Robust Multibit Decoding and Detection of Multiplicative Watermarks for Fingerprint Images

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1 JOURNAL OF MULTIMEDIA, VOL. 5, NO. 2, APRIL 2 67 Robust Multibit Decoding and Detection of Multiplicative Watermarks for Fingerprint Images Khalil Zebbiche*, Foued Khelifi # and Ahmed Bouridane* * School of Electronics, Electrical Engineering and Computer Science, Queen s University of Belfast, Belfast BT7 NN, UK {kzebbiche, A.Bouridane}@qub.ac.uk # Department of Electronic Imaging and Media Communications (EIMC, School of Informatics, University of Bradford, Bradford BD7 DP, UK F.Khelifi@bradford.ac.uk Abstract In this paper, multibit watermark decoding and detection structures of fingerprint images are proposed. The watermark is hidden within the high frequencies coefficients of the discrete wavelet transform (DWT which are statistically modeled by generalized Gaussian distribution. The structure of the decoder and the detector are based on the maximum-likelihood (ML method. For flexibility purposes, the original image is not necessary during the decoding and the detection processes. Analytical expressions for performance measures such as the probability of error in watermark decoding and probabilities of false alarm and detection in watermark detection are derived and contrasted with experimental results. The results obtained are very attractive when considering a number of commonly used attacks and the proposed detector and decoder have been shown to outperform similar detectors/decoders existing in the literature. They also show that the overall performances of both decoder and detector are dependent on the fingerprint image characteristics, namely, on the size of the ridges area relative to the size of the fingerprint image. Index Terms Watermark decoding, watermark detection, fingerprint images, multibit watermarking I. INTRODUCTION The term biometric refers to the identification of a person on the basis of their physiological measurements or behavioral traits; biometrics can be used to verify and authenticate the identity of individuals. Associated technologies are employed in the fields of law enforcement, user access applications, e-commerce, etc. There exist a range of available biometric techniques, such as fingerprint, face recognition, iris recognition, voice identification, etc. Fingerprint-based authentication is the most mature, proven and widely used biometric technique []. Although biometric-based systems have advantages over knowledge-based and token-based systems they are not fully secure since the integrity of biometric templates/data is vulnerable to various risks and attacks. The reliability of a biometric system depends on its effectiveness and Manuscript received February 5 28; revised November 27 28; accepted February Corresponding author Khalil Zebbiche, kzebbiche@qub.ac.uk. security against unauthorized modification and misuse. Increased security of biometric data is crucial to promote the wide spread utilization of biometric technologies [2]. Recently, a number of security techniques such as encryption and watermarking have been introduced in the literature. For example, in the case of biometric encryption, a number of techniques have been adopted [3] [8]. A comprehensive analysis of biometric cryptosystems is presented in [9], where the weaknesses of the approaches in [3], [4] and the impracticality of the systems in [7], [8] have been discussed. In addition, the work presented in [] shows the vulnerability of the systems [6] and [5]. Thus, biometric encryption does not yet provide satisfactory security. Watermarking techniques have been used to protect biometric data and attractive results have been obtained [2], [] [3]. The amount of information that can be stored in a watermark is application dependent. For copy protection purposes, a payload of one bit, also referred to as onebit watermarking, is usually sufficient. In this case, watermarks serve as verification codes and the role of the receiver is to detect the presence or absence of a given watermark in the host media. Thus, watermark detection is a binary hypothesis test, for which the probabilities of false alarm (i.e. wrong decision that a given watermark has been inserted and detection (i.e. correctly deciding that a given watermark is embedded can be defined and used to assess the performance of the detector. Early detectors were based on computing the correlation between the watermarked media and the watermark itself [4], [5]. Due to the simplicity of its application, a correlationbased detection is usually preferred; this approach is optimal only when the embedding process follows an additive rule, and the host media is drawn from Gaussian distributions. This is not the case for most applications. More recently, optimum detection schemes have been proposed for multiple domains such as Discrete Cosine Transform (DCT, Discrete Wavelet Transform (DWT, Discrete Fourier Transform (DFT,... etc. The schemes are modeled with different statistical models, such as 2 ACADEMY PUBLISHER doi:.434/jmm

2 68 JOURNAL OF MULTIMEDIA, VOL. 5, NO. 2, APRIL 2 Gaussian, Laplacian, generalized Gaussian distribution (GGD, Weibul distribution,... etc., and can be used in in both additive watermarking [6], [7] and non-additive (multiplicative watermarking [8], [9]. For the protection of intellectual property rights multibit watermarking techniques are used. Hidden information may be comprised of ownership identifiers, transaction dates, serial numbers, etc. Multibit watermarking involves the correct extraction (decoding of information using a secret key. Optimum decoding of a multibit watermark has been considered in [6], [2] [22]. The works in [6] and [2] are concerned with additive watermarks embedded within DCT coefficients modeled by GGD features. The problem of multibit decoding for multiplicative watermarking has been addressed in [2] and [22]; in [2] the watermark is embedded in the DFT coefficients, modeled using a Weibull distribution, while in [22] a general statistical procedure based on a total efficient score vector for both GGD and Weibull distributions is proposed. In most cases, this will lead to an associated error probability for the extracted information. This error probability can be