1044,-0.0355,0,0.0039,-0.0020,-0.0020,0.0236,0.0552,-0.0217,-0.0394,-0.0177,0.0020,0.0020,-0.0099,0.0394,0.1497,-0.0473,-0.1162,-0.0256,0.0059,0.0315,0.0552,0.0059,-0.0611,-0.0039,0.0020,0,0.0630,-0.0887,-0.0217,0.0315,-0.0296,0.0217,0.0630,-0.0690,-0.0177,0.1399,0.1024,0,-0.2581,-0.0020,0.0591,0.2009,0,-0.2206)；
接下来，对于SIFT特征点A的128维R-SIFT描述子差值进行二值化，见图19，获得如下所示的BR-SIFT描述子：
A:(0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 1 0 1 1 0 1 0 0 1 0 1 0 1 1 0 0 0 11 0 1 1 1 0 1 0 0 1 0 1 0 0 0 0 1 1 0 1 0 1 0 0 1 0 1 0 0 0 1 1 1 1 0 1 0 1 01 1 0 1 0 0 0 1 1 1 1 1 0 1 1 0 1 1 0 0 1 0 1 0 0 1 0 1 0 1 1 0 1 1 0 0 1 1 11 0 1 1 1 0 1 0 0 1 1 1 0 1 1 0 0 1)；
按二值化公式：上述SIFT特征点A的128维R-SIFT描述子差值中的第一个数字是-0.0099，则被二值化为0，第二个数字是0.0708，则被二值化为1，以此类推，一直到最后一个数字0.0079，则被二值化为1。
同理，对于SIFT特征点a～j的128维的R-SIFT描述子差值进行二值化，获得如下所示的BR-SIFT描述子：
a:(1 1 1 1 1 0 0 1 1 1 0 0 0 0 1 0 1 1 0 0 1 0 0 1 1 1 0 1 0 0 0 0 00 0 0 1 1 0 0 1 0 0 1 0 1 0 1 1 0 1 0 1 1 0 0 1 0 0 1 0 1 1 1 1 1 1 1 0 1 0 01 0 0 1 1 0 0 1 1 1 1 1 0 1 0 1 1 0 0 0 1 0 0 0 1 1 0 1 0 1 1 0 1 1 0 0 1 0 01 1 1 0 0 1 0 1 0 1 1 0 1 0 0 1 1)；
b:(0 1 1 1 0 1 0 0 1 0 1 0 0 1 0 1 1 0 1 0 0 1 0 0 1 0 1 0 1 1 0 1 00 1 0 0 1 1 0 1 0 1 0 1 1 0 1 1 1 0 0 1 0 1 0 1 1 0 0 1 0 0 1 1 1 0 1 1 0 1 00 1 0 0 1 0 0 0 1 1 0 1 1 0 0 1 0 1 0 1 1 1 1 0 1 1 0 1 1 0 0 1 0 0 1 1 0 1 00 1 1 1 1 0 1 0 1 1 0 1 1 0 1 0 1)；
c:(0 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 0 1 0 0 1 0 1 0 00 0 1 1 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 1 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 1 0 01 0 1 0 0 1 0 1 1 0 1 0 1 1 1 1 1 0 1 1 0 1 0 0 1 1 1 0 1 1 1 1 1 1 0 1 0 0 01 1 1 0 0 1 0 1 1 0 1 0 1 1 0 1 0)；
d:(0 1 1 1 1 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 1 0 1 0 1 0 1 1 0 0 0 0 00 0 0 1 1 1 0 1 0 0 1 1 1 1 1 1 0 1 0 1 1 0 0 0 0 0 0 1 1 1 0 1 0 1 1 0 0 0 10 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 1 1 1 0 0 1 0 1 1 0 1 0 0 1 1 0 1 1 1 0 0 11 0 1 0 1 0 0 1 1 0 1 0 0 1 1 0 1)；
e:(0 1 1 1 1 0 0 1 1 1 0 0 1 1 0 1 1 1 1 0 1 0 0 0 0 1 0 1 0 1 0 0 11 0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 0 1 1 1 1 0 0 1 1 1 1 0 0 0 0 1 0 1 1 1 1 0 01 0 0 1 1 0 0 1 1 0 0 1 0 1 0 1 1 0 0 0 1 1 0 1 1 1 0 1 0 0 0 1 1 0 0 0 1 1 01 0 1 0 1 1 0 0 1 1 1 0 0 1 0 0 0)；
