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摘要: 遥感影像变化检测一直是国际遥感领域研究的热点和难点,尽管各国学者对变化检测问题进行了大量深入的研究,但是目前尚未出现一种普适性强、适用于所有情况的通用方法。随着遥感对地观测技术的快速发展和应用,变化检测技术体系也在不断地发展和演化。回顾了多时相遥感影像变化检测技术的发展历程,对多时相遥感影像变化检测方法的分类体系进行了归纳总结,从变化检测预处理、变化检测方法、精度评价3个方面详细总结了变化检测研究的最新进展,并指出了变化检测面临的核心困难及可能的应对措施,以期推动遥感影像变化检测研究更加深入的发展。Abstract: Change detection for remote sensing imagery is the process to determine difference of the same object or phenomenon at different times. Real-time automatic change detection technology is of great significance for excavating potential of image data and maintaining the current situation of geospatial data. With the development of remote-sensing earth observation technology, varieties of remote-sensing sensors for different tasks have emerged. Change detection is also diversified with the coming up of multi-resolution remote-sensing data, with advanced theories and techniques developed for continuously different sensors. This paper reviews the development of multi-temporal remote sen-sing image change detection technologies and summarizes the classification system of multi-temporal remote sensing image change detection. And the latest developments in change detection research are summarized from three aspects:pre-processing, change detection strategies and accuracy assessment. This paper also points out the challenges that change detection is facing and possible countermeasures, in the hope of deepening the research into change detection technology for remote sensing images.
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矢量地图是国家基础设施建设与地球信息科学研究的基础数据,在测绘、国土、农林、规划、交通等领域都占据着重要地位[1-2]。一方面,矢量地图要充分发挥自身的使用价值,就必须在数据开放共享方面作出突破;另一方面,矢量地图的开放共享对其自身的安全保护构成了巨大威胁:作为数字产品的一种,矢量地图极容易被复制、篡改以及传播,使得地图盗版、侵权等非法行为变得十分便利[3-5]。因此,矢量地图开放共享与安全保护之间的矛盾已经成为数字化、网络化时代亟待解决的重要问题。
