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Semi-fragile watermarking for image authentication with sensitive tamper localization in the wavelet domain
Measurement 46 (2013) 367–373
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Semi-fragile watermarking for image authentication with sensitive tamper localization in the wavelet domain Radu O. Preda University Politehnica of Bucharest, Faculty of Electronics, Telecommunications and Information Technology, Bucharest, Romania
a r t i c l e
i n f o
Article history: Received 7 April 2012 Received in revised form 27 June 2012 Accepted 12 July 2012 Available online 21 July 2012 Keywords: Multimedia security Digital watermarking Image authentication
a b s t r a c t This paper proposes a novel image authentication scheme in the wavelet domain. The scheme uses a semi-fragile watermark to detect and precisely locate malicious tampering in images. The wavelet coefficients selected for embedding are randomly permuted with a secret key, achieving high security. A bit of the watermark is embedded in a group of coefficients by means of quantization. The experimental results show, that our algorithm achieves high image quality and high tampering detection resolution at a low watermark payload, compared to block-based authentication schemes. Thanks to the random permutation, the watermark is protected against local attacks. We have also conducted experiments to demonstrate the robustness of the watermark against mild to moderate JPEG compression. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Digital watermarking can be classified into three different categories: robust, fragile and semi-fragile watermarking. A robust watermark should be able to resist intentional or unintentional manipulations, while a fragile watermark is intended to be destroyed even after the smallest unintentional manipulation. Some important applications for robust watermarking are fingerprinting, data mining and copyright protection [1–12]. The third category, semi-fragile watermarking [3,13,14], uses watermarks that have the ability to resist unintentional manipulations caused by common image processing operations like JPEG compression and are fragile against intentional, malicious manipulations. The main application field of fragile and semi-fragile watermarking is image and video content authentication. This paper focuses on using a semi-fragile watermark for image authentication. Most of the image authentication techniques use a blockbased concept in the spatial, Discrete Cosine Transform (DCT) or wavelet domain [15–21] for detecting the tam-
E-mail address: [email protected] 0263-2241/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.measurement.2012.07.010
pered regions in the image. The original image is partitioned into blocks, and each block is embedded with its own watermark using a secret key. However, most of these schemes are vulnerable to counterfeiting attacks and they cannot discriminate between intentional tampering and unintentional image processing distortions [22,23]. In such approaches, the tamper detection resolution is limited to the block size. Smaller block sizes and higher watermark payloads are necessary to improve the detection resolution, resulting in a considerable degradation of the image quality. A specific attack against image authentication is the collage attack, introduced by Holliman and Memon in [24]. Using this attack, a counterfeiter can combine independently authenticated blocks to produce forged content. This attack is thus undetectable by conventional block-based watermarking techniques. The scheme proposed in this paper focuses on eliminating the drawbacks of block-based schemes, using a Discrete Wavelet Transform (DWT) based approach and random permutation of wavelet coefficients. Our algorithm improves the tamper detection localization; unlike conventional block-based methods, the exact tampered region is detected. The watermark payload is significantly lowered, increasing the image quality. The algorithm can also
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distinguish between intentional tampering and unintentional mild to moderate JPEG compression. Mathematical morphology can be used to improve the detection results [25–29]. Our method can also be used for other multimedia applications [30–43]. The remainder of this paper is organized as follows. In Section 2 we present the proposed image authentication scheme in the wavelet domain, showing the block diagrams of the watermark encoder and decoder and detailing the steps of the algorithm. Section 3 contains the experimental results and performances of the proposed scheme and conclusions are given in Section 4. 2. The proposed image authentication scheme in the wavelet domain Fig. 2. Wavelet decomposition on L = 3 resolution levels. Gray sub-bands (n = 2) selected for watermark embedding.
This section describes the proposed image authentication scheme. The block diagram of the watermark encoder is shown in Fig. 1. The watermark embedding process is described in the following:
(6) The weighted mean mi of every group i of permuted wavelet coefficients is obtained using the following equation:
(1) The original, grayscale image is transformed into the wavelet domain using a 2D-DWT decomposition on L resolution levels. (2) The detail wavelet coefficients from the LHn, HLn and HHn Wavelet sub-bands of resolution level n L are selected. For example, in Fig. 2, the coefficients of the second Wavelet decomposition are chosen for further processing. Selecting higher resolution subbands for watermark embedding gives a better tampering localization, but decreases the resilience of the algorithm to common, unintentional image processing operations. (3) The selected wavelet coefficients are concatenated in a 1D vector C and randomly permuted using a secret key K into a new vector C0 . This process assures that coefficients corresponding to the same spatial location will be separated in C0 . (4) The sequence C0 of permuted coefficients is divided into groups of d coefficients. Parameter d controls the watermark payload of the proposed scheme. A watermark bit will be embedded in every group of d coefficients. A smaller group size will result in a bigger watermark payload and thus in a higher degradation of the image quality and a smaller size of the maximal localizable tampered area, but will not decrease the detection resolution of the scheme. (5) The watermark, a binary random sequence w, is generated using the secret key K and serves as the authentication code. w has the same length as the number of wavelet coefficient groups.