f:(1 1 1 1 1 0 0 1 1 1 0 0 1 0 0 1 1 1 0 1 1 0 0 0 1 1 0 1 0 0 1 1 10 0 1 1 1 0 0 1 0 1 0 0 0 1 1 1 0 0 1 1 1 0 1 0 0 1 1 0 0 1 1 1 0 1 1 1 1 1 10 0 0 1 1 0 0 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 01 0 1 1 1 0 0 0 1 1 1 0 0 1 0 0 0)；
g:(1 0 1 1 0 1 0 1 1 0 1 1 0 0 0 1 1 1 1 0 0 1 0 1 1 0 1 0 0 1 0 1 01 0 1 0 1 1 0 1 1 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 1 0 0 1 0 0 0 1 1 1 1 1 0 0 11 1 0 0 1 1 0 0 1 1 0 1 1 0 0 1 0 1 0 0 1 1 0 0 1 0 0 1 1 0 0 1 0 0 0 1 1 1 10 1 0 1 1 1 1 0 1 1 0 0 1 1 0 1 0)；
h:(1 1 0 1 1 0 0 1 1 1 0 0 1 0 1 1 1 0 0 1 1 1 0 0 1 1 0 1 1 0 1 0 10 0 1 1 1 0 0 1 0 0 1 1 0 1 0 0 0 1 0 1 1 1 0 1 0 0 0 1 1 0 1 1 0 1 0 0 1 1 00 0 1 0 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 1 0 1 1 0 0 0 1 1 0 1 1 0 0 0 1 1 00 1 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0)；
i:(1 1 0 1 1 1 0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 1 1 1 0 1 0 0 0 0 1 0 10 0 1 1 1 0 0 1 1 0 0 1 1 0 1 1 0 1 0 1 1 1 0 1 1 0 0 1 1 0 1 1 1 1 0 0 1 1 10 0 1 1 1 1 1 1 1 0 1 0 0 0 1 1 0 0 1 1 1 1 1 1 1 1 0 1 0 0 1 1 0 0 1 1 1 1 10 1 1 0 0 1 0 0 1 0 0 0 1 1 0 1 0)；
j:(1 1 0 1 1 0 0 1 1 1 0 0 1 1 0 1 1 0 0 1 1 0 0 1 1 1 0 1 1 0 0 1 10 0 1 1 1 1 0 0 0 1 1 1 0 0 1 0 1 0 1 0 1 1 0 0 1 1 0 0 1 0 1 0 1 1 0 0 1 1 10 1 1 0 0 1 1 1 0 1 1 0 0 1 1 0 0 1 1 0 0 0 1 1 0 1 1 0 0 0 1 1 1 1 0 0 1 1 10 0 1 0 1 1 0 0 1 1 1 0 0 1 1 1 0)；
下一步，对于a～j共10个SIFT特征点的BR-SIFT描述子分别进行逆序编码，获得二值描述子MBR-SIFT，如下所示：
a:(0 1 1 1 1 0 0 0 1 1 0 0 0 0 0 1 0 1 1 0 1 0 0 1 0 1 0 1 1 0 0 0 11 0 1 1 0 0 1 0 0 1 0 1 0 0 0 1 1 0 1 1 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 0 1 0 1 0 0 1 0 1 0 1 1 0 1 1 0 0 1 1 1 10 1 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1)；
b:(1 0 1 1 0 1 0 1 1 0 1 0 0 0 1 0 1 0 1 0 0 1 0 0 1 0 1 0 0 0 0 0 10 1 0 0 1 1 0 1 1 0 0 1 0 0 1 0 0 0 0 1 0 1 0 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 0 1 0 1 1 0 0 0 1 0 0 1 0 1 0 1 0 0 1 1 0 1 10 1 0 0 1 0 1 0 1 1 0 1 1 0 1 0 0)；
c:(0 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0 1 0 1 0 0 1 0 1 1 0 0 1 11 1 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 1 0 1 0 0 1 1 0 1 1 0 1 1 0 1 1 0 1 0 0 1 1 10 0 1 0 1 1 0 1 1 0 1 0 0 1 0 0 1)；