除了制定完善的法律、规章、条例和制度外,矢量地图的安全保护更需要从技术手段上提供有力支撑[6]。近年来,数字水印技术在矢量地图的安全保护工作中发挥了重要作用。早期的矢量地图数字水印算法大多为空间域算法,通过修改地图顶点坐标实现水印信息嵌入[7-9],算法的稳健性不够理想。许多学者通过地图分块[10]、要素分类[11]、顶点分组[12]等方法进行水印嵌入单元划分,在一定程度上提高了水印信息的冗余性,进而提升了水印算法抗增删点、噪声和缩放攻击的能力。通过建立地图顶点与水印值的映射关系使水印信息“均匀”地分布在载体地图中[13],可提升算法抗地图裁剪、分幅等攻击的能力。基于差值扩张方法修改相邻地图顶点之间的距离嵌入水印[14],也可有效提升算法的稳健性,但水印嵌入过程对原始数据精度的扰动较大,影响含水印数据的正常使用。通过向原始矢量地图中增加冗余顶点实现水印嵌入[15],可避免对原始数据的精度产生扰动,但算法抵抗数据压缩的能力不强。选择矢量地图特征点[16]、关键图层或顶点[17]作为水印嵌入载体,能够显著提高算法抗数据压缩的能力。
与空间域算法不同,变换域算法可以将水印信息非显性地嵌入载体数据中,实现水印信息在载体数据中的均匀分布,相较于空间域算法,稳健性可得到大幅提升[18-19]。离散傅里叶变换(discrete Fourier transform, DFT)系数在几何变换(平移、旋转和缩放)下具有不变性特征,在矢量地图数字水印技术中被广泛应用。通过对DFT系数进行放大并优选水印嵌入量化步长,可有效提升水印信息的不可见性[20]。离散余弦变换(discrete cosine transform, DCT)能够很好地将能量集中在低频区域,在矢量地图数字水印算法中也得到了较多应用;选择矢量地图的噪声不敏感区域进行水印嵌入,可以显著提升水印嵌入容量、不可见性及稳健性[21]。作为一种常用的数学变换方式,离散小波变换(discrete wavelet transform, DWT)在矢量地图数字水印算法中也得到了应用;通过对矢量地图进行均等网格划分,并将每个网格视为栅格图像中的“像素”,利用基于DWT的栅格图像数字水印算法将水印嵌入矢量地图数据,可有效提升算法的不可见性和稳健性[22]。
总体上,已有研究主要侧重于面向矢量地图的数字水印嵌入方法,通过优化水印嵌入位置和嵌入方法提升水印嵌入容量、水印算法的不可见性和稳健性,水印检测过程通常为水印嵌入的逆过程。水印提取后,缺乏针对提取结果进行误码自检测和纠正的有效方法,版权水印检测效果还有很大优化空间,数字水印技术在矢量地图数据安全保护中的应用还存在很大的局限性。
本文针对上述问题,从水印提取结果自优化的角度对矢量地图版权水印检测效果提升方法进行了研究。在水印信息长度的约束下,设计了一种具备自纠错能力的混合水印信息(包含原始版权水印信息及纠错码和校验码)构造方法;顾及混合水印信息和矢量地图数据特征,设计了面向矢量地图的混合水印信息嵌入及检测方法。
1 混合水印信息构造
含水印矢量地图数据在实际应用中易受到各类有意或无意的攻击,导致水印提取结果中难免会存在部分误码,对水印检测及版权认证产生影响。为实现水印提取结果的误码自检测与纠正,本文设计了一种具备自纠错能力的混合水印信息构造方法(图1):首先对版权水印信息进行纠错编码与校验编码,然后将纠错码、校验码与版权水印信息同时嵌入载体数据;同时,考虑到纠错码和校验码的引入会导致水印信息总长度大幅增加,影响水印算法稳健性,基于无损数据压缩方法对版权水印信息、纠错码及校验码进行压缩编码,约束水印长度。
混合水印信息构造包括3个步骤:
1) 将版权水印信息中所有码值按行列顺序组织为一个二维序列,并分别基于行、列方向相邻码值间的异或运算生成版权水印信息的行向和列向纠错码。行/列向纠错码中各行/列最后一位的值,根据版权水印信息中该行/列的首、尾码值异或运算生成。纠错编码的实例如图2所示。
2)以行为单位对纠错码的码值进行循环冗余校验(cyclic redundancy check, CRC)编码。以图2(b)中的行向纠错码数据为例,其循环冗余校验编码如图3所示。每行元素中的右4位为生成的校验位;使用的生成多项式为:
(1) 上述生成多项式的选择为示例,在实际应用中可根据需求灵活选择(校验位长度与式中最高次幂相同)。