used as a measure of the performance of a watermarking system. Note that error probability increases with the number of bits in the hidden message. Thus there is a practical limit on the length of secret messages that can be conveyed. Another issue associated with multibit watermarking is the problem of assessing the presence of a multibit watermark. This is considered more complex than one-bit watermark detection because the hidden bits are unknown to the detector. Multibit detection is usually tackled heuristically by first estimating the hidden message and then verifying the presence of the message. The first attempt to theoretically derive the structure of an optimum detector is given in [6], where an additive watermarking scheme is considered. Optimum multibit detection structures for multiplicative watermarks have also been derived in [2], [22]. The main goal of this paper is to propose new optimum decoding and detection techniques for multibit, multiplicative watermarks hosted by generalized Gaussian features; which are classically encountered in image watermarking in the DWT domain. The problem of decoding and detection is formulated theoretically based on a maximum-likelihood (ML estimation scheme which requires an accurate statistical modeling of the host data. This theoretical formulation allows for the derivation of optimal decoding and detector structures for the generalized Gaussian model. This optimality of the proposed decoder and detector depends on the accuracy of the GGD to model the statistics of the host data. A theoretical analysis permits the determination of useful mathematical model for use in the performance assessment. The parameters of the GGD can be directly estimated from the watermarked image (i.e. blind watermarking. This makes the proposed decoder and detector more suitable in real applications. The results given in this paper are concerned with fingerprint images. However, the proposed decoder and detector can be applied to any other data that can be accurately modeled using GGD. The paper is organized as follows: In Section II, a statistical analysis which models high-frequency DWT coefficients of fingerprint images is presented. A description of watermark generation and the embedding process are given in Section III. Then, in Sections IV and V, the proposed multibit watermark decoding (extraction and detection schemes are described and analyzed. Optimum mathematical expressions for performance measures are obtained. Theoretical results are compared with empirical data obtained through experimentation in Sections IV- C and V-B for the watermark decoder and detector, respectively. Finally, conclusions are drawn in Section VI. II. MODELING DWT COEFFICIENTS OF FINGERPRINT IMAGES The most evident structural characteristics of a fingerprint is a pattern of interleaved ridges and valleys. Ina fingerprint image, ridges (also called ridge lines are dark whereas valleys are bright. Ridges and valleys often run in parallel; sometimes they bifurcate and sometimes they terminate [23]. Furthermore, a fingerprint image is rich in textures and details information. It has been found that edges and textures are usually confined to the DWT coefficients of the high frequency subbands. Watermarking in the DWT is also very robust to compression methods such as Wavelet Scalar Quantization (WSQ [24] which is the standard adopted by the FBI and many other investigation agencies. In the literature, it is claimed that a good probability distribution function (pdf approximation for a marginal density of coefficients, at a particular subband produced by various type of wavelet transforms, may be achieved by adaptively varying two parameters of the GGD density [25], [26]. This is defined as: f X (x i ; α, β = ( β 2αΓ(/β exp ( β xi α where Γ(. is the Gamma function, Γ(z = e t t z dt, z >. The parameter α is referred to as the scale parameter and it models the width of the pdf peak (standard deviation and β is called the shape parameter and it is inversely proportional to the decreasing rate of the peak. Note that β =and β =2 yield Laplacian and Gaussian distributions, respectively. The parameters α and β can be estimated as described in [27]. The optimal value of β may be different for each DWT coefficient, but for practical reasons a constant value is used. To verify whether the distribution of the DWT coefficients of fingerprint images can be approximately modeled by a GGD, one can examine the Quantile- Quantile (Q-Q plots of the DWT coefficients of a set of real test images (see Fig. which are chosen in order to take into account the different visual quality of fingerprint images [28]. Thus allowing the modeling results to be more general and reliable. A Q-Q plot ( 2 ACADEMY PUBLISHER

3 JOURNAL OF MULTIMEDIA, VOL. 5, NO. 2, APRIL 2 69 Q Q Plot for Image2 Q Q Plot for Image Random Samples Quantiles Random Samples Quantiles Random Samples Quantiles DWT Coefficients Quantiles (a Q Q Plot for Image Random Samples Quantiles DWT Coefficients Quantiles (b Q Q Plot for Image DWT Coefficients Quantiles (c DWT Coefficients Quantiles Figure 2. Q-Q plots of DWT coefficients of sample images for the generalized Gaussian distribution: (a Image2, (b Image22, (c Image2 5 and (d Image6 (d (a (c Figure. Test images with different visual quality: (a Image2, (b Image22, (c Image2 5 and (d Image6 is a graphical technique for determining if two data sets are generated from populations having a common distribution. For example, if two data sets are taken from two populations with the same distribution, the (b (d points should fall approximately along a reference line. The greater the departure from this reference line, the greater the evidence that the two data sets have been generated from populations with different distributions. In our experiments, for a given fingerprint image we first estimate the parameters α and β from the DWT coefficients and then generate a large number of random samples drawn from a GGD having the estimated parameters α and β [29]. The quantiles of the real DWT coefficients against the quantiles of the random generated samples are plotted. As can be seen from Fig. 2 (a-d, most of the + marks follow a straight line for Image6, deviating slightly from the reference line for Image22 and Image2 but with a more significant deviation for Image2 5. In general, the Q-Q plots for all fingerprint images show that the GGD provides an accurate fit for the DWT coefficients. Experiments performed with other test images have very similar plots. Images (2, 22 and 6 are expected to yield better watermark decoding and detection performance than that for Image2 5. It is worth noting that in Image2 5, the region of interest (or the ridges area is somewhat small when compared to the overall size of the image (i.e. most of it is composed 2 ACADEMY PUBLISHER