mi ¼
d X ð1Þj jci ðjÞj
ð1Þ
j¼1
where ci(j) denotes the jth coefficient of group i. The weight (1)j is used to make the scheme more robust to common image processing operations that, in most cases, change the entire image and would not modify the weighted mean. (7) The watermarked mean mw i is obtained by quantization of mi to the nearest even or odd quantization level according to the value of the corresponding watermark bit wi, using the following equation:
(
mw i
¼
bmi =Q c Q
if mod2ðbmi =Q cÞ ¼ wi
bmi =Q c Q þ Q
if mod2ðbmi =Q cÞ – wi
;
where bc is the integer part operator and mod2 is the remainder after division by 2.
(8) For every group i of coefficients, the weighted mean mi is changed to the watermarked mean mw i by modifying the wavelet coefficient ci,max(j) with the highest absolute value. Because of the random permutation operation every group should have at least one coefficient with high absolute value. The updating of ci,max(j) is done as follows:
w j cw i;max ðjÞ ¼ c i;max ðjÞ þ ð1Þ signðc i;max ðjÞÞ mi mi where cw i;max ðjÞ is the watermarked coefficient and
Secret key K n Original image
DWT
Wavelet subbands selection
Random permutation
ð2Þ
d
watermark
Coefficient grouping
Watermark embedding
Inverse permutation
Fig. 1. Block diagram of the proposed watermark encoder.
IDWT
Waterm. image
ð3Þ
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signðxÞ ¼
1 if x 6 0 1 if x > 0
(3) All coefficients are permuted back to their original position using the inverse permutation with the secret key. The coefficients flagged as potentially tampered should be now spread all over the subbands. The actual tampered regions should have a high density of flagged coefficients. The other flagged coefficients should be isolated and distributed like random noise. They are false positives and can be claimed as authentic. (4) For a selected resolution level n we will have three sub-bands, LHn, HLn and HHn, with flagged and non-flagged coefficients. We will construct a binary authentication matrix A of the same size (M/2n) (N/2n) as the sub-bands. A(x,y) = 1 if there is a flagged coefficient at the same position (x,y) in any of the HL, LH, or HH sub-bands. (5) The isolated ‘‘1’’ bits in the authentication matrix A will be removed through filtering. (6) Locations incorrectly flagged as tampered are further eliminated by successive erosion and dilation, using a disk of radius R pixels and a square of size S S as structural elements. The ‘‘1’’ bits in the filtered and eroded authentication matrix should now correctly indicate the tampered locations. (7) The flagged positions in A are then mapped back to the spatial domain to indicate the actual tampered locations.
ð4Þ
(9) After updating the coefficients with the highest absolute value from every group, the inverse permutation is applied using the secret key K. (10) Finally, the Inverse 2D-DWT is calculated to obtain the watermarked image. The block diagram of the proposed watermark extractor and authenticator is shown in Fig. 3. The watermark extraction process and image authentication is described in the following: (1) The watermarked, possibly tampered image is transformed into the wavelet domain using a 2D-DWT decomposition on L resolution levels. (2) The detail wavelet coefficients from the LHn, HLn and HHn Wavelet sub-bands are selected for watermark extraction. (3) The selected wavelet coefficients are concatenated. Using a secret key K, the same random permutation is performed. (4) The sequence of permuted coefficients is divided into groups of d coefficients. (5) The weighted mean m0i of every group of coefficients is calculated using Eq. (1). (6) A watermark bit w0i is extracted from the weighted mean of every group of d coefficients using Eq. (5). The Bit Error Rate (BER) between the extracted watermark w0 and the original watermark w will be calculated in Section 3 for different parameter choices.
w0i ¼ mod2 bm0i =Q c
Because the authentication matrix A is of size (M/2n) (N/2n), every location in A points to an actual region in the image of size 2n 2n. As a result, the maximum detection resolution of our algorithm is 2n 2n. The sensitivity of the tampering detection can be adapted by selecting the quantization step size Q, choosing the filter size in step 5 and the size of the structural element used for erosion and dilation in step 6 of the authentication process. A larger Q will increase the sensitivity, but will decrease the perceptual quality of the watermarked image. A larger filter or a bigger structural element for erosion and dilation will reduce the sensitivity, but will also reduce the probability of false alarms as a result of common image processing operations. A trade-off has to be found for specific applications. The security of the proposed image authentication system is ensured by the secret key used to control the ran-
ð5Þ
To authenticate the image the following steps need to be done: (1) First, the original watermark w is locally generated using the secret key K. If the extracted watermark w0 matches the original one, the image is authentic. If not, the following steps will determine if the image was tampered. (2) If a bit of the extracted watermark w0i does not match the original one wi, all coefficients belonging to group i are flagged as potentially tampered.