d:(1 0 0 1 1 0 0 0 1 1 0 0 0 0 1 1 1 0 0 1 1 0 1 0 0 1 1 0 1 0 1 0 01 1 0 0 0 1 0 0 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 1 0 0 0 1 1 1 10 1 1 1 0 0 1 0 1 0 1 0 1 1 0 0 1)；
e:(1 0 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 0 1 1 0 0 0 1 1 0 0 1 0 1 1 10 0 1 1 1 0 0 1 1 1 0 1 0 0 0 1 0 0 1 1 1 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 1 0 0 0 0 1 0 1 0 1 1 1 0 0 1 1 1 0 0 1 1 0 01 1 0 1 0 1 0 1 1 1 1 0 1 0 0 0 1)；
f:(1 1 0 1 1 0 0 0 1 1 0 0 0 0 0 0 1 1 0 1 1 0 0 0 1 1 1 0 0 0 1 1 10 0 0 1 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 1 1 1 0 0 0 1 0 1 1 1 1 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 1 1 1 0 1 0 1 1 0 0 0 1 1 00 0 1 1 0 1 0 0 1 1 1 0 0 1 0 0 0)；
g:(1 1 1 0 0 1 0 0 1 0 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 0 0 0 0 1 0 1 00 0 0 1 1 1 0 1 1 0 0 1 1 0 1 1 0 0 1 1 0 1 0 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 0 1 0 0 0 0 1 1 1 1 0 1 1 0 0 1 0 0 1 0 1 0 10 1 0 1 1 0 1 0 0 1 0 1 1 0 0 0 0)；
h:(0 1 0 1 1 0 0 0 1 1 0 0 1 0 0 0 1 0 0 1 1 0 0 0 1 1 0 1 1 1 0 1 10 0 1 1 1 0 0 1 0 0 1 1 1 0 1 1 0 0 1 1 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 0 1 0 1 1 0 0 1 0 0 1 1 0 1 1 0 0 0 1 1 01 0 1 0 0 1 0 0 1 1 0 0 0 1 1 0 1)；
i:(0 1 0 0 1 1 0 0 1 0 0 0 1 0 0 1 0 1 0 0 1 1 1 0 1 1 0 1 1 0 0 1 00 0 0 0 1 1 0 0 1 1 0 1 0 0 1 0 0 0 0 0 1 1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 1 1 0 0 0 1 1 00 0 1 1 1 1 0 1 0 0 0 0 0 1 0 1 1)；
j:(1 0 0 1 1 0 0 0 1 1 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 1 0 1 1 00 0 1 1 0 0 0 0 1 1 1 0 0 1 1 0 1 1 1 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0 1 0 1 0 1 0 1 1 0 0 0 1 1 1 0 0 0 0 1 1 00 1 1 0 0 1 0 0 0 1 1 0 0 1 1 0 0)；
图20显示了SIFT特征点A的二值描述子MBR-SIFT，具体构造方法如下：先将SIFT特征点A的二值描述子BR-SIFT(0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 1 0 1 1 0 1 0 0 1 0 10 1 1 0 0 0 1 1 0 1 1 1 0 1 0 0 1 0 1 0 0 0 0 1 1 0 1 0 1 0 0 1 0 1 0 0 0 1 11 1 0 1 0 1 0 1 1 0 1 0 0 0 1 1 1 1 1 0 1 1 0 1 1 0 0 1 0 1 0 0 1 0 1 0 1 1 01 1 0 0 1 1 1 1 0 1 1 1 0 1 0 0 1 1 1 0 1 1 0 0 1)的128位按位取反，得到(1 0 01 0 1 1 1 0 0 1 1 