35 1 Vol. 35, No. 1 2009 1 ACTA AUTOMATICA SINICA January, 2009 1 1, Zernike Krawtchouk,. Krawtchouk, SVR,.,,.,,, Zernike, Krawtchouk TP391 An SVR Based Image Watermarking Detection Algorithm against Geometric Attacks XU Zi-Han 1 WANG Xiang-Yang 1 Abstract According to the support vector regression (SVR), a new image watermarking detection algorithm against geometric attacks is proposed in this paper, in which the steady pseudo-zernike moments and Krawtchouk moments are utilized. The main steps of watermark detecting procedure include: 1) some low-order Krawtchouk moments are calculated as the eigenvectors; 2) the appropriate kernel function is selected for training, and an SVR training model can be obtained; 3) the actual output is predicted by using the well trained SVR; 4) the digital watermark is extracted from the corrected test image. Experimental results show that the proposed watermarking detection algorithm is not only robust against common signals processing, but also robust against some geometric attacks. Key words Image watermarking, geometric attack, support vector regression (SVR), pseudo-zernike moment, Krawtchouk moment (Digital watermarking),,,.,.,, 2007-09-18 2008-01-12 Received September 18, 2007; in revised form January 12, 2007 (60773031, 60873222), () (A200702), () (03-06), () (ZK205014), () (KJS0602) Supported by National Natural Science Foundation of China (60773031, 60873222), the Open Foundation of State Key Laboratory for Novel Software Technology (Nanjing University) (A200702), the Open Foundation of State Key Laboratory of Information Security of China (03-06), the Open Foundation of Key Laboratory of Image Processing and Image Communication (Nanjing University of Posts and Communications) (ZK205014), the Open Foundation of Jiangsu Province Key Laboratory for Computer Information Processing Technology (Soochow University) (KJS0602) 1., 116029 1. School of Computer and Information Technology, Liaoning Normal University, Dalian 116029 DOI: 10.3724/SP.J.1004.2009.00023, [1 4]. Dong [2 4] Fourier-Mellin Radon Zernike. [5 7]. Fu [8] (Support vector machine, SVM). SVM, SVM,. (Support vector regression, SVR), Zernike Krawtchouk,.,,. 1, Zernike, Zernike, Zernike, Zernike.
24 35 256 F = {f(x, y), 1 x M, 1 y N},, f(x, y) x y, : 1.. Key 1 W = {w i, i = 1,, L},, L, w i {0, 1}. 2. Zernike. Zernike,, Zernike, {V mn (x, y)}. (x 2 + y 2 1), V mn (x, y) = V mn (r, θ) = R mn (r) exp(jnθ) (1) m, n, n m. r θ, r = x2 + y 2, θ = tan 1 (y/x). R mn (r) (Radial polynomial), m n ( 1) s (2m + 1 s)r m s R mn (r) = s!(m + n + 1 s)!