3)利用霍夫曼编码方法对原始版权水印信息和生成的纠错码及校验码进行无损压缩,并将三者的压缩编码结果合并,生成最终的混合水印信息。以图2(a)中的原始版权水印信息为例,首先按行列顺序将其分割为字符串序列(每4个字符组成一个序列,若末尾剩余字符串不足4个则以0补齐),结果为“0110”“1110”“0110”“0100”“0111”;然后,将各字符串用字母A~P代替(字符串与字母的对应关系见表1),结果为G、O、G、E和H;最后,对获取的字母进行霍夫曼编码。最终,将原始版权水印信息以及纠错码和校验码的霍夫曼编码结果作为待嵌入的混合水印信息。
表 1 字符串与字母的对应关系Table 1. Correspondence Between Strings and Letters字符串 字母 字符串 字母 0000 A 1000 I 0001 B 1001 J 0010 C 1010 K 0011 D 1011 L 0100 E 1100 M 0101 F 1101 N 0110 G 1110 O 0111 H 1111 P 2 混合水印信息分类嵌入
混合水印信息中,纠错码可以检测和纠正版权水印信息中的部分误码,且纠错效果依赖纠错码自身的质量;校验码可以发现并纠正纠错码中的误码,对于提升纠错码质量并优化版权水印检测结果十分重要。因此,在混合水印信息各组成部分中,校验码的重要性最高,纠错码次之,版权
水印信息的重要性最低。同时,含水印矢量地图数据在应用中,数据压缩、删点、裁剪等操作或攻击通常不会针对特征点(特征点一旦丢失或被篡改,对数据的应用价值将产生严重影响),因此特征点的稳定性远高于非特征点[18]。基于上述分析,本文设计了一种面向矢量地图的混合水印信息分类嵌入方法,步骤如下:
1)提取矢量地图特征点,并对地图顶点进行分组。对于线状要素和面状要素,首先采用道格拉斯-普克算法提取特征点(使用阈值
),将矢量地图顶点划分为特征点集 和非特征点集 ;然后对特征点集 中的顶点继续进行特征点提取(使用阈值 且 ),将 中的顶点划分为特征点集 和非特征点集 。 2)将校验码、纠错码和版权水印信息分别嵌入顶点集
、 和 中的顶点。水印嵌入过程的步骤为: (1)基于
中的顶点坐标,计算矢量地图虚拟中心点坐标 ,计算公式为: (2) 式中,
为 中顶点数量; 、 分别为第 个顶点的横、纵坐标值的整数部分; 表示向下取整函数。 (2)以虚拟中心点为极点,将点集
、 和 中的顶点直角坐标转换为极坐标。对于任一顶点 ,其极坐标 的计算公式为: (3) (3)计算每个地图顶点对应的水印值。对于任一顶点
(其极坐标为 ),其对应的水印值 的计算公式为: (4) 式中,
为 的整数部分; 为待嵌入的水印信息; 为水印信息长度; 表示取余运算; 为将变长输入转换为定长输出的哈希函数。 (4)将水印信息嵌入地图顶点极坐标。对于任一地图顶点
,令 为其极坐标、 为其对应的水印值,水印嵌入公式为: (5) 式中,
为水印嵌入强度; 和 分别为取一个小数的整数、小数部分的函数。 (5)将所有地图顶点的含水印极坐标转换为直角坐标。对于任一顶点(设其含水印极坐标为
),其含水印直角坐标 的计算公式为: (6) 式中,
为矢量地图虚拟中心点坐标。 经过上述步骤处理后,混合水印信息中的校验码、纠错码和原始版权水印信息分别被嵌入了顶点集
、 和 中的顶点极坐标中。在水印提取后,可先利用校验码检测并纠正纠错码中的误码,然后利用差错控制后的纠错码检测并纠正版权水印信息中的误码,最终实现版权水印检测效果提升的目标。 3 版权水印检测优化
本文设计的数字水印模型中,水印提取是水印嵌入的逆过程。水印提取后,基于校验码与纠错码提取结果可以实现版权水印提取结果中部分误码的自检测与纠正、优化水印检测效果,具体方法如下:
1)混合水印信息提取与地图内容恢复。依据水印嵌入的逆过程可以准确提取嵌入的混合水印信息并恢复原始地图内容,步骤如下:
(1)含水印矢量地图顶点分组。如§2步骤1)所述,首先基于特征点提取方法(使用阈值
)将含水印矢量地图顶点划分为特征点集 和非特征点集 ;然后对特征点集 中的顶点继续进行特征点提取(使用阈值 且 ),将 中的顶点划分为特征点集 和非特征点集 。 (2)虚拟中心点计算。基于
中顶点坐标计算虚拟中心点坐标 ,计算方法参照式(2)。 (3)顶点极坐标转换。首先,以计算获取的虚拟中心点为极点将所有地图顶点直角坐标转换为极坐标。极坐标计算方法参照式(3)。
(4)顶点水印值提取和原始顶点坐标恢复。首先,分别从顶点集
、 和 中的顶点极坐标中提取校验码、纠错码和版权水印信息。对于任一顶点(设其极坐标为 ),其坐标中的水印值(设为 )的计算公式为: (7) 然后,将水印值从顶点极坐标中移除,获取不含水印的顶点极坐标。
