Multi-bit Watermarking Scheme Based on Addition of Orthogonal Sequences Xinpeng Zhang, Shuozhong Wang, and Kaiwen Zhang Communication & Information Engineering, Shanghai University, Shanghai 200072, China
[email protected],
[email protected],
[email protected]
Abstract. In this paper, a scheme of watermark embedding based on a set of orthogonal binary sequences is introduced. The described technique is intended to be incorporated into various public watermarking frameworks developed for different digital media including images and audio signals. Unlike some previous methods using PN sequences in which each sequence carries only one bit of the watermark data, the proposed approach maps a number of bits to a single sequence from an orthogonal set. Both analytical and experimental studies show that, owing to the full exploitation of information carrying capability of each binary sequence, the performance is significantly improved compared with previous methods based on a one-bit-per-sequence technique.
1
Introduction
Watermark is a digital code embedded imperceptibly and robustly in the host data and typically contains information about the owner, origin, status, and/or destination of the data [1,2]. In terms of embedding capacity, watermarking schemes can be classified into single-bit and multiple-bit schemes. In single-bit schemes, the detection results are simply binary, namely, “marked” or “not-marked”. It is often important for the purpose of IPR protection, however, to embed more information into the host signal such as the name and address of the owner. Therefore, a larger information embedding capacity is desirable. Since there are conflicts between imperceptibility, robustness and capacity, compromises must be sought. Watermarking by adding pseudo-random (PN) sequences to the host data was employed in many techniques. The types of host include color images [3], audio signals [4], vertex coordinates of polygonal models [5], etc. The method is applicable in spatial domain [3,4], Fourier transform domain [5], DCT domain [6], wavelet domain [79], and other domains [10-12]. To achieve better performances, various techniques have been proposed. For example, watermark signals can be pretreated before insertion to enhance robustness [4]. Adjusting watermark strength referenced to the host data amplitude can provide better imperceptibility [7,8,11]. It is also helpful to adapt the watermark strength to visual effects with respect to frequency locations and local luminance [13]. Some other algorithms employ masking effects in spatial and/or frequency domains when inserting watermarks [9,14,15]. Robustness of multi-bit watermarking schemes based on adding PN sequences against different attacks has been studied [16]. However it is rather difficult for these methods to provide a high embedding capacity since the sequences must be long enough to ensure sufficient robustness. In view of this, other methods that are not V. Gorodetsky et al. (Eds.): MMM-ACNS 2003, LNCS 2776, pp. 407–418, 2003. © Springer-Verlag Berlin Heidelberg 2003
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based on addition, such as quantization watermarking [17,18], different energy watermarking (DEW) [19] and non-additive watermarking [20], have emerged. The reason that embedding capacity of schemes using addition of PN sequences is low is that the information carrying capability of each sequence has not been fully exploited. In this regard, we propose an improved multi-bit scheme using a set of orthogonal binary sequences, leading to significant improvements in performance. This technique can be incorporated into various public-watermarking frameworks based upon addition of binary sequences and developed for various digital media including images and audio signals. The paper is organized as follows. Section II analytically discusses performances of multi-bit watermarking schemes based on addition of PN sequences and using a one-bit-per-sequence strategy. Section III proposes a novel scheme using orthogonal sequences to achieve increased capacity. In Section IV, performance of the new method is studied, and simulation results presented. Section V concludes the paper.
2
Multi-bit Watermarking Based on One-Bit-per-Sequence Scheme
Multi-bit watermarking using a one-bit-per-sequence scheme is a straightforward extension of the single-bit methods. A single-bit method adds a PN sequence as a watermark into host data. Cross-correlation between the received data and the known watermark is computed in detection. If the correlation is greater than a predefined threshold, the received data is judged as marked, otherwise not-marked. Suppose that I is the host data. S is a PN sequence of length N whose elements are either +1 or −1. The embedding scheme can be expressed as:
I ’( j ) = I ( j ) + α S ( j ),
j = 0, 1, , N − 1 ,
(1)
where I’ is the watermarked signal, and α the strength of the mark. Modifying the watermark amplitude according to the host data, or introducing characteristics of the human perseptual system, H, to improve imperceptibility, Equation (1) is modified as
I ’( j ) = I ( j ) + α H ( j ) S ( j ),
j = 0, 1, , N − 1 ,
(2)
where H is related to perceptual models and may be a function of frequencies and spatial/temporal properties. In the presence of additive interference (channel noise or hostile attack), the received signal becomes
I ’’( j ) = I ’( j ) + N ( j ) .
(3)
In this study, the host data are pre-processed in some way before embedding in order to achieve spectrum equalization, that is, to make each coefficient possess a uniform energy statistically. For example, shuffling the host data pseudo-randomly prior to transform can remove correlation between adjacent samples [21,22]. Therefore, the coefficients in the transform domain are i.i.d. Gaussian with a zero mean and an identical standard deviation I. With spectrum equalization, Equation (1), instead of (2), can be used to simplify analysis, and make it possible to directly study the relation
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between the watermarking performance and the host data energy. In addition, since watermarked data may be subjected to channel noise or undergo compression coding, spectrum equalization provides advantages that the additive interference can be considered as white Gaussian noise. Similar to the single-bit scheme, multi-bit watermarking uses more than one PN sequence, each representing one bit in the watermark. To be embedded into N coefficients in the host, a meaningful watermark is first converted into an LS-bit binary array W, each bit taking +1 or −1. In most cases, N is significantly greater than LS, therefore LS nearly independent PN sequences, each N bits long, can be found:
Su , Sv =
N −1
∑ S u ( j ) S v ( j ) ≈ 0, j =0
u , v = 0,1, , L − 1; u ≠ v .