1 1 0 0 1 0 0 1 0 1 1 0 1 0 1 0 0 1 1 1 0 0 1 0 0 0 1 0 1 10 1 0 1 1 1 1 0 0 1 0 1 0 1 1 0 1 0 1 1 1 0 0 0 0 1 0 1 0 1 0 0 1 0 1 1 1 0 00 0 0 1 0 0 1 0 0 1 1 0 1 0 1 1 0 1 0 1 0 0 1 0 0 1 1 0 0 0 0 1 0 0 0 1 0 1 10 0 0 1 0 0 1 1 0)，然后对A方向中的第0-15位(1 0 0 1 0 1 1 1 0 0 1 1 1 1 0 0)，保持第15位位置不变，其余第0-14位按倒序输出，得到(0 1 1 1 1 0 0 1 1 1 0 1 0 0 10)，接着，对B方向中的第0-15位(1 0 0 1 0 1 1 0 1 0 1 0 0 1 1 1)，保持第15位位置不变，其余第0-14位按倒序输出，得到(1 1 0 0 1 0 1 0 1 1 0 1 0 0 1 1)，以此类推，对H方向中的第0-15位(0 0 0 1 0 1 1 0 0 0 1 0 0 1 1 0)，保持第15位位置不变，其余第0-14位按倒序输出，得到(1 1 0 0 1 0 0 0 1 1 0 1 0 0 0 0)；接着，将H方向与B方向对应的16个二值数值交换，同理，完成G方向与C方向，以及F方向与D方向的数值交换，这样就完成了二值描述子MBR-SIFT的构造。同理，可以得到SIFT特征点a～j的二值描述子MBR-SIFT。
SIFT特征点A的二值描述子BR-SIFT为(0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 1 0 11 0 1 0 0 1 0 1 0 1 1 0 0 0 1 1 0 1 1 1 0 1 0 0 1 0 1 0 0 0 0 1 1 0 1 0 1 0 01 0 1 0 0 0 1 1 1 1 0 1 0 1 0 1 1 0 1 0 0 0 1 1 1 1 1 0 1 1 0 1 1 0 0 1 0 1 00 1 0 1 0 1 1 0 1 1 0 0 1 1 1 1 0 1 1 1 0 1 0 0 1 1 1 0 1 1 0 0 1)，SIFT特征点a的二值描述子BR-SIFT为(1 1 1 1 1 0 0 1 1 1 0 0 0 0 1 0 1 1 0 0 1 0 0 1 1 1 01 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 1 0 1 0 1 1 0 1 0 1 1 0 0 1 0 0 1 0 1 1 1 1 11 1 0 1 0 0 1 0 0 1 1 0 0 1 1 1 1 1 0 1 0 1 1 0 0 0 1 0 0 0 1 1 0 1 0 1 1 0 11 0 0 1 0 0 1 1 1 0 0 1 0 1 0 1 1 0 1 0 0 1 1)，将两者的对应位分别作异或操作，结果为：
A与a异或:(1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 1 0 0 0 1 00 0 1 1 0 1 0 0 0 1 1 0 1 1 1 1 0 1 0 1 1 1 1 0 0 0 0 0 1 1 0 1 0 0 0 0 1 0 00 0 1 0 0 1 1 1 0 1 0 0 0 0 1 1 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 1 0 1 1 0 1 0 10 1 1 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 1 0)；
同理，将SIFT特征点A的二值描述子BR-SIFT分别与b～j的二值描述子BR-SIFT分别作异或操作，结果为：
A与b异或:(0 0 0 1 1 1 0 0 0 1 1 0 0 1 1 0 1 1 0 0 1 1 0 1 1 1 1 1 0 10 1 1 1 1 1 1 0 1 1 1 0 0 0 0 1 0 1 0 0 0 1 1 1 1 0 0 1 1 0 1 0 1 0 0 0 0 0 11 1 1 1 1 1 0 1 0 1 1 0 0 1 1 0 1 0 0 1 1 0 0 1 0 1 0 0 1 1 1 0 1 0 0 1 0 1 01 0 1 0 0 0 0 1 1 1 0 0 0 1 1 0 1 1 0 0)；
A与c异或:(0 0 1 1 0 0 1 0 1 0 0 1 1 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 0 01 0 1 1 0 0 0 1 1 1 0 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0 0 1 1 1 0 0 1 1 0 00 0 1 0 0 0 0 0 1 1 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 01 1 1 1 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 1)；