Secret key K n Waterm. image
DWT
d
Wavelet subbands selection
Authentication and tampering localization
Random permutation
Erosion + dilation
Coefficient grouping
Filtering
Watermark extraction
Inverse permutation
Extracted watermark
Possibly tampered groups
Locally generated watermark
Watermark comparison
Secret key K Fig. 3. Block diagram of the proposed watermark decoder and image authentication.
R.O. Preda / Measurement 46 (2013) 367–373
dom permutation of wavelet coefficients and generation of the original watermark. There can be distinct keys for these two operations or a single key. Without knowing the secret key(s) an attacker cannot design the correct coefficient permutation or a duplicate of the original watermark. The proposed scheme is immune to the Vector Quantization (VQ) attack because, in our algorithm, unlike blockbased methods, where the authentication of each block depends only on the content of the block itself, the wavelet coefficients of a group are selected randomly from all over the image.
60
block-based method proposed method (n=1, d=8)
55
proposed method (n=1, d=12) proposed method (n=1, d=16)
PSNR (dB)
370
50 45 40 35 30 4
3. Experimental results
8
12
16
20
Quantization step size Q To determine the performances of the proposed image authentication scheme 100 images of different sizes were used. We have evaluated our algorithms in terms of image quality, localization capability of the tampering and robustness to JPEG compression with different quality factors. Table 1 shows the image quality and decoding results of the proposed method for different choices of the wavelet resolution level n for watermark embedding, quantization step size Q and group size d, where PSNR is the mean Peak Signal to Noise Ratio and BER is the mean decoding Bit Error Rate of 100 test images. The PSNR values are above 40 dB, except Q = 16 (d = 4 and d = 8) and Q = 20 (d = 4, d = 8 and d = 12), where small distortion are also visible in the watermarked images. In Fig. 4 we compare our technique to a traditional block-based image authentication scheme. For a blockbased approach to achieve a detection resolution of 2n 2n, it has to embed at least one watermark bit in every block of 2n 2n pixels of the image. In comparison, for the same detection resolution, our approach needs to embed a watermark bit in a group of wavelet coefficients of the nth Wavelet decomposition level. In Fig. 4 we have chosen
Fig. 4. Quality of the watermarked images for different group sizes, compared to traditional block-based image authentication schemes.
a detection resolution of 2 2 pixels, n = 1 and d = 4, d = 8 and d = 12. We can see that our approach achieves very high image quality compared to the block-based techniques. Next, we test the capacity of our approach to detect the tampering. For this purpose, in the image in Fig. 5a two regions were tampered: the face of the woman in white was replaced by another face and the beer can was completely removed from the image. First we embed the watermark in the first Wavelet decomposition level (n = 1), using groups of d = 8 wavelet coefficients and the quantization step size Q = 8. Fig. 5c shows the potentially tampered locations in the image in white, before refining the authentication result through filtering. Because n = 1 the detection resolution of the algorithm is 2 2 pixels and the smallest ‘‘noise’’ dot has also 2 2 pixels. We can see that the white dots are clustered in the regions where the actual tampering has taken place.