4 7 JOURNAL OF MULTIMEDIA, VOL. 5, NO. 2, APRIL 2 by smooth area or background. The DWT coefficients can be divided into sequences where each sequence is used to hide one bit (see Section III below. The partition of the coefficients must be carried out in such a way that the sequences can also be modeled by a GGD. It has been experimentally found that the simplest and most efficient way to divide a subband is to use two-dimensional (2-D non overlapping blocks. III. WATERMARK EMBEDDING The DWT subbands coefficients are used to embed the watermark. It is well known that a DWT decomposition at level l produces : (i a low resolution subband (LL, (ii high resolution horizontal subbands (HL l,hl l, HL, (iii high resolution vertical subbands (LH l,lh l, LH and (iv high resolution diagonal subbands (HH l,hh l, HH. A watermark should be embedded in high resolution subbands where the human eye is less sensitive to noise and distortions [3], [3]. Let x[n] be a 2-D real sequence representing one of the subbands used to hold the watermark (i.e. HL l, LH l or HH l [Note that all three subbands can be used to carry the watermark, depending on the size of the information bit to be hidden and also the application]. Let m[n] be a pseudo-random sequence uniformly distributed in [, +], which is generated using a pseudo-random sequence generator (PRSG initialized by a secret key K. In this paper, a vector notation in boldface typesetting is used to represent 2-D indices. Assume that the watermark carries a secret message, which is mapped by an encoder to a binary sequence b = {b b 2...b Nb } of N b bits (by denoting + for bit and for bit. The information bits b are hidden as follows: Step : The sequence x[n] is partitioned into N b nonoverlapping blocks { } N b i=. In the following, we denote by x i [k] the set of DWT coefficients belonging to block,wherex i [k] x j [k] = for i j and N b i= x i[k] =x[n]. The number of coefficients in any block depends on whether a perceptual mask is used or not. If a perceptual mask is used, the number of coefficients per block will vary according to the nature of the mask and the coefficients in each block. Otherwise, all interior blocks should have the same size; Step 2: The watermark sequence m[n] is divided into N b non-overlapping chunks {m i [k]} N b i= where m i[k] m j [k] = for i j and N b i= m i[k] =m[n], sothat, each chunk m i [k] is associated to one block x i [k] and both are used to carry one information bit b i. The number of elements in block x i [k] is the same as in its associated chunk m i [k]; Step 3: Each element of a chunk m i [k] is multiplied by + or - according to its associated information bit b i.the result of this multiplication is an amplitude modulated watermark w i where w i [k] =m i [k]b i ; Step:4: Finally, the watermark is embedded as follows: y i [k] =(+λm i [k]b i x i [k] (2 where y i [k] represents the set of the watermarked coefficients belonging to block. λ is a value used to control the strength of the watermark by amplifying or attenuating the watermark effect on each DWT coefficient so that the watermark energy is maximized while the alterations suffered by the image are kept invisible. The embedding process is summarized in Fig. 3. IV. HIDDEN INFORMATION DECODING The task of the decoding process is to extract the hidden information sequence b, bit-by-bit, from the possible information sequences {b j } 2N b j=. In practice, since the watermarked image is usually altered by intentional or unintentional attacks, the hidden information cannot be completely recovered and errors may occur. An efficient decoder estimates ˆb with a low error probability. Consequently, the key idea is to develop a criterion that minimizes the probability of error. A. Optimum Decoder for the Generalized Gaussian Model By assuming that all possible information bit sequences {b j } 2N b j= are equally probable, a maximum-likelihood (ML criterion can be used to minimize the probability of error and hence derive a structure for an optimum decoder. An optimum ML decoder would decide ˆb {b j } 2N b j=,such that: ˆb =argj= 2 N b max f y (y[n] m[n],b j (3 where y[n] represents the set of DWT coefficients of the watermarked image, f y (y m,b j is the pdf of the set y[n] conditioned to the events m[n] and b j. By assuming that: (i the DWT coefficients y[n] are statistically independent and (ii the hidden sequence b and the values in m[n] are independent of each other, Eq. (3 can be expressed by: N b ˆb =argj= 2 N b max f yi (y i [k] m i [k],b ji (4 i= where y i [k] indicates the DWT coefficients of the block carrying the bit b i, and m i [k] is a set from m[n] associated to the bit b i. The decision criterion for bit b i can be expressed as: ˆb i =arg max bi {,+} f yi (y i [k] m i [k],b i Bi [ ] (5 B = sign i f yi (y i [k] m i [k], + f yi (y i [k] m i [k], According to the multiplicative rule used to embed the watermark(see Eq. (2, the pdf f yi (y of a marked coefficient y i [k] subject to a watermark value m i [k]b i can be computed by: ( y i [k] f yi (y i [k] m i [k],b i = f xi +λm i [k]b i +λm i [k]b i (6 2 ACADEMY PUBLISHER