(5)地图顶点不含水印直角坐标计算。将获取的顶点不含水印极坐标转换为直角坐标,方法参考式(6)。
2)版权水印检测及纠错。水印提取后,首先对提取结果进行霍夫曼解码,然后利用校验码和纠错码对版权水印信息提取结果进行误码检测和纠正,从而优化版权水印检测效果,步骤如下:
(1)纠错码提取结果差错控制。将纠错码与校验码进行合并(结果形式如图3所示),然后以行为单位对纠错码进行误码检测:用各行的值除以生成多项式系数(与混合水印信息构造过程中使用的生成多项式系数相同,见式(1)),若得数为0,则该行元素中不存在误码,将该行所有元素标记为“可信”元素;否则,根据余数判断出错的码值(以图3中第1行数据为例,余数与出错位之间的对应关系见表2)并对其进行纠正(取反)。
表 2 余数与出错位的对应关系Table 2. Correspondence Between Remainders and Dislocations余数 出错位 余数 出错位 0000 无 0011 5 0101 1 1000 6 1011 2 0100 7 1100 3 0010 8 0110 4 0001 9 (2)版权水印信息提取结果质量评价。基于差错控制后的行向纠错码和列向纠错码对版权水印信息提取结果中的元素进行质量评价,筛选“可信”元素。令
为行向纠错码, 为列向纠错码, 为版权水印信息。对于 中任一元素 ,若 和 都“可信”且下式中条件成立,则标记其为“可信”: (8) (3)版权水印信息提取结果误码检测与纠正。遍历版权水印信息提取结果中的每一个“可信”元素,检测并纠正版权水印信息中的误码。对于版权水印信息提取结果中的任一元素
:若 “不可信”且 “可信”,则令 ;若 “不可信”且 “可信”,则令 。 (4)重复步骤(3),直至所有“可信”元素处理完毕。
4 数字水印模型性能测试与分析
为测试本文设计的数字水印模型的综合性能,利用5幅矢量地图数据(数据为ESRI Shapefile格式)进行了仿真实验。实验用的原始版权水印图像见图4(图像大小64×48像素),实验的软硬件环境如下:中央处理器为Intel Core i7-8700 (3.20 GHz),随机存取存储器32 GB,操作系统为Windows 10 Professional 64-bit,模型开发平台为.NET 5.0,模型开发语言为Visual C#,地图引擎为ArcGIS Engine 10.2。实验矢量地图数据见图5,其基本属性见表3。
表 3 实验矢量地图数据基本属性信息Table 3. Basic Attribute Information of Experimental Vector Map Data矢量地图 顶点数量/个 x坐标范围 y坐标范围 M01 50 362 [525 906.942 198 596,551 873.293 302 004] [3 510 038.946 350 692,3 514 418.357 030 126] M02 53 888 [548 677.147 787 786,551 873.293 316 376] [3 476 498.368 236 518,3 479 170.777 547 691] M03 55 248 [553 970.275 999 775,556 450.364 688 622] [3 509 553.780 099 213,3 514 093.764 811 436] M04 229 515 [540 407.308 824 611,556 136.685 007 801] [3 436 908.383 376 304,348 960.834 592 413 4] M05 192 570 [40 435 288.344 740 412,40 439 197.231 339 764] [3 487 778.279 717 544,3 506 166.176 337 725] 4.1 实验结果
首先基于图4中的版权水印图像,利用本文设计的混合水印信息构造方法生成混合水印信息,版权水印信息的纠错编码结果见图6,纠错码
的循环冗余编码结果见图7。
然后,利用本文设计的方法对版权水印信息、纠错码以及校验码进行霍夫曼编码,并统计编码后的数据压缩率。结果见表4,表明混合水印信息的各组成部分的长度都得到了有效压缩。