Table 1 Mean PSNR and BER values for the watermarked images. Q
d
n=1
n=2
n=3
PSNR
BER (%)
PSNR
BER (%)
PSNR
BER (%)
4
4 8 12 16
48.09 51.09 52.86 54.10
1.16 0.24 0.16 0.15
54.14 57.16 58.93 60.18
0.51 0.36 0.32 0.39
60.18 63.18 64.94 66.20
32.31 37.58 40.61 41.74
8
4 8 12 16
42.10 45.12 46.87 48.10
4.85 0.92 0.34 0.19
48.14 51.12 52.91 54.16
0.75 0.05 0.02 0.02
54.12 57.20 58.92 60.22
0.24 0.15 0.22 0.19
12
4 8 12 16
38.62 41.58 43.33 44.60
9.65 2.52 0.97 0.49
44.61 47.62 49.38 50.62
1.98 0.16 0.04 0.02
50.64 53.64 55.37 56.60
0.22 0.02 0.02 0.01
16
4 8 12 16
36.16 39.09 40.85 42.10
14.53 4.87 2.15 1.12
42.13 45.11 46.87 48.13
3.53 0.37 0.08 0.02
48.16 51.14 52.89 54.20
0.48 0.02 0.02 0.01
20
4 8 12 16
34.26 37.17 38.90 40.17
18.94 7.56 3.68 2.10
40.20 43.19 44.94 46.18
5.31 0.78 0.17 0.07
46.19 49.22 51.00 52.23
0.79 0.06 0.00 0.01
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Fig. 5. (a) original image, (b) image with two tampered regions, marked in red, (c) authenticated image before filtering for n = 1, d = 8 and Q = 8, (d) authenticated image after filtering and mathematical morphology operations for n = 1, d = 8 and Q = 8, (e) authenticated image before filtering for n = 2, d = 8 and Q = 8, (f) authenticated image after filtering and mathematical morphology operations for n = 2, d = 8 and Q = 8. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Then, we filter the authentication matrix with a ‘‘cross’’ shaped binary filter of size F = 5. The filtered authentication matrix is then successively eroded and dilated using a disk of radius R = 1 and a square of size 3 3 as structural elements. Fig. 5d shows the refined authentication result after filtering and mathematical morphology operations. In Fig. 5e and f we depict the authentication results before and after refinement using the following parameters: n = 2, d = 8 and Q = 8. In this case, the detection resolution of the algorithm is 2n 2n = 4 4 pixels. We can see that, in both cases, the proposed scheme detects the tampered regions correctly. We also test the robustness of the proposed scheme against non-malicious distortions produced by JPEG compression. JPEG is the most common used standard for compressing still images and it is possible, that the watermarked image undergoes JPEG compression before it suffers intentional manipulation.
Thus, a desired property of an authentication scheme is the resilience to mild to moderate JPEG compression. An image should be deemed as authentic, even if it has been compressed using a medium to high JPEG quality factor. For this reason, the watermark is embedded in the original image using different parameters, like resolution level n, quantization step size Q and size of the wavelet coefficient groups d and the watermarked image is compressed with JPEG quality factors ranging from 100 to 50. Then, the watermark is extracted and the decoding BER is calculated. The BER performance results are shown in Fig. 6 for n = 1 and Fig. 7 for n = 2. As expected, the graphs show that embedding the watermark in a higher Wavelet level makes it more robust to JPEG compression. The reason for this is that the coefficients from higher Wavelet sub-bands are less modified by JPEG compression. The quantization step size Q and the size d of the wavelet coefficient groups also influences the robustness of the
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Acknowledgement
Bit Error Rate (%)
50%
This research activity was supported by UEFISCDI Romania under the Grant PN-II-RU-TE-2011-3-0261/ No.10/2011.
40% 30% n=1,Q=12,d=4 n=1,Q=12,d=8 n=1,Q=12,d=12 n=1,Q=12,d=16 n=1,Q=20,d=4 n=1,Q=20,d=8 n=1,Q=20,d=12 n=1,Q=20,d=16
20% 10% 0% 50
60
References
70
80
90
100
JPEG quality factor Fig. 6. Detection performance of the proposed scheme after JPEG compression for n = 1 and different quantization step sizes and coefficient group sizes.
Bit Error Rate (%)
50% 40% 30% n=2,Q=12,d=4 n=2,Q=12,d=8 n=2,Q=12,d=12 n=2,Q=12,d=16 n=2,Q=20,d=4 n=2,Q=20,d=8 n=2,Q=20,d=12 n=2,Q=20,d=16
20% 10% 0% 50
60
70
80
90
100
JPEG quality factor Fig. 7. Detection performance of the proposed scheme after JPEG compression for n = 2 and different quantization step sizes and coefficient group sizes.
scheme against compression. Increasing Q results in a lower decoding BER after JPEG compression, but also produces a higher distortion in the image. A smaller group size d will increase the robustness, but, on the other hand, it also increases the watermark payload. A compromise between these parameters has to be found for specific applications.
4. Conclusions In this paper we have proposed a new image authentication scheme using a semi-fragile watermark that can detect and locate malicious tampering in images. The embedding and extraction of the authentication watermark is done in the DWT domain. Our technique achieves high image quality and high tampering detection resolution at a low watermark payload. Thanks to the random permutation of the wavelet coefficients before embedding, the watermark is protected against local attacks, like, for example, the VQ attack. The embedded watermark is also robust to mild to moderate JPEG compression by selecting the appropriate embedding parameters.