5 JOURNAL OF MULTIMEDIA, VOL. 5, NO. 2, APRIL 2 7 Figure 3. Block diagram of the watermark embedding process. where f x (x indicates the pdf of the original, nonmarked coefficients. Substituting f x (x with Eq. (, the pdf of the marked coefficients y i [k] conditioned to the event m i [k] and b i =+is given by: β i f yi (y i [k] m i [k], + = 2α i Γ( β i +λm i [k] ( exp y i [k] α βi +λm i i [k] β i Similarly, the pdf of the marked coefficients conditioned to the event m i [k] and b i = is given by: β i f yi (y i [k] m i [k], = 2α i Γ( β i λm i [k] ( exp y i [k] α βi λm i i [k] β i By substituting Eq. (7 and Eq. (8 in Eq. (5 and adopting a logarithmic formulation, we obtain: [ ( λmi [k] ˆb i =sign ln +λm i [k] ( + ] β y i [k] y i [k] i βi α βi λm i i [k] +λm i [k] (9 By letting and z i = α βi i ( y i [k] λm i [k] T i = ln βi ( +λmi [k] λm i [k] y i [k] +λm i [k] β i Eq. (9 can be expressed in a simple formulation as: ˆb i = { +, if zi >T i ;, otherwise. (7 (8 ( ( (2 B. Performance Analysis Once the decoder structure has been designed, it is worth deriving the theoretical probability of making an error when decoding a bit (also known as bit error rate ( in the absence of attacks. The value z i is a sum of statistically independent random variables, so according to the central limit theorem (CLT, its pdf can be approximated as a normal distribution for an appropriately large number of samples. Therefore, we consider modeling z i by a Gaussian distribution with mean and variance under hypotheses b i =+and b i = that can be estimated from the given data. Assuming that the watermarked image is unaltered and from Eq. 2, the coefficients y i [k] can be substituted by ( + λm i [k]x i [k] under hypothesis b i =+.Themeanµ and variance σ 2 of z under the hypotheses b i =+are: and µ = E[z i b i =+] = [ ] +λmi [k] βi α βi λm i i [k] E[ x i βi ] βi = [ ] +λmi [k] βi β i λm i [k] βi (3 σ 2 = Var[z i b i =+] = E[z i E[z i ] b i =+] 2 = [ ] 2 (4 +λmi [k] βi β i λm i [k] βi In a similar fashion, the mean µ and variance σ 2 of z i under hypothesis b i = are computed by substituting ( λm i [k]x i [k] for y i [k], thus: and µ = E[z i b i = ] = β i σ 2 = Var[z i b i = ] = β i [ λm i[k] βi +λm i [k] βi [ λm i[k] βi +λm i [k] βi ] (5 ] 2 (6 2 ACADEMY PUBLISHER

6 72 JOURNAL OF MULTIMEDIA, VOL. 5, NO. 2, APRIL 2 2 Monte Carlo simulation Analytical whether the hidden message was correctly recovered or not. This procedure has been carried out for different strength values, λ. Fig. 4 illustrates the average results obtained on 5 real fingerprint images chosen from [28] and by using different random sequences. It can be seen that the decreases as the strength λ increases. For Monte Carlo simulations and under a normality assumption, the results obtained are very similar especially at low watermark strength values. This similarity confirms the validity of the theoretical analysis of the under the normality assumption of z i Strength Figure 4. Comparison between the actual bit error rate computed through Monte Carlo simulations and the error rate set under a normality assumption. The mean (µ,µ and variance (σ,σ 2 ofz 2 i can be computed from the given data (i.e. the DWT coefficients of the original image since they only depend on the distribution parameter β i and the sequence m i [k]. The is given by: = 2 [p (z i >T i b i = + p (z i <T i b i =+] (7 where p (z i <T i b i =+is the error probability of mistaking bit for, which is given by: p (z i <T i b i =+= p (z i >T i b i =+ = f(z i b i =+dz i T i ( (8 = 2 erfc T i µ 2σ 2 and p (z i > T i b i = is the error probability of mistaking bit for, defined as: p (z i >T i b i = = T i f zi (z i dz i ( = (9 2 erfc T i µ 2δ 2 C. Experimental Results Extensive experiments were conducted in order to evaluate the performance of the proposed decoder when operating on real fingerprint images and to assess its robustness in the presence of different attacks, namely WSQ compression, mean filtering and additive white Gaussian noise (AWGN. In all experiments, real fingerprint images of size have been used, taken from Fingerprint Verification Competition FVC 2, DB3 database [28]. These images have been chosen for their different visual quality. In all tests, the watermark has been embedded in the HL 3, LH 3 and HH 3 subbands, obtained after a wavelet transformation of each image by DWT using Daubechies wavelet at the 3 rd decomposition level. Also, a blind watermark decoding is used so that the parameters α i and β i of each block are directly estimated from the DWT coefficients of the watermarked image by assuming that λ is sufficiently small to not alter the visual quality of the original image. To make a comparison as fair as possible, the performance of the proposed decoder has been compared against a similar and related decoding technique proposed by Song [22]. The decoder proposed in [22] performs a multibit watermark estimation in the DWT domain and uses a GGD to describe the DWT coefficients that hold the watermark according to a multiplicative rule. where ercf(. is the complementary error function. In order to evaluate the error introduced by the normality assumption, the analytical has been compared against the actual calculated through Monte Carlo Simulations. First, the number of coefficients per bit has been fixed to 256 and a set of pseudo-random sequences have been generated. Then, a set of typical parameters (i.e. α i sandβ i s has been estimated from real fingerprint images. At this stage, the analytical can be evaluated using Eq. (7. As for Monte Carlo simulations, a large number of random samples drawn from a set of GGD having the desired parameters have been generated, as described in [29]. Eventually, such samples have been used to hide a set of randomly generated messages. These watermarked samples have been considered to verify 2 Analytical Empirical Song s Watermark Strength Figure 5. Comparison between The empirical, analytical and, computed for different value of the strength λ. As a first step, one needs to compare the actual obtained when watermarking real fingerprint images with 2 ACADEMY PUBLISHER

7 JOURNAL OF MULTIMEDIA, VOL. 5, NO. 2, APRIL 2 73 for Image 2 for Image ( (3..5 ( (29.2 Compressin rate (bpp (a for Image ( ( ( (29.2 Compression rate (bpp (b for Image 6 2. ( ( ( (3.2 Compression rate (bpp (c 2. ( ( ( (3.2 Compression rate (bpp Figure 6. Robustness against WSQ compression with increasing bits per pixel. Results refer to fingerprint images shown in Fig.. The watermark strength λ =.26. The corresponding value of PSNR is given between brackets. (d for Image 2 for Image 22 Proposed technique Song decoder 2 4 ( ( ( ( (3.3 SNR(dB (a for Image ( ( ( ( (3.8 SNR(dB (b for Image ( ( ( ( (29.2 SNR (db (c 2 4 ( ( ( (3.9 2 (29. SNR(dB Figure 7. Robustness against white Gaussian noise addition with decreasing SNR. Results refer to fingerprint images shown in Fig.. The watermark strength λ =.26. The corresponding value of PSNR is given between brackets. (d 2 ACADEMY PUBLISHER