A与d异或:(0 0 0 1 0 0 0 1 0 0 0 0 1 1 1 1 1 0 1 0 0 0 1 1 1 1 1 0 1 00 0 1 1 0 1 0 0 1 1 1 0 1 1 0 1 1 1 0 1 1 1 1 0 0 0 1 0 1 0 1 1 0 1 0 1 1 0 01 0 0 1 1 1 0 1 0 0 0 0 1 1 1 1 1 1 0 1 1 1 0 0 1 1 0 0 1 1 1 1 1 1 0 1 1 1 01 1 0 1 1 0 1 1 1 0 1 0 1 0 0 1 0 1 0 0)；
A与e异或:(0 0 0 1 0 0 0 1 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 1 0 0 0 0 1 10 0 0 0 0 1 0 0 0 1 0 1 0 0 1 0 1 0 0 1 1 0 1 0 0 0 0 1 0 1 0 0 1 1 0 1 1 0 10 0 1 0 0 1 1 1 0 1 0 0 1 1 1 1 0 0 0 0 0 0 1 1 0 0 1 0 1 1 1 1 1 0 0 0 0 0 10 0 1 1 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0 1)；
A与f异或:(1 0 0 1 0 0 0 1 0 0 0 0 1 0 1 0 1 0 1 1 0 0 0 1 1 0 0 0 1 01 1 0 1 0 0 0 0 0 1 1 0 0 0 1 0 1 1 0 1 0 0 1 0 0 1 1 0 0 1 0 0 0 0 0 1 1 0 10 1 0 1 0 1 1 1 0 1 1 1 1 1 1 1 0 1 0 1 0 0 0 1 0 1 0 1 0 1 0 1 1 1 0 0 0 0 00 0 1 1 1 0 0 1 1 0 0 0 0 0 0 1 0 0 0 1)；
A与g异或:(1 1 0 1 1 1 0 1 0 1 1 1 0 0 1 0 1 0 0 0 1 1 0 0 1 1 1 1 1 10 1 1 0 0 0 1 0 1 1 1 1 1 0 0 0 0 1 1 0 1 0 1 1 1 0 0 1 1 0 1 0 1 1 0 0 1 0 11 0 0 0 1 1 0 1 1 1 1 0 0 1 1 0 1 0 0 1 1 0 1 1 0 0 0 0 0 1 1 0 1 0 0 1 0 0 00 0 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 0 1 1)；
A与h异或:(1 0 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 1 1 0 0 0 0 01 0 0 1 0 0 0 0 0 1 1 0 1 1 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1 0 1 1 1 0 0 1 1 1 00 1 1 1 0 0 0 1 1 1 0 0 1 1 1 1 0 1 0 0 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 10 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 1 0 1)；
A与i异或:(1 0 1 1 0 1 0 1 0 1 0 1 1 0 0 1 0 0 1 1 0 1 1 0 0 0 0 1 1 01 0 0 1 0 0 0 0 0 1 1 1 1 0 0 1 0 1 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 0 0 1 1 00 1 0 1 0 0 1 1 1 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1 0 1 1 0 1 1 1 1 1 1 0 1 0 1 00 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 1)；
A与j异或:(1 0 1 1 0 0 0 1 0 0 0 0 1 1 1 0 1 1 1 1 0 0 0 0 1 0 0 0 0 00 1 0 1 0 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 0 0 1 0 1 1 0 0 0 1 1 0 1 0 1 1 00 1 0 1 1 0 0 0 1 0 0 1 0 0 0 1 0 1 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 0 0 1 0 10 0 0 0 1 0 1 1 0 0 0 0 0 0 0 1 0 1 1 1)；