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Measurement journal homepage: www.elsevier.com/locate/measurement
Semi-fragile watermarking for image authentication with sensitive tamper localization in the wavelet domain Radu O. Preda University Politehnica of Bucharest, Faculty of Electronics, Telecommunications and Information Technology, Bucharest, Romania
a r t i c l e
i n f o
Article history: Received 7 April 2012 Received in revised form 27 June 2012 Accepted 12 July 2012 Available online 21 July 2012 Keywords: Multimedia security Digital watermarking Image authentication
a b s t r a c t This paper proposes a novel image authentication scheme in the wavelet domain. The scheme uses a semi-fragile watermark to detect and precisely locate malicious tampering in images. The wavelet coefficients selected for embedding are randomly permuted with a secret key, achieving high security. A bit of the watermark is embedded in a group of coefficients by means of quantization. The experimental results show, that our algorithm achieves high image quality and high tampering detection resolution at a low watermark payload, compared to block-based authentication schemes. Thanks to the random permutation, the watermark is protected against local attacks. We have also conducted experiments to demonstrate the robustness of the watermark against mild to moderate JPEG compression. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Digital watermarking can be classified into three different categories: robust, fragile and semi-fragile watermarking. A robust watermark should be able to resist intentional or unintentional manipulations, while a fragile watermark is intended to be destroyed even after the smallest unintentional manipulation. Some important applications for robust watermarking are fingerprinting, data mining and copyright protection [1–12]. The third category, semi-fragile watermarking [3,13,14], uses watermarks that have the ability to resist unintentional manipulations caused by common image processing operations like JPEG compression and are fragile against intentional, malicious manipulations. The main application field of fragile and semi-fragile watermarking is image and video content authentication. This paper focuses on using a semi-fragile watermark for image authentication. Most of the image authentication techniques use a blockbased concept in the spatial, Discrete Cosine Transform (DCT) or wavelet domain [15–21] for detecting the tam-
E-mail address: [email protected] 0263-2241/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.measurement.2012.07.010
pered regions in the image. The original image is partitioned into blocks, and each block is embedded with its own watermark using a secret key. However, most of these schemes are vulnerable to counterfeiting attacks and they cannot discriminate between intentional tampering and unintentional image processing distortions [22,23]. In such approaches, the tamper detection resolution is limited to the block size. Smaller block sizes and higher watermark payloads are necessary to improve the detection resolution, resulting in a considerable degradation of the image quality. A specific attack against image authentication is the collage attack, introduced by Holliman and Memon in [24]. Using this attack, a counterfeiter can combine independently authenticated blocks to produce forged content. This attack is thus undetectable by conventional block-based watermarking techniques. The scheme proposed in this paper focuses on eliminating the drawbacks of block-based schemes, using a Discrete Wavelet Transform (DWT) based approach and random permutation of wavelet coefficients. Our algorithm improves the tamper detection localization; unlike conventional block-based methods, the exact tampered region is detected. The watermark payload is significantly lowered, increasing the image quality. The algorithm can also
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distinguish between intentional tampering and unintentional mild to moderate JPEG compression. Mathematical morphology can be used to improve the detection results [25–29]. Our method can also be used for other multimedia applications [30–43]. The remainder of this paper is organized as follows. In Section 2 we present the proposed image authentication scheme in the wavelet domain, showing the block diagrams of the watermark encoder and decoder and detailing the steps of the algorithm. Section 3 contains the experimental results and performances of the proposed scheme and conclusions are given in Section 4. 2. The proposed image authentication scheme in the wavelet domain Fig. 2. Wavelet decomposition on L = 3 resolution levels. Gray sub-bands (n = 2) selected for watermark embedding.
This section describes the proposed image authentication scheme. The block diagram of the watermark encoder is shown in Fig. 1. The watermark embedding process is described in the following:
(6) The weighted mean mi of every group i of permuted wavelet coefficients is obtained using the following equation:
(1) The original, grayscale image is transformed into the wavelet domain using a 2D-DWT decomposition on L resolution levels. (2) The detail wavelet coefficients from the LHn, HLn and HHn Wavelet sub-bands of resolution level n L are selected. For example, in Fig. 2, the coefficients of the second Wavelet decomposition are chosen for further processing. Selecting higher resolution subbands for watermark embedding gives a better tampering localization, but decreases the resilience of the algorithm to common, unintentional image processing operations. (3) The selected wavelet coefficients are concatenated in a 1D vector C and randomly permuted using a secret key K into a new vector C0 . This process assures that coefficients corresponding to the same spatial location will be separated in C0 . (4) The sequence C0 of permuted coefficients is divided into groups of d coefficients. Parameter d controls the watermark payload of the proposed scheme. A watermark bit will be embedded in every group of d coefficients. A smaller group size will result in a bigger watermark payload and thus in a higher degradation of the image quality and a smaller size of the maximal localizable tampered area, but will not decrease the detection resolution of the scheme. (5) The watermark, a binary random sequence w, is generated using the secret key K and serves as the authentication code. w has the same length as the number of wavelet coefficient groups.