8 74 JOURNAL OF MULTIMEDIA, VOL. 5, NO. 2, APRIL 2 for Image 2 for Image x3(3.36 5x5( x7(28.2 Filter size (a for Image x3( x5(3.88 7x7(3.2 Filter size (b for Image 6 2 3x3( x5(3.79 7x7(3.2 Filter size (c 2 3x3( x5(3.5 7x7(3.2 Filter size Figure 8. Robustness against mean filtering with increasing filter size. Results refer to fingerprint images shown in Fig.. The watermark strength λ =.26. The corresponding value of PSNR is given between brackets. (d the analytical analysis described in Section IV- B. Fig. 5 shows the average results from the same 5 fingerprint images used to derive the analytical and different pseudo-random sequences, each hosting N b =36bits (2 information bits/subband. The number of coefficients per information bit is set to 256 coefficients/bit (block size =6 6 and the watermark has been inserted with different values of λ. As can be seen from Fig. 5, our proposed decoder outperforms the one proposed by Song for all values of the strength λ. In addition, both the empirical and the analytical results are similar especially for small strength values, λ; the difference is proportional to the watermark strength. This is justified by the fact that the analytical is derived from the original images (i.e. the parameters αs andβs are estimated from DWT coefficients of the original images while these parameters have been estimated from watermarked images to compute the empirical error. The values of the estimated parameters from the watermarked images diverge from the original ones against the increasing watermark strength. For the sake of completeness, extensive experiments have also been conducted to assess the performance of the proposed decoder in terms of robustness and to compare it against the decoder proposed by Song [22]. Three sets of experiments have been carried out which aim to measure the robustness of the watermark against WSQ compression, mean filtering and AWGN. In all tests, the value of the strength λ is set to.26 and the number of coefficients per bit is fixed to 256. Each attack has been applied several times, by varying the attack strength and reporting the average value of over different pseudo random sequences. Here, we only display the results of the four fingerprint images shown in Fig., the results obtained from other test images are very similar. Robustness against WSQ compression is of crucial importance due to the need of reducing the size of fingerprint images for storage (especially, in large databases and transmission purposes. To assess the performance of the two decoders, we iteratively applied WSQ compression to the watermarked fingerprint images using the WSQ viewer [32] and varying the bit-rate value measured by bits per pixel (bpp. The results obtained are given in Fig. 6. Even though the compression ratio is over a wide range of values (from bpp to.25 bpp, the proposed decoder performs very well. If one refers to Song s method, the obtained with the proposed decoder is smaller for all images and bit-rate values. It is worth mentioning that even the value of peak signalto-noise ratio (PSNR is small (< 34 for all images, the WSQ compression does not affect the integrity of the fingerprint image (i.e. the ridges region, the visual alteration can only be seen in the background areas for very high compression ratios. The results are as expected since the wavelet-based watermarking is very robust to the wavelet-based compression including WSQ compression. 2 ACADEMY PUBLISHER

9 JOURNAL OF MULTIMEDIA, VOL. 5, NO. 2, APRIL 2 75 Fig. 7 shows the results for of watermarked fingerprint images corrupted by additive white Gaussian noise with different value of signal-to-noise ratio (SNR. For all images, our proposed decoder provides attractive results and significantly outperforms Song s method. Severe visual image degradations occur at a SNR of 3 db or less, where the PSNR is smaller than 36. In general, the white Gaussian noise is spread over the whole image and it does not affect significantly the performance of the two decoders. The results for degradations due to a linear mean filtering are depicted in Fig. 8 where the watermarked fingerprint images are blurred with different filter sizes. Although the of the proposed decoder is less than that of Song s decoder all images and all filter sizes, the results are reasonably close especially for Image6 which exhibits a degraded visual quality. Note that mean filtering affects the quality of the images even for the smallest size 3 3 where the PSNR is below 33. Unlike AWGN, a mean filtering affects dramatically the performance of the two decoders since, in essence, this type of filtering smoothes the image and attenuates the shape of edges and texture which are well confined in the the high frequency DWT subbands and hold an important part of information, represented by the watermark. V. WATERMARK DETECTION The role of a detector is to decide whether a given image contains a watermark generated with a given key. Although the multibit watermarking is different from the one-bit case, an optimum detector for multibit watermark can be designed following the same approach used for one-bit optimum detector. The watermark detection problem can be mathematically formulated as a binary hypothesis test as follows: H : y[n] =(+λm[n]bx[n]; H : y[n] =x[n]; The hypothesis H states to saying that the DWT coefficients are marked by the sequence m[n], modulated by any bit sequence from the 2 N b possible bit sequences. Likewise, hypothesis H states that y[n] does not carry any watermark. The likelihood ratio, denoted by Λ(y, is defined as: Λ(y = f y(y[n] H f y (y[n] H (2 where f y (y[n] H and f y (y[n] H represent the pdf of y[n] conditioned to the events H and H, respectively. By assuming that: (i the information bits b and the values in m[n] are independent of each other, and (ii the DWT coefficients used to carry the watermark are statistically independent. The pdf f y (y[n] H is obtained by integrating the 2 N b possible bit sequences: N b f y (y[n] H = f yi (y i [k] m i [k] i= N b [ = fyi (y i [k] m i [k], p(b i = i= + f yi (y i [k] m i [k], +p(b i =+ ] (2 By assuming a priori equal probabilities (i.e. p(b i = = p(b i = + = /2, Eq. (2 can be written as follows: f y (y[n] H = N b i= [ f yi (y i [k] m