表 4 霍夫曼编码统计结果Table 4. Statistical Results of Hoffman Coding水印信息 版权水印 行向纠错码及校验码 列向纠错码及校验码 原始长度 3 072 3 264 3 264 编码长度 2 104 2 382 2 093 压缩率 0.68 0.73 0.64 通过一组仿真实验对矢量地图特征点提取结果的稳定性进行了验证:首先提取5幅实验矢量地图的特征点,然后采用本文设计的方法嵌入混合水印信息,最后从5幅含水印矢量地图数据中提取特征点。实验结果表明,水印嵌入过程对矢量地图的特征点提取结果没有影响。
对混合水印信息的嵌入结果进行了统计分析,结果见表5。由表5可知,所有水印值都被重复嵌入了一个或多个地图顶点,在理论上可以保证所设计的数字水印模型在各类常规变化和恶意攻击下的稳健性。
表 5 水印嵌入统计结果Table 5. Statistical Results of Watermark Embedding矢量地图 水印平均嵌入次数 未嵌入水印数 M01 7.65 0 M02 8.19 0 M03 8.40 0 M04 34.89 0 M05 29.27 0 4.2 数字水印模型性能分析
1)无损性分析。由水印信息提取和检测过程可知,水印提取后,理论上可以恢复载体数据中的顶点坐标。为验证本文设计的数字水印模型的无损性,基于5幅实验矢量地图数据进行了仿真实验:首先将混合水印信息嵌入矢量地图数据,然后提取水印并恢复地图内容,最后计算原始地图顶点与水印提取后的顶点间的坐标差。实验结果表明,水印提取后所有地图顶点坐标都被恢复,验证了该数字水印模型的无损性。
2)不可见性分析。如§2所述,水印嵌入过程仅修改矢量地图顶点坐标的小数部分,并且可通过调整水印嵌入强度来约束顶点坐标的扰动(本文实验中水印嵌入强度设置为5)。理论上,水印嵌入对原始矢量地图内容在视觉上不会产生显著影响。不可见性分析示例见图8,证明了该数字水印模型的不可见性(即使在局部缩放模式下,也很难从视觉上区分矢量地图内容在水印嵌入前后的差异)。
为进一步定量评估所设计数字水印模型的不可见性,采用最大误差(maximum error,
)和均方根误差(root mean square error, )两个指标计算了水印嵌入引起的地图顶点误差。 和 的计算方法为: (9) 其中,
、 分别表示 和 的值;n表示地图顶点数量; 为取最大值函数; 和 分别表示第 个地图顶点的原始坐标和含水印坐标。 此外,将本文设计的数字水印模型与两种代表性矢量地图数字水印方案(文献[19]方法和文献[20]方法)在不可见性方面的表现进行了比较,结果见表6。与其他主流的矢量地图数字水印方案相比,本文设计的数字水印模型在不可见性方面表现优异(
和 均小于1×10-5)。 3)水印容量分析。本文设计的数字水印模型中,每个顶点中嵌入一个水印值,因此其水印容量等于地图顶点数量。以水印容量为指标,将该数字水印模型与两种代表性矢量地图数字水印方案(文献[19]方法和文献[20]方法)进行了对比分析。结果见表7,该数字水印模型的水印容量属于主流水平。
4)稳健性分析。(1)地图顶点重排序。顶点重排序是矢量地图数据常见的攻击类型之一,会改变含水印矢量数据的组织结构,从而影响水印提取结果。本文设计的数字水印模型中,水印嵌入过程的关键步骤包括特征顶点提取、极坐标转换等,都与地图顶点的顺序无关。因此,顶点重新排序操作不会影响水印提取和检测效果。同时,仿真实验结果证明了本文设计的数字水印模型在顶点重排序操作下具有很强的稳健性。以M01为例(图形要素数量为338),水印模型抗顶点重排序攻击的仿真实验结果见表8。采用归一化相关系数(normalized correlation, NC)对载体数据攻击后版权水印检测精度进行定量化表示,其计算方法可参考文献[4]。
表 8 数字水印模型抗地图顶点重排序实验结果Table 8. Experimental Results of Digital Watermarking Model in Resisting Map Vertex Reordering模拟攻击 具体攻击过程 版权水印检测结果(NC) 一 将第1、20、50、70、90、120个要素分别与第338、318、288、268、248、218个要素交换存储顺序 1.00 二 将第1至第10个要素分别与第329至第338个要素交换存储顺序 1.00 三 将第1至第169个要素分别与第170至第338个要素交换存储顺序 1.00 (2)地图平移和旋转。由水印嵌入过程可知,由于地图顶点极坐标的稳定性,本文所提出的数字水印模型在地图平移和旋转操作下是稳健的。通过一组实验进行了验证,实验结果见表9,可见所设计的数字水印模型在不同强度的平移和旋转操作下都具有很强的稳健性。