mi ¼
d X ð1Þj jci ðjÞj
ð1Þ
j¼1
where ci(j) denotes the jth coefficient of group i. The weight (1)j is used to make the scheme more robust to common image processing operations that, in most cases, change the entire image and would not modify the weighted mean. (7) The watermarked mean mw i is obtained by quantization of mi to the nearest even or odd quantization level according to the value of the corresponding watermark bit wi, using the following equation:
(
mw i
¼
bmi =Q c Q
if mod2ðbmi =Q cÞ ¼ wi
bmi =Q c Q þ Q
if mod2ðbmi =Q cÞ – wi
;
where bc is the integer part operator and mod2 is the remainder after division by 2.
(8) For every group i of coefficients, the weighted mean mi is changed to the watermarked mean mw i by modifying the wavelet coefficient ci,max(j) with the highest absolute value. Because of the random permutation operation every group should have at least one coefficient with high absolute value. The updating of ci,max(j) is done as follows:
w j cw i;max ðjÞ ¼ c i;max ðjÞ þ ð1Þ signðc i;max ðjÞÞ mi mi where cw i;max ðjÞ is the watermarked coefficient and
Secret key K n Original image
DWT
Wavelet subbands selection
Random permutation
ð2Þ
d
watermark
Coefficient grouping
Watermark embedding
Inverse permutation
Fig. 1. Block diagram of the proposed watermark encoder.
IDWT
Waterm. image
ð3Þ
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signðxÞ ¼
1 if x 6 0 1 if x > 0
(3) All coefficients are permuted back to their original position using the inverse permutation with the secret key. The coefficients flagged as potentially tampered should be now spread all over the subbands. The actual tampered regions should have a high density of flagged coefficients. The other flagged coefficients should be isolated and distributed like random noise. They are false positives and can be claimed as authentic. (4) For a selected resolution level n we will have three sub-bands, LHn, HLn and HHn, with flagged and non-flagged coefficients. We will construct a binary authentication matrix A of the same size (M/2n) (N/2n) as the sub-bands. A(x,y) = 1 if there is a flagged coefficient at the same position (x,y) in any of the HL, LH, or HH sub-bands. (5) The isolated ‘‘1’’ bits in the authentication matrix A will be removed through filtering. (6) Locations incorrectly flagged as tampered are further eliminated by successive erosion and dilation, using a disk of radius R pixels and a square of size S S as structural elements. The ‘‘1’’ bits in the filtered and eroded authentication matrix should now correctly indicate the tampered locations. (7) The flagged positions in A are then mapped back to the spatial domain to indicate the actual tampered locations.
ð4Þ
(9) After updating the coefficients with the highest absolute value from every group, the inverse permutation is applied using the secret key K. (10) Finally, the Inverse 2D-DWT is calculated to obtain the watermarked image. The block diagram of the proposed watermark extractor and authenticator is shown in Fig. 3. The watermark extraction process and image authentication is described in the following: (1) The watermarked, possibly tampered image is transformed into the wavelet domain using a 2D-DWT decomposition on L resolution levels. (2) The detail wavelet coefficients from the LHn, HLn and HHn Wavelet sub-bands are selected for watermark extraction. (3) The selected wavelet coefficients are concatenated. Using a secret key K, the same random permutation is performed. (4) The sequence of permuted coefficients is divided into groups of d coefficients. (5) The weighted mean m0i of every group of coefficients is calculated using Eq. (1). (6) A watermark bit w0i is extracted from the weighted mean of every group of d coefficients using Eq. (5). The Bit Error Rate (BER) between the extracted watermark w0 and the original watermark w will be calculated in Section 3 for different parameter choices.
w0i ¼ mod2 bm0i =Q c
Because the authentication matrix A is of size (M/2n) (N/2n), every location in A points to an actual region in the image of size 2n 2n. As a result, the maximum detection resolution of our algorithm is 2n 2n. The sensitivity of the tampering detection can be adapted by selecting the quantization step size Q, choosing the filter size in step 5 and the size of the structural element used for erosion and dilation in step 6 of the authentication process. A larger Q will increase the sensitivity, but will decrease the perceptual quality of the watermarked image. A larger filter or a bigger structural element for erosion and dilation will reduce the sensitivity, but will also reduce the probability of false alarms as a result of common image processing operations. A trade-off has to be found for specific applications. The security of the proposed image authentication system is ensured by the secret key used to control the ran-
ð5Þ
To authenticate the image the following steps need to be done: (1) First, the original watermark w is locally generated using the secret key K. If the extracted watermark w0 matches the original one, the image is authentic. If not, the following steps will determine if the image was tampered. (2) If a bit of the extracted watermark w0i does not match the original one wi, all coefficients belonging to group i are flagged as potentially tampered.