i [k], 2 + ] (22 f yi (y i [k] m i [k], + To simplify the notation in the sequel, the 2-D index k is omitted from y i [k] and m i [k]. The pdf of the marked coefficients y i conditioned to the value m i and b i ( or + can be expressed by the pdf of the original DWT coefficients x, sothat: [ Nb ] i= y 2 Bi λm i f x ( i λm i Λ(y = Nb i= [ f x (y i ] [ Nb ] (23 y i Bi + i= 2 Nb i= +λm i f x ( [ f x (y i ] +λm i A. Optimum Detection for the Generalized Gaussian Model If we assume that the DWT coefficients of the original image follow a GGD, then a log-likelihood function l(y ln Λ(y is given by: { N b l(y = ln(2+ i= [ ( ln λm i + ( +λm i. exp. exp [ ( yi [ βi ]] β i α i λm i [ ( yi [ βi ]] ]} β i α i +λm i (24 where α i and β i are the parameters of the generalized Gaussian pdf for the coefficients x i belonging to block. The decision rule reveals that an image is watermarked by the sequence m[n] (H is accepted only if l(y exceeds a threshold T. By employing the Neyman-Pearson criterion, the threshold is obtained in such a way that the probability of detection P det is maximized, subject to a fixed false alarm probability Pfa. By fixing the value of P fa,the threshold T can be obtained using the equation: P fa = P (l(y >T H = T f l (l(ydl(y (25 2 ACADEMY PUBLISHER

10 76 JOURNAL OF MULTIMEDIA, VOL. 5, NO. 2, APRIL 2 Figure 9. Block diagram of the watermark decoding/detection process. where f l (l(y is the pdf of l(y conditioned to H.The problem now is to derive a good estimate of f l (l(y. By using the central limit theorem, Barni et al. [2] models l(y by a Gaussian pdf with mean µ = E[l(y H ] and σ 2 = Var[l(Y H ]. Under these assumptions, Eq. (25 can be expressed by: ( Pfa = 2 erfc T µ (26 2σ 2 where erfc(. is the complementary error function, so: T = erfc (2Pfa 2σ 2 + µ (27 For the sake of simplicity, the mean µ and the variance σ 2 are usually estimated numerically by evaluating l(y for n fake sequences {m j [n] :m j [n] [, +]; j n}, so that the estimated mean and variance of l(y are given by: ˆµ = n l j (y (28 n and ˆσ 2 = n j= n (l j (y ˆµ 2 (29 j= where l j (y represents the log likelihood ratio corresponding to the sequence m j [n]. The selection of n involves a trade-off between computational complexity and accuracy of results. The higher n is, the better the estimates to µ and σ 2 are but the higher computational complexity is, and vice versa. We found in [33] that a good estimation of µ and σ 2, with reasonable computational complexity, can be obtained by letting n = 5. The performance of the watermark detection is measured in terms of its probability of false alarm (P fa and its probability of correct detection (P det for a given image. The P fa is given by Eq. (26, while the P det is expressed by: ( P det = 2 erfc λ µ 2σ 2 (3 where µ and σ 2 represent the mean and variance of the likelihood ratio l[y] under hypothesis H, respectively. The mean µ and the variance σ 2 can be estimated as the mean and the variance of l[y] under H and by substituting y i [k] by ( + m i [k]λb i x i [k] and b i can be substituted by + or - in Eq. (24. The experiments reveal that there is a slight difference between µ and σ 2 estimated under b =+and µ and δ estimated under b =. By inserting Eq. (27 in Eq. (3, P det can be expressed as a function of P fa, µ and σ 2,hencethe receiver operating characteristic (ROC of the watermark detector can be computed from the given image (i.e. the DWT coefficients of the original image. B. Experimental results In order to reliably measure the actual performance of the proposed detector, extensive experiments have been conducted with various test images used to evaluate the performance of the decoder of the previous section. In these experiments, the watermarks are generated and embedded following the procedure described in Section III. Also, the performance of the proposed detector has been compared against the one proposed by Song [22]. The theoretical ROC curves are derived for the proposed detector using Eq. (3. The experimental ROC curves are computed by measuring the performance of the actual watermark detection system by calculating the P det from real watermarked images. Experiments are then conducted by comparing the log-likelihood ratio with the corresponding threshold for each value of the theoretical false alarm and for randomly generated watermark sequences. The P fa is set to the range 5 to and the value of the strength λ is fixed to value.. The ROC curves in Fig. (a-(c indicate that the proposed detector clearly outperforms Song s detector, except for the case of Image6 (Fig. (d Song s detector performs slightly better than the proposed one but the difference of the ROC curves is not as significant as for the other images. Fig. (a-(d clearly show that the empirically obtained ROC curves verify the theoretical ones for all images. The performance of the detector depends highly on the image characteristics in the DWT 2 ACADEMY PUBLISHER

11 JOURNAL OF MULTIMEDIA, VOL. 5, NO. 2, APRIL ROC curves for Image 2 Analytical Empirical Song s Detector Probability of False Alarm (a ROC curves for Image 2 5 Analytical Empirical Song s Detector Probability of False Alarm (c ROC curves for Image 22 Analytical Empirical Song s Detector Probability of False Alarm (b ROC curves for Image 6 Analytical Empirical Song s Detector Proboility of False Alarm Figure. Empirical and analytical ROC curves for the DWT coefficients of the test images. The watermark strength λ has been set to.. (d domain. For instance, one can notice the large difference between the ROC curves of Image2 and Image2 5. The results for Images2 are very attractive and P det is above.87 for all values of P fa. The ROC curves for Image22 and Image6 are quite similar. On the other hand, Image2 5 provides the worst results; this is consistent with the modeling results of Section II, where it was shown that for this image the GGD does not really fit its high-frequency DWT coefficients. A similar situation arose from the results of optimum decoder, where the probability of bit error for Image2 5 was very high. Note that the strength λ used is very low.; increasing the value of λ will enhance the performance of the proposed detector. The performance of the detection schemes is also evaluated when watermarks of varying strength are embedded in