(m n s)! s=0 (2) m, n Zernike Z mn = m + 1 f(x, y)[v mn (x, y)] dxdy π x 2 +y 2 1 (3), m = 0, 1, 2, ; f(x, y) ; ; n 0 n m. 3. Zernike. a) Zernike. M max, Zernike. M max = 20 (, ); b) n = 4i (i = 0, 1, 2, ) Zernike,., Zernike S = {Z mn, m M max, n 0, n 4i} (4), Key 2 Zernike S L Zernike Z = (Z p1q 1,, Z pl q L ). Zernike A = (A p1q 1,, A pl q L ). 4.. Zernike, [ ] A Apiq p iq i = i d(w i ) +d(w i ), i = 1, 2,, L (5), [ ],, d( ) Key 3, d(1) = /2 + d(0), d(0) [0, 1]., Zernike A = (A p1q 1,, A pl q L ), q i 0, A pi, q i,. 5.. : Zernike f (x, y) f (x, y) = f O (x, y) f Z (x, y) (6), f O (x, y), f Z (x, y) Zernike, L f Z ( ) = Z piq i V piq i ( ) + Z pi, q i V pi, q i ( ) (7) i=1 Zernike f Z (x, y) L f Z ( ) = Z p iq i V piq i ( ) + Z p i, q i V pi, q i ( ) (8) i=1, f (x, y) = f (x, y) + f Z (x, y) (9) 2 Krawtchouk, SVR. Krawtchouk, SVR, SVR. SVR,.. 2.1,., Krawtchouk 4 Q 00, Q 01, Q 10, Q 11 ( f 1, f 2, f 3, f 4 ), SVR. f(x, y) M N, (m + n) Krawtchouk Q nm Q mn = M 1 N 1 x=0 y=0 K n (x; p 1, N 1) K m (y; p 2, M 1)f(x, y) (10)
1期 徐紫涵等: 可有效抵抗一般性几何攻击的数字水印检测方法 其中 s K n (x; p, N 1) = Kn (x; p, N 1) Ã! ω(x; p, N 1) ρ(n; p, N 1) (11) N px (1 p)n x x µ n n! 1 p n ρ(n; p, N ) = ( 1) p ( N )n ω(x; p, N ) = (12) (13) µ 1 Kn (x; p, N ) = ak,n,p x = 2 F1 n, x; N ; p k=0 n X k x, n = 0, 1, 2,, N, N > 0, p (0, 1) (14) 其中, 超几何分布函数 2 F1 定义为 2 F1 (a, b; c; z) = X (a)k (b)k z k k=0 (c)k k! 25 成 MIMO 系统, SVR 的结构为 4 个输入, 核函数采 用 RBF 径向基函数. 通过训练学习, 即可获得 SVR 训练模型. 2.3 待检测图像的几何校正 基于 SVR 的待检测图像校正过程为: 步 骤 1. 计 算 出 待 检 测 图 像 F 的 4 个 低 阶 Krawtchouk 矩 (f f 1, f f 2, f f 3, f f 4 ), 并将其作为训练特 征向量. 步 骤 2. 以 4 个 低 阶 Krawtchouk 矩 (f f 1, f f 2, f f 3, f f 4 ) 作 为 输 入 向 量, 利 用 已 经 获 得 的 SVR 训练模型对输出向量进行数据预测, 从而得 到相应的输出向量值 (即几何变换参数 t x, t y, s, θ ). 步骤 3. 利用所得到的几何变换参数 t x, t y, s, θ 对待检测图像 F 进行几何校正, 从而得到待检测图 像 F 的校正结果 F. 图 1 给出了几何校正的结果示 意图. (15) ak 的表达式为 ak = a(a + 1)(a + 2) (a + k 1) 2.2 (16) SVR 训练模型的获得 相对于神经网络而言, SVR 具有更强的泛化能 力和学习能力. SVR 是 SVM 在回归学习中的应 用, 其基本思想是: 对于给定训练样本点 {(x1, y1 ), (x2, y2 ),, (xn, yn )} X R (其中, X 表示输入 样本空间), 通过 SVR 训练回归一个函数 f (x), 使 由该函数求出的每个输入样本的输出值和输入样本 所对应的目标值相差不超过误差 ε, 同时使回归出的 函数尽量平滑. 为了获得 SVR 训练模型, 我们首先在一定范围 内随机平移 (包括 X 方向 Y 方向) 旋转和缩放原 始图像 F 以产生 K 个训练样本图像 F k, 然后计算 出每个训练样本图像 F k 的 4 个低阶 Krawtchouk 矩 (ff k1, f k2, f k3, f k4 ), k = 1, 2,, K 并将其作为训练特征向量. 同时, 将相应的变换 (X 方向平移 Y 方向平移 旋转和缩放等) 参数 tkx, tky, sk, θk (k = 1, 2,, K) 作为训练目标值, 于 是可得到训练样本 Ωk = (ff k1, f k2, f k3, f k4, tkx, tky, sk, θk ), k = 1, 2,, K 考虑到平移 旋转和缩放构成对图像的线性变换, 任 何一个变换对其他参数没有影响, 因此, 4 个输出之 间没有耦合. 为此, 本文采用 4 个 SVR 并行结构构 (a) 待检测图像 1 (b) 校正后的图像 1 (a) Test image Lena (b) The corrected image Lena (c) 待检测图像 2 (d) 校正后的图像 2 (c) Test image Barbara (d) The corrected image Barbara 图1 Fig. 1 SVR 几何校正结果示意图 SVR geometric corrections 2.4 数字水印的提取 水印提取是水印嵌入的逆过程. 本文讨论的数 字水印检测算法属于目标检测算法, 即在检测数字 水印时不需要原始载体图像. 设校正后的待检测图 像为 F, 则数字水印检测过程如下: 步骤 1. 计算出校正后待检测图像 F 的伪 Zernike 矩, 见式 (3).