接下来，将SIFT特征点A的二值描述子BR-SIFT分别与SIFT特征点a～j的二值描述子MBR-SIFT进行异或操作，结果为：
A与a异或:(0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 01 0 1 1 0 1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0)；
A与b异或:(1 1 0 1 1 1 0 1 0 1 1 0 0 0 0 1 1 1 0 0 1 1 0 1 1 1 1 1 1 00 0 0 1 1 1 1 0 1 1 1 1 1 0 0 0 0 1 1 1 0 1 1 1 1 0 0 1 1 0 1 0 1 0 1 1 0 1 01 0 1 1 0 1 0 0 0 1 1 0 0 1 1 0 1 0 0 1 1 0 0 1 1 0 0 0 0 1 1 1 0 0 0 1 0 1 01 0 0 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 0 1)；
A与c异或:(0 0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 00 1 0 0 1 1 0 1 0 1 0 0 1 1 1 0 0 0 0 1 1 1 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 1 01 0 1 1 0 1 0 0 0 1 1 0 1 1 1 1 0 1 0 0 0 1 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 0 10 0 0 0 1 0 1 1 0 0 1 0 1 0 0 1 0 0 0 0)；
A与d异或:(1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 0 0 1 1 0 01 0 1 0 1 1 1 1 1 1 0 1 0 0 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 0 1 1 1 0 1 1 0 1 01 0 1 1 0 1 0 0 0 1 1 1 1 1 1 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 1 0 0 00 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0)；
A与e异或:(1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 1 1 0 0 1 0 01 1 0 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 01 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 1 1 1 0 1 1 1 1 0 0 0 0 00 1 1 1 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0)；
A与f异或:(1 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 0 0 1 1 0 1 1 1 01 1 0 1 0 1 0 0 0 1 0 1 0 1 0 1 1 0 1 1 0 1 1 0 1 0 1 0 0 0 1 1 0 0 1 1 0 1 01 0 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 0 0 0 1 1 0 0 0 1 1 0 1 1 0 0 0 0 0 0 10 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1)；
A与g异或:(1 0 0 0 1 1 0 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 1 1 1 0 1 1 10 1 1 1 0 1 0 0 1 1 1 1 1 0 0 1 0 1 0 1 0 0 1 1 1 0 0 1 1 0 1 0 1 0 1 1 0 1 01 0 1 1 0 1 0 0 0 1 1 0 0 1 1 0 1 0 0 1 1 0 1 0 1 1 1 0 1 1 1 0 1 0 0 1 0 1 10 1 0 0 0 1 0 1 1 1 0 1 0 1 1 0 1 0 0 1)；
A与h异或:(0 0 1 1 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 0 0 0 1 1 0 0 0 0 10 1 0 1 0 0 0 0 0 1 1 0 1 1 0 1 0 1 0 1 0 0 1 0 0 0 1 0 0 0 1 1 1 1 1 1 0 1 01 0 1 1 0 1 0 0 0 1 1 0 1 1 1 0 0 0 0 1 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 0 10 0 1 1 1 0 1 0 0 0 0 0 0 1 0 1 0 1 0 0)；