DWT coefficients. For this purpose, we define the Watermark to Document Ratio (WDR as in [34]: ( σ 2 WDR =log w (3 with σ 2 w = N σ 2 x N wj 2,σx 2 = N j= N x 2 j (32 j= where w represents the watermark inserted and is given by λm i b i x i, x is the watermarked data and N is the number of data samples used to carry the watermark and which also refers to the original host data (i.e. the original DWT coefficients. The WDR determines the amplitude of the watermarks where a small value of WDR correspond to a high perceptual quality since, in this case, the host data document (i.e. DWT coefficients has good immunity to the watermarking process. Note that as a rule of thumb for image watermarking, WDRs below -2 db are required to keep the watermark imperceptible [35]. For the test images presented in Fig., watermarks of varying strength λ are embedded in the DWT coefficients, leading to different values of σw 2 and WDR. For these watermarks, we determine both the probability of false alarm and the probability of true detection. We then consider two cases: first, we fix the probability of false alarm and we calculate the corresponding probabilities of detection. Then we fix the probability of detection to compute the corresponding probabilities of false alarm. In the former case, we set the false alarm probability to the value P fa = 9 and in the latter case we consider P det =.99. From the statistics of the likelihood ratios of the detector and the predetermined P fa and P det,wethen estimate the corresponding thresholds for the likelihood ratio tests. For fixed P fa we use (33 and for fixed P det the threshold for the detector can be given by: λ = erfc (2P det 2δl 2 + µ l (33 Finally, from Eq. (26 and Eq. (3, we calculate the probability of detection and false alarm for all the WDR values whose results are depicted in Fig. and Fig. 2, respectively. Note that in Fig. (a, (b and (d, a WDR value greater than -42 db corresponds to a relative weak watermark strength to some extent (i.e. λ.2 that 2 ACADEMY PUBLISHER

12 78 JOURNAL OF MULTIMEDIA, VOL. 5, NO. 2, APRIL 2 Detector Performance for Image2 Detector Performance for Image (.5 56(. 48(.5 42(.2 38(.25 34( (a Detector Performance for Image2 5 7(.5 56(. 48(.5 42(.2 38(.25 34( (b Detector Performance for Image (.5 56(. 48(.5 42(.2 38(.25 34(.3 (c 7(.5 56(. 48(.5 42(.2 38(.25 34(.3 Figure. Probability of detection for watermarks of varying strength λ parameterized by the WDR. The P fa = 9. The corresponding value of λ is given between brackets. (d.7 Detector Performance for Image2 Detector Performance for Image Probability of False Alarm Probability of False Alarm (.5 56(. 48(.5 42(.2 38(.25 34(.3 Probability of False Alarm (a Detector Performance for Image2 5 7(.5 56(. 48(.5 42(.2 38(.25 34(.3 Probability of False Alarm (b Detector Performance for Image6 7(.5 56(. 48(.5 42(.2 38(.25 34(.3 (c 7(.5 56(. 48(.5 42(.2 38(.25 34(.3 Figure 2. Probability of false alarm for watermarks of varying strength parameterized by the Watermark to Document Ratio. The P det =.99. The corresponding value of the strength λ is given between brackets. (d 2 ACADEMY PUBLISHER

13 JOURNAL OF MULTIMEDIA, VOL. 5, NO. 2, APRIL 2 79 can be detected with a probability of. For Image2 5, the values WDR for which the probability equals are above -38 db and correspond to a relatively strong watermark strength λ.25. It can also be noticed that the performance of the detector depends not only on the WDR, but on the specific characteristics of the image as well. For example, comparing Fig. 2(b and (c, one can observe that a stronger watermark must be embedded in image2 5, which exhibits less detail information, in order for it to be reliably detected. On the other hand, for images having more details such as Image2, a weaker (by about db watermark is required to obtain the same probability of detection. This result makes an intuitive sense, since the amount of the watermark inserted depends on the amplitude of the coefficient itself in multiplicative watermarking and a detailed image produces DWT coefficients with relatively higher amplitudes than a smooth one. Similarly, in Fig. 2, it can be seen that more false alarms tend to occur in Image2 5 for the same WDR. This can also be explained intuitively, since DWT coefficients of smooth images are relatively small which require an insertion of weak watermarks for invisibility purposes. However, in such a case, the detector cannot make significant difference and may lead to a false decision. Fig. and 2 show that the proposed detector provides attractive results and can reliably detect a watermark in low WDR margins (i.e., even if the watermark has very low strength or it is subject to an attack that partially eliminates it thus decreasing its power σ 2 w. VI. CONCLUSIONS This paper proposes new optimum multibit, multiplicative watermarking decoding and detection methods in the DWT domain for fingerprint images. The proposed techniques are based on the statistical properties of the high-frequency DWT coefficients. The original image is not required in the watermark decoding and detection processes, which makes the algorithms highly flexible for real applications. The proposed decoder and detector utilize a generalized Gaussian model, which accurately describes the DWT coefficients of the fingerprint images. The accuracy of this model has been verified through experimental investigation. Optimal structures for both watermark decoding (extraction and watermark detection has been derived using a ML scheme. Theoretical assessments of the performance of the proposed decoder and detector (such as the probability of error in decoding and the probabilities of false alarm and detection in watermark detection have been derived. The analytical results are compared with the empirical ones; both indicate that the approach is robust even in the presence of attacks such as WSQ compression, mean filtering and white noise addition. The overall performances for both decoder and detector are dependent on the fingerprint image characteristics. This dependence is, however, not related to the quality of the fingerprint image or to the clarity of the ridge lines but it depends on the size of the ridges area relative to the size of the fingerprint image. The bigger the ridges area, the higher the performance of the proposed decoder and detector. In this paper, we have not taken into account the influence of visual masking on the performance of the proposed decoder and detector. It is hoped that the use of perceptual masking will further improve the results in future work. REFERENCES [] A. k. Jain, S. Prabhakar, and L. Hong, A multichannel approach to fingerprint classification, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 2, no. 4, pp , April 999. [2] A. k. Jain and U. Uludag, Hiding biometric data, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 25, no., pp , November 23. 