Secret key K n Waterm. image
DWT
d
Wavelet subbands selection
Authentication and tampering localization
Random permutation
Erosion + dilation
Coefficient grouping
Filtering
Watermark extraction
Inverse permutation
Extracted watermark
Possibly tampered groups
Locally generated watermark
Watermark comparison
Secret key K Fig. 3. Block diagram of the proposed watermark decoder and image authentication.
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dom permutation of wavelet coefficients and generation of the original watermark. There can be distinct keys for these two operations or a single key. Without knowing the secret key(s) an attacker cannot design the correct coefficient permutation or a duplicate of the original watermark. The proposed scheme is immune to the Vector Quantization (VQ) attack because, in our algorithm, unlike blockbased methods, where the authentication of each block depends only on the content of the block itself, the wavelet coefficients of a group are selected randomly from all over the image.
60
block-based method proposed method (n=1, d=8)
55
proposed method (n=1, d=12) proposed method (n=1, d=16)
PSNR (dB)
370
50 45 40 35 30 4
3. Experimental results
8
12
16
20
Quantization step size Q To determine the performances of the proposed image authentication scheme 100 images of different sizes were used. We have evaluated our algorithms in terms of image quality, localization capability of the tampering and robustness to JPEG compression with different quality factors. Table 1 shows the image quality and decoding results of the proposed method for different choices of the wavelet resolution level n for watermark embedding, quantization step size Q and group size d, where PSNR is the mean Peak Signal to Noise Ratio and BER is the mean decoding Bit Error Rate of 100 test images. The PSNR values are above 40 dB, except Q = 16 (d = 4 and d = 8) and Q = 20 (d = 4, d = 8 and d = 12), where small distortion are also visible in the watermarked images. In Fig. 4 we compare our technique to a traditional block-based image authentication scheme. For a blockbased approach to achieve a detection resolution of 2n 2n, it has to embed at least one watermark bit in every block of 2n 2n pixels of the image. In comparison, for the same detection resolution, our approach needs to embed a watermark bit in a group of wavelet coefficients of the nth Wavelet decomposition level. In Fig. 4 we have chosen
Fig. 4. Quality of the watermarked images for different group sizes, compared to traditional block-based image authentication schemes.
a detection resolution of 2 2 pixels, n = 1 and d = 4, d = 8 and d = 12. We can see that our approach achieves very high image quality compared to the block-based techniques. Next, we test the capacity of our approach to detect the tampering. For this purpose, in the image in Fig. 5a two regions were tampered: the face of the woman in white was replaced by another face and the beer can was completely removed from the image. First we embed the watermark in the first Wavelet decomposition level (n = 1), using groups of d = 8 wavelet coefficients and the quantization step size Q = 8. Fig. 5c shows the potentially tampered locations in the image in white, before refining the authentication result through filtering. Because n = 1 the detection resolution of the algorithm is 2 2 pixels and the smallest ‘‘noise’’ dot has also 2 2 pixels. We can see that the white dots are clustered in the regions where the actual tampering has taken place.