表 9 数字水印模型抗地图平移和旋转实验结果(NC)Table 9. Experimental Results of Digital Watermarking Model in Resisting Map Translation and Rotation(NC)矢量地图 地图平移/m 地图旋转/(°) 13.65 102.78 23.5 78.2 M01 1.00 1.00 1.00 1.00 M02 1.00 1.00 1.00 1.00 M03 1.00 1.00 1.00 1.00 M04 1.00 1.00 1.00 1.00 M05 1.00 1.00 1.00 1.00 (3)随机增删点。随机增删点是矢量地图数据的两种常见攻击,前者会在载体数据中引入若干干扰顶点,后者会导致多个含水印地图顶点的丢失,都会影响水印信息提取的准确率。本文设计的数字水印模型中,每个水印值被同时嵌入多个地图顶点,并在水印提取阶段采用统计方法进行最优水印值选取。因此,该数字水印模型理论上具备较强的抗随机增点攻击能力。另外,水印提取后,设计的版权水印信息误码自检测和纠正方法也可以进一步优化版权水印检测效果。
通过一组仿真实验对该数字水印模型抗随机增删点攻击的能力进行了验证。首先将生成的混合水印信息嵌入5幅实验矢量地图(见图5),然后将不同比例(10%~70%)的顶点加入含水印矢量地图数据中(或从中移除)。最后,从随机增/删点攻击后的含水印数据中提取混合水印信息,并利用本文设计的方法进行版权水印信息检测效果优化。实验结果(图9)表明:①本文设计的水印信息提取结果自纠错方法可以有效提升版权水印信息检测效果;②攻击强度越小,版权水印信息提取结果的自纠错效果越好;③该数字水印模型在随机增点攻击下的稳健性略优于在随机删点攻击下的稳健性。
(4)地图简化和裁剪。矢量地图数据经常会受到有意或无意的地图简化和裁剪攻击。前者保留地图特征点、删除非特征点,后者保留目标区域中的地图顶点、删除其他顶点。与随机删点攻击相似,地图简化和剪裁操作会导致部分含水印顶点丢失,影响水印提取结果的准确率。本文设计的数字水印模型中,版权水印信息和纠错码被嵌入在非特征点中,循环冗余校验码被嵌入在特征点中。因此,相较于版权水印信息和纠错码,循环冗余校验码在含水印数据中相对稳定。理论上,可以基于循环冗余校验码提取结果检测和纠正纠错码及版权水印信息中的部分误码。
为评估本文设计的数字水印模型抗地图简化和剪裁攻击的能力,进行了仿真实验,并将本文设计的水印模型与两种代表性矢量地图数字水印方案(文献[19]方法和文献[20]方法)进行了对比分析。实验结果(图10)表明,本文设计的数字水印模型具有更强的抗地图简化和剪裁攻击的能力。另外,该水印模型抗地图简化的能力比抗地图裁剪的能力更强。
5 结 语
本文设计并实现了一种基于版权水印信息差错控制编码的矢量地图自纠错数字水印模型。为了使嵌入的水印信息具备自纠错能力,设计了一种混合水印信息构造方法,将版权水印数据及其纠错码和校验码结合生成待嵌入水印信息。同时,考虑到纠错码和校验码的引入将导致嵌入水印信息总长度的增加,对水印嵌入效果及算法稳健性都会产生影响,为约束水印信息总长度,设计了一种面向水印信息的无损压缩方法。水印提取后,可以基于纠错码和校验码检测并纠正版权水印信息中的部分误码。实验结果表明,本文设计的数字水印模型具有理想的水印容量、无损性、不可见性和稳健性。
本文设计的数字水印模型可以在水印总长度的约束下实现水印信息的误码自检测和纠正,有两个方面的工作值得进一步研究。首先,应深入研究更有效的数字水印信息无损压缩方法,进一步提升算法对小数据量矢量地图数据的适应能力。此外,本文选择地图顶点极坐标作为水印信息嵌入载体,虽然抵抗常规变换和攻击的能力较强,但在地图缩放攻击下非常脆弱。因此,应进一步研究矢量地图几何不变量的构造以及基于几何不变量的水印嵌入方法,以增强数字水印模型在几何变换下的稳健性。
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