A与i异或:(0 0 1 0 0 1 0 0 0 1 0 0 1 0 1 0 0 0 1 0 0 1 1 1 1 0 0 0 0 00 1 1 1 0 1 1 0 1 1 0 1 0 0 0 0 0 1 1 1 0 1 0 0 1 0 1 1 0 1 0 1 1 1 1 1 0 1 01 0 1 1 0 1 0 0 0 1 1 0 1 1 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 10 0 1 0 1 0 0 1 0 0 1 1 1 1 0 1 0 0 1 0)；
A与j异或:(1 1 1 1 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 0 0 0 1 1 0 0 1 0 01 1 1 1 0 0 0 1 0 1 0 1 0 1 1 0 1 1 1 0 1 0 0 1 1 1 1 0 0 1 0 0 0 1 1 1 0 1 01 0 1 1 0 1 0 0 0 1 1 0 1 0 1 1 1 1 0 1 0 1 1 1 1 1 0 0 1 1 0 1 0 1 0 1 0 0 10 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 0 1)；
SIFT特征点A的二值描述子BR-SIFT与SIFT特征点a～j的二值描述子BR-SIFT的汉明距离分别为：52,68,49,72,49,55,64,54,62,56；
SIFT特征点A的二值描述子BR-SIFT与SIFT特征点a～j的二值描述子MBR-SIFT的汉明距离分别为：17,71,55,52,48,54,70,52,56,64；
取两者中的较小者作为SIFT特征点对间的相似距离R，因此，SIFT特征点A与SIFT特征点a～j的相似性距离分别为：17,68,49,52,48,54,64,52,56,56；
SIFT特征点A与SIFT特征点a～j的相似性距离R由小到大排序分别为：17,48,49,52,52,54,56,56,64,68；
根据最近邻匹配，distratio设为0.65，最小值和次小值分别为17和48，且17<(48*0.65)，所以SIFT特征点A与SIFT特征点a匹配。
为进一步说明本发明对镜像翻转变化图像匹配的效果，我们分别选取了一组具有水平镜像翻转变化的匹配图像对(定义为实验序号1)和另一组具有垂直镜像翻转变化的匹配图像对(定义为实验序号2)的2组实验，然后由计算机使用本发明进行图像匹配，现将本发明的该2组实验与以下三种方法比较。一为D.G.Lowe.Distinctive image featuresfrom scale-invariant keypoints[J].International Journal of Computer Vision,2004,60(2):91-110.一文中的SIFT方法(以下简称SIFT方法)；二为Chun-Che Chen,Shang-Lin Hsieh,Using binarization and hashing for efficient SIFT matching[J].Journal of Visual Communication and Image Representation,30(2015)86–93.一文中的二值化方法结合汉明距离(以下简称Chen’方法)；三为Wengang Zhou,HouqiangLi.BSIFT:Toward data-independent codebook for large scale image search[J].IEEE Transactions on Image Processing,2015,24(03):967–979.一文中的二值化方法结合汉明距离(以下简称Zhou’方法)；表1为上述三种方法和本发明的实验数据比较。图像匹配结果如下：
表1：
表1列出SIFT方法、Chen’方法、Zhou’方法和本发明的实验序号1和实验序号2的两组实验中提取的SIFT特征点数目、匹配SIFT特征点对的数目、错误匹配点对的数目、匹配准确率、匹配查全率和处理时间等实验结果，其中，匹配准确率的计算公式为：
匹配准确率＝(匹配SIFT特征点对的数目–错误匹配点对数目)/匹配SIFT特征点对的数目
匹配查全率＝(匹配SIFT特征点对的数目–错误匹配点对数目)/两幅待匹配图像对中SIFT特征点较少的数目
从表1中的数据可以看出，无论从匹配准确率还是匹配查全率来说，本发明远超其余三种方法，而在处理时间方面，本发明仅略高于Chen’方法，而相对于SIFT方法和Zhou’方法，本发明有明显降低。上述实验结果说明本发明在保证处理时间的同时，很好地解决了SIFT方法和BSIFT方法对于镜像翻转变化敏感的问题。