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14 8 JOURNAL OF MULTIMEDIA, VOL. 5, NO. 2, APRIL 2 [6] J. R. Hernandez, M. Amado, and F. Perez-Gonzales, DCT-domain watermarking techniques for still images: Detector performance analysis and a new structre, IEEE Transactions on Image Processing, vol. 9, no., pp , January 2. [7] A. Briassouli, P. Tsakalides, and A. Stouraitis, Hidden messages in heavy-tails: DCT-domain watermark detection using alpha-stable models, IEEE Transactions on Multimedia, vol. 7, no. 4, pp. 7 75, August 25. [8] M. Barni, F. Bartolini, A. D. Rosa, and A. Piva, A new decoder for the optimum recovery of nonadditive watermarks, IEEE Transaction on Image Processing, vol., no. 5, pp , May 2. [9] Q. Cheng and T. S. Huang, Robust optimum detection of transform domain multiplicative watermarks, IEEE Tansactions on Signal Procesing, vol. 5, no. 4, pp , April 23. [2] F. Perez-Gonzales, J. R. Hernandez, and F. Balado, Approaching the capacity limit in image watermarking: A perspective on coding techniques of data hiding applications, Signal Processing, vol. 8, no. 6, pp , June 2. [2] M. Barni, F. Bartolini, A. D. Rosa, and A. Piva, Optimum decoding and detection of multiplicative watermarks, IEEE Transactions on Signal Processing, vol. 5, no. 4, pp. 8 23, April 23. [22] K. S. Song, Blind efficient scores detection and decoding of multibit watermarks, in Proceedings of SPIE, the International Society for Optical Engineering, vol. 595, August 25, pp [23] D. Maltoni, D. Maio, A. k. Jain, and S. Prabhakar, Handbook of Fingerprint Recognition. New York: Springer, June 23. [24] WSQ Gray-Scale Fingerprint Image Comprssion Specification, U.S. Federal Bureau of Invetigation, February 993. [25] G. Wouwer, P. Scheunders, and D. Dyck, Statistical texture characterization from discrete wavelet representation, IEEE Transaction on Image Processing, vol. 8, pp , April 999. [26] S. Mallat, A theory for multiresolution signal decomposition: The wavelet representation, IEEE Transaction on Pattern Recognition and Machine Intelligent, vol., pp , July 989. [27] M. N. Do and M. Vetterli, Wavelet-based texture retreival using generalized gaussian density and kullback-leibler distance, IEEE Transaction on Image Processing, vol., no. 2, pp , February 22. [28] Fingerprint verification competition, [29] M. Nardon and P. Pianca, Simulation techniques for generalized gaussian densities, University of Venice, Working paper series 45/26, November 26. [3] X. G. Xia, C. G. Bonklet, and G. R. Acre, Wavelet transform based watermark for digital images, Optics Express, vol. 3, no. 2, pp , December 998. [3] G. C. Langelaar, I. Styawan, and R. L. Lagendijk, Watermarking digital image and video data: A state-of-art overview, IEEE Signal Processing Magazine, vol. 7, no. 5, pp. 2 46, Septembre 2. [32] WSQ viewer (version 2.7, [33] k. Zebbiche, F. Khelifi, and A. Bouridane, Optimum detection of multiplicative-multibit watermarking for fingerprint images, in Proceedings of the 2nd International Conference on Biometrics (ICB27, vol. 4642/27, August 27, pp [34] J. J. Eggers and B. Girod, Quantizaion effects on digital watermarks, Signal Processing, vol. 8, no. 2, pp , February 2. [35] J. K. Su and B. Girod, Power-spectrum condition for energy-efficient watermarking, in Proceedings of the International Conference on Image Processing (ICIP999, vol., October 999, pp Khalil Zebbiche received the Ingenieur d Etat degree in Computer Science from the Ecole Polytechnique, Algiers, Algeria, in 23. In Septembre 25, he joined the Queens University of Belfast, Belfast, UK, as a research student and received the PhD degree from the School of Computer Science in 28. From 23 to 25, he was a research scientist at the Algerian National Centre for Research and Development. He is currently holding a senior research position at the Algerian National Centre for Research and Development, Algeria. His research interests include biometrics, security, image watermarking, digital signal and image processing and information theory. Fouad Khelifi received the Ingenieur d Etat degree in electrical engineering from the University of Jijel, Algeria, in 2, the Magistere degree in electronics from the University of Annaba, Algeria, in 23. He then joined the Queens University of Belfast, Belfast, UK, as a research student and received the PhD degree from the School of Computer Science in 27. From 23 to 24, he was a Lecturer at the University of Jijel. He is currently holding a research position in Digital Media & Systems Research Institute, School of Computing, Informatics, and Media, University of Bradford, UK. His research interests include image coding, image watermarking, digital signal and image processing, artificial intelligence, pattern recognition and classification. Ahmed Bouridane received the Ingenieur d Etat degree in electronics from Ecole Nationale Polytechnique of Algiers (ENPA, Algeria, in 982, the M.Phil. degree in electrical engineering (VLSI design for signal processing from the University of Newcastle-Upon-Tyne, U.K., in 988, and the Ph.D. degree in electrical engineering (computer vision from the University of Nottingham, U.K., in 992. From 992 to 994, he worked as a Research Developer in telesurveillance and access control applications. In 994, he joined Queens University Belfast, Belfast, U.K., initially as Lecturer in computer architecture and image processing. He is now a Reader in computer science, and his research interests are in imaging for forensics and security, biometrics, homeland security, image/video watermarking and cryptography. He has authored and co-authored more than 8 publications. Dr. Bouridane is a Senior Member of IEEE. 2 ACADEMY PUBLISHER