26 35 2. Key 2 L Zernike Z = (Zp 1q 1,, Zp L q L ). Zernike A = (A p 1q 1,, A p L q L ). 3.., Key3 d( ), d(1) = /2 + d(0), d(0) [0, 1].,, d(0), d(1) A p iq i, i = 1, 2,, L [ A ] (A piq p iq i ) Qj = i d(j) + d(j), j = 0, 1 (17) (17), (A p iq i ) 0 (A p iq i ) 1, i = 1,, L., A p iq i, w i = a rg min ((A p j {0,1} iq i ) Qj (A p iq i )) 2, i = 1,, L (18), (18) : 1) A p iq i dis0 = ((A p iq i ) 0 A p iq i ) 2 dis1 = ((A p iq i ) 1 A p iq i ) 2 ; 2) 1), t = dis0 dis1; 3) 2), t < 0, wi = 0;, wi = 1. 3, ()., 128 128 8 bit Lena Mandrill Barbara, 64 bit., = 2.0, K = 50. SVR RBF. 2 ( ) Lena Mandrill Barbara.,. 1 2 ( BER). 4, Zernike Krawtchouk,. : 1) Zernike, Krawtchouk, SVR, ; 2) SVR, ; 3). Table 1 1 ( BER) The watermark detection results for common signal processing Lena Mandrill Barbara 70 0 0 0 JPEG 50 0 0 0 30 0 0.063 0 0 0 0 0.063 0 0.031 0 0.031 0 0 0 0 +70 JPEG 0 0 0 +70 JPEG 0 0 0 + 0.031 0 0.063 + 0 0 0.031 + + 0.156 0.188 0.281 2 ( BER) Table 2 The watermark detection results for various attacks Lena Mandrill Barbara 5 o 0.188 0.094 0.219 45 o 0.156 0.094 0.219 0.5 0 0 0.063 2 0 0 0 5 0 0 0 30 0 0 0 5 0 0 0 30 0 0 0c 0 0 0 0.031 0 0 2 + 5 o 0 0 0 45 o + ( 30) 0 0 0 JPEG 70 + + + 0.5 0.031 0.063 0.094
1期 徐紫涵等: 可有效抵抗一般性几何攻击的数字水印检测方法 (a) 含水印图像 Lena (PSNR = 41.365 db) (a) The watermarked image Lena (b) 含水印图像 Mandrill (PSNR = 42.106 db) (b) The watermarked image Mandrill 图2 Fig. 2 27 (c) 含水印图像 Barbara (PSNR = 40.406 db) (c) The watermarked image Barbara 数字水印的嵌入效果 The watermarked images References 1 Licks V, Jordan R. Geometric attacks on image watermarking system. IEEE Multimedia, 2005, 12(3): 68 78 2 Dong P, Brankov J G, Galatsanos N P, Yang Y Y, Davoine F. Digital watermarking robust to geometric distortions. IEEE Transactions on Image Processing, 2005, 14(12): 2140 2150 3 Simitopoulos D, Koutsonanos D E, Strintzis M G. Robust image watermarking based on generalized radon transformations. IEEE Transactions on Circuits and Systems for Video Technology, 2003, 13(8): 732 745 4 Parameswaran L, Anbumani K. A robust image watermarking scheme using image moment normalization. Proceedings of World Academy of Science, Engineering and Technology, 2006, 13: 239 243 5 Wang Xiang-Yang, Wu Jun, Hou Li-Min. A feature-based digital image watermarking algorithm. Acta Electronica Sinica, 2007, 35(7): 1318 1322 (王向阳, 邬俊, 侯丽敏. 一种基于图像特征点的数字水印嵌入方法. 电子学报, 2007, 35(7): 1318 1322) 6 Lee H Y, Kim H, Lee H K. Robust image watermarking using local invariant features. Optical Engineering, 2006, 45(3): 1 11 7 Seo J S, Yoo C D. Image watermarking based on invariant regions of scale-space representation. IEEE Transactions on Signal Processing, 2006, 54(4): 1537 1549 8 Fu Y G, Shen R, Lu H. Watermarking scheme based on support vector machine for color images. Electronics Letters, 2004, 40(16): 986 987 徐紫涵 辽宁师范大学硕士研究生. 主 要研究方向为数字水印技术. E-mail: xzh0122@163.com (XU Zi-Han Master student at Liaoning Normal University. Her main research interest is digital watermarking.) 王向阳 辽宁师范大学计算机与信息技 术学院教授. 主要研究方向为信息隐藏 与数字水印 多媒体信息处理技术. 本文 通信作者. E-mail: wxy37@126.com (WANG Xiang-Yang Professor at School of Computer Science and Information Technology, Liaoning Normal University. His research interest covers information hiding, digital watermarking, and multimedia information processing. Corresponding author of this paper.)