另外，本发明通过对分别具有旋转、尺度、视角、亮度、模糊变化的图像对进行匹配，匹配SIFT特征点对的数目和错误匹配SIFT特征点对的数目分别为(190,53,163,25,25)和(3,0,0,4,4)。可见，本发明解决了在图像匹配过程中，SIFT方法或BSIFT方法对图像镜像翻转变化敏感的问题，同时，也保证了对旋转、尺度、视角、亮度、模糊变化的不变性。
以上详细描述了本发明的较佳具体实施例。应当理解，本领域的普通技术人员无需创造性劳动就可以根据本发明的构思作出诸多修改和变化。因此，凡本技术领域中技术人员依本发明的构思在现有技术的基础上通过逻辑分析、推理或者有限的实验可以得到的技术方案，皆应在由权利要求书所确定的保护范围内。

Claims (10)

1.一种新型的二值SIFT描述子及其图像匹配方法，其特征在于，包括步骤：S1：构建描述子步骤；S2：图像匹配步骤；
其中，所述S1：构建描述子步骤包括：
S11：分别提取待匹配图像对的SIFT特征点；
S12：计算128维SIFT特征点描述子；
S13：对所述128维SIFT特征点描述子进行重构，得到128维R-SIFT描述子；
S14：计算所述128维R-SIFT描述子的相邻值之间的差值；
S15：二值化R-SIFT描述子，得到128位二值描述子BR-SIFT；
S16：构建翻转图的二值描述子MBR-SIFT；
所述S2：图像匹配步骤包括：
S21：对于待匹配图像对中的SIFT特征点对计算相似距离；
S22：根据最近邻匹配进行所述SIFT特征点对的相似性判断；
S23：输出所述SIFT特征点匹配后的图像对。
2.如权利要求1所述的一种新型的二值SIFT描述子及其图像匹配方法，其特征在于，所述的提取待匹配图像对的SIFT特征点，其具体步骤为：对图像进行归一化预处理后，将图像放大并进行预滤波以剔除噪声；将可变尺度高斯卷积核和输入图像卷积得到图像的尺度空间，在高斯差分DOG尺度空间中检测局部极值以作为SIFT特征点，得到SIFT特征点后，去除其中对比度低和稳定性差的SIFT特征点。
3.如权利要求1所述的一种新型的二值SIFT描述子及其图像匹配方法，其特征在于，所述计算所述128维SIFT特征点描述子的获取方式包括：以SIFT特征点为中心，将其周围区域分为4×4个小块，计算每个小块中包含的8个方向的梯度直方图，每个方向给定一个数值，得到一个128维的向量，由此获得所述SIFT特征点的128维描述子。
4.如权利要求1所述的一种新型的二值SIFT描述子及其图像匹配方法，其特征在于，所述的对128维SIFT特征点描述子进行重构，得到所述128维R-SIFT描述子的具体方式包括：把所述SIFT特征点周围的4×4共16个小块中的第2列与第4列改为逆序输出；将所述的16个小块再按8方向重组，由此得到重构后的128维R-SIFT描述子。
5.如权利要求1所述的一种新型的二值SIFT描述子及其图像匹配方法，其特征在于，使用计算所述128维R-SIFT描述子相邻值之间的差值。
6.如权利要求1所述的一种新型的二值SIFT描述子及其图像匹配方法，其特征在于，所述二值化R-SIFT描述子包括使用得到128位二值描述子BR-SIFT。
7.如权利要求1所述的一种新型的二值SIFT描述子及其图像匹配方法，其特征在于，所述的构建翻转图的二值描述子MBR-SIFT，其具体步骤包括：先将所述二值描述子BR-SIFT的128位按位取反，然后对于各方向中的第0-15位，保持第15位位置不变，其余第0-14位按倒序输出；接着，将H方向与B方向对应的16个二值数值交换，完成G方向与C方向，以及F方向与D方向的数值交换。
8.如权利要求1所述的一种新型的二值SIFT描述子及其图像匹配方法，其特征在于，所述对于待匹配图像对中的SIFT特征点对计算相似距离的具体步骤包括：分别计算第一幅待匹配图像中第一SIFT特征点的二值描述子BR-SIFT与第二幅待匹配图像中第二SIFT特征点的二值描述子BR-SIFT和MBR-SIFT之间的汉明距离，取两者中的较小者作为SIFT特征点对间的相似距离R。
9.如权利要求1所述的一种新型的二值SIFT描述子及其图像匹配方法，其特征在于，所述根据最近邻匹配进行SIFT特征点对的相似性判断，其具体步骤为：对于一幅待匹配图像中的SIFT特征点A，将所述SIFT特征点A分别与另一幅待匹配图像的所有SIFT特征点构成SIFT特征点对，计算所有所述SIFT特征点对之间的相似距离R，将R由小到大排序，再将最小值与次小值相比，若比值小于预先设定值distratio，则认为所述SIFT特征点A与所述另一幅待匹配图像中的所述相似距离R最小值所对应的SIFT特征点匹配。
10.如权利要求9所述的一种新型的二值SIFT描述子及其图像匹配方法，其特征在于，所述比值大于所述预先设定值distratio，则认为所述SIFT特征点A与所述另一幅待匹配图像中的所述相似距离R最小值所对应的SIFT特征点不匹配。
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