Table 1 Mean PSNR and BER values for the watermarked images. Q
d
n=1
n=2
n=3
PSNR
BER (%)
PSNR
BER (%)
PSNR
BER (%)
4
4 8 12 16
48.09 51.09 52.86 54.10
1.16 0.24 0.16 0.15
54.14 57.16 58.93 60.18
0.51 0.36 0.32 0.39
60.18 63.18 64.94 66.20
32.31 37.58 40.61 41.74
8
4 8 12 16
42.10 45.12 46.87 48.10
4.85 0.92 0.34 0.19
48.14 51.12 52.91 54.16
0.75 0.05 0.02 0.02
54.12 57.20 58.92 60.22
0.24 0.15 0.22 0.19
12
4 8 12 16
38.62 41.58 43.33 44.60
9.65 2.52 0.97 0.49
44.61 47.62 49.38 50.62
1.98 0.16 0.04 0.02
50.64 53.64 55.37 56.60
0.22 0.02 0.02 0.01
16
4 8 12 16
36.16 39.09 40.85 42.10
14.53 4.87 2.15 1.12
42.13 45.11 46.87 48.13
3.53 0.37 0.08 0.02
48.16 51.14 52.89 54.20
0.48 0.02 0.02 0.01
20
4 8 12 16
34.26 37.17 38.90 40.17
18.94 7.56 3.68 2.10
40.20 43.19 44.94 46.18
5.31 0.78 0.17 0.07
46.19 49.22 51.00 52.23
0.79 0.06 0.00 0.01
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Fig. 5. (a) original image, (b) image with two tampered regions, marked in red, (c) authenticated image before filtering for n = 1, d = 8 and Q = 8, (d) authenticated image after filtering and mathematical morphology operations for n = 1, d = 8 and Q = 8, (e) authenticated image before filtering for n = 2, d = 8 and Q = 8, (f) authenticated image after filtering and mathematical morphology operations for n = 2, d = 8 and Q = 8. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Then, we filter the authentication matrix with a ‘‘cross’’ shaped binary filter of size F = 5. The filtered authentication matrix is then successively eroded and dilated using a disk of radius R = 1 and a square of size 3 3 as structural elements. Fig. 5d shows the refined authentication result after filtering and mathematical morphology operations. In Fig. 5e and f we depict the authentication results before and after refinement using the following parameters: n = 2, d = 8 and Q = 8. In this case, the detection resolution of the algorithm is 2n 2n = 4 4 pixels. We can see that, in both cases, the proposed scheme detects the tampered regions correctly. We also test the robustness of the proposed scheme against non-malicious distortions produced by JPEG compression. JPEG is the most common used standard for compressing still images and it is possible, that the watermarked image undergoes JPEG compression before it suffers intentional manipulation.
Thus, a desired property of an authentication scheme is the resilience to mild to moderate JPEG compression. An image should be deemed as authentic, even if it has been compressed using a medium to high JPEG quality factor. For this reason, the watermark is embedded in the original image using different parameters, like resolution level n, quantization step size Q and size of the wavelet coefficient groups d and the watermarked image is compressed with JPEG quality factors ranging from 100 to 50. Then, the watermark is extracted and the decoding BER is calculated. The BER performance results are shown in Fig. 6 for n = 1 and Fig. 7 for n = 2. As expected, the graphs show that embedding the watermark in a higher Wavelet level makes it more robust to JPEG compression. The reason for this is that the coefficients from higher Wavelet sub-bands are less modified by JPEG compression. The quantization step size Q and the size d of the wavelet coefficient groups also influences the robustness of the
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Acknowledgement
Bit Error Rate (%)
50%
This research activity was supported by UEFISCDI Romania under the Grant PN-II-RU-TE-2011-3-0261/ No.10/2011.
40% 30% n=1,Q=12,d=4 n=1,Q=12,d=8 n=1,Q=12,d=12 n=1,Q=12,d=16 n=1,Q=20,d=4 n=1,Q=20,d=8 n=1,Q=20,d=12 n=1,Q=20,d=16
20% 10% 0% 50
60
References
70
80
90
100
JPEG quality factor Fig. 6. Detection performance of the proposed scheme after JPEG compression for n = 1 and different quantization step sizes and coefficient group sizes.
Bit Error Rate (%)
50% 40% 30% n=2,Q=12,d=4 n=2,Q=12,d=8 n=2,Q=12,d=12 n=2,Q=12,d=16 n=2,Q=20,d=4 n=2,Q=20,d=8 n=2,Q=20,d=12 n=2,Q=20,d=16
20% 10% 0% 50
60
70
80
90
100
JPEG quality factor Fig. 7. Detection performance of the proposed scheme after JPEG compression for n = 2 and different quantization step sizes and coefficient group sizes.
scheme against compression. Increasing Q results in a lower decoding BER after JPEG compression, but also produces a higher distortion in the image. A smaller group size d will increase the robustness, but, on the other hand, it also increases the watermark payload. A compromise between these parameters has to be found for specific applications.
4. Conclusions In this paper we have proposed a new image authentication scheme using a semi-fragile watermark that can detect and locate malicious tampering in images. The embedding and extraction of the authentication watermark is done in the DWT domain. Our technique achieves high image quality and high tampering detection resolution at a low watermark payload. Thanks to the random permutation of the wavelet coefficients before embedding, the watermark is protected against local attacks, like, for example, the VQ attack. The embedded watermark is also robust to mild to moderate JPEG compression by selecting the appropriate embedding parameters.
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