(4)
Multiplied by W(i), these sequences are superimposed to produce the embedded mark: L −1
I ’= I + ∑ α S W (i ) S i ,
(5)
k =0
where αS is the strength of watermarking based on single-bit-per-sequence scheme. In watermark extraction, cross-correlation is calculated:
ρi =
1 N
N −1
(6)
∑ I ’’( j ) Si ( j ) . j =0
The mutual influence tamongst different watermark bits is considered negligible due to the approximate independence between the PN sequences as shown in Equation (4). By introducing spectral equalization, any additive interference can be modeled by a zero mean i.i.d. Gaussian process with standard deviation N. According to the central limit theorem, the output of the cross-correlation satisfies Gaussian distribution:
σ I2 + σ N2 ρ i ~ N W (i ) α S , N
,
(7)
where W(i) is either +1 or −1. Thus, a decision criterion is obtained, and the embedded watermark bits can be extracted:
1 W ’(i ) = − 1
ρi ≥ 0 ρi < 0
(8)
The error probability in extracting each bit is:
N BER S = 1 − Φ α S 2 σ I + σ N2
.
(9)
If all transforms used in this scheme are orthogonal, the watermark energy in the transform domain is equal to that in the time/space domain,
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ES,mark = LS N α S . 2
(10)
The parameters ES,mark, BERS, and LS can be used to represent imperceptibility, robustness, and embedding capacity, respectively. It is obvious from Equations (9) and (10) that there are conflicts between these basic specifications. With the same values of I and N, any improvement in one of the three specifications can only be made at some cost of the other two. It is clear that simply extending a single-bit scheme by superposition of mutually independent sequences to achieve multi-bit embedding is not satisfactory because of the direct conflicts between the three basic specifications. Achieving a higher capacity by using a one-bit-per-sequence scheme implies increasing the total watermark energy therefore inevitably sacrificing the robustness and imperceptibility. The problem is that every PN sequence is only mapped to a single bit in the watermark, and the information carrying capacity is not fully exploited. In order to resolve this problem, a novel scheme is introduced in the next section.
3
3.1
Multi-bit Watermarking with Addition of Orthogonal Sequences Embedding Procedure
The key to the proposed approach is a mapping between a set of orthogonal sequences and groups of bits in the embedded data so that each sequence can carry more than one bit. The embedding procedure is as follows. i) Assume that there are N coefficients in the host signal available to modification for watermark hiding. Thus, a total of N orthogonal sequences, Hadamard codes for example, with a length of N bits and element values of either +1 or −1 can be found. ii) Divide the N binary sequences into R = N /M subsets denoted S0, S1, … , SR−1, m where M = 2 . Each subset contains M sequences: {S0,0, S0,1, … , S0, M−1}, {S1,0, S1,1, … , S1, M −1}, … , {SR−1,0, SR−1,1, … , SR−1, M−1}. iii) Convert a meaningful watermark into binary, and expand the binary sequence by padding zeros to yield an array of length LM = 2 mR. Truncate the binary sequence if the length is greater than LM. iv) Segment the LM bit binary sequence into 2R sections of length m. The m-bit binary numbers in these sections may be referenced to in decimal, denoted W = {W(0), W(1), … , W(2R−1)}. v) Divide W into two halves: W1 = {W(0), W(1), … , W(R−1)}, and W2 = {W(R), W(R+1), … , W(2R−1)}, and map the M possible values in each pair, W(i) and W(i+R) from the two halves respectively, to the M sequences in the subset of the same index i. vi) Add the sequences in Si corresponding to W(i), i = 0, 1, … , R−1, to the host data, and subtract the sequences in Si corresponding to W(i+R), i = 0, 1, … , R−1, from the host data, respectively. The arrangements of the watermark-carrying sequences and the watermark bits, and the mapping between them are illustrated in Figure 1. In this way, each sequence
Multi-bit Watermarking Scheme Based on Addition of Orthogonal Sequences
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carries m watermark bits, and all together LM bits carried by 2R orthogonal sequences are embedded. Note that W(i) and W(i+R) are independently embedded if they are different. Otherwise, instead of subtracting Si,W(i+R), Si,W(i+R)+1 is added to the host data where operation +1 in the subscripts are modulo-R. The watermark to be embedded is now given in the following expression:
S i ,W (i ) − S i ,W (i + R ) Sˆ i = S i ,W (i ) + S i ,W (i )+1
W (i) ≠ W (i + R) . W (i) = W (i + R)
S0
S1
SR−1
W(0)
W(1)
W(R−1)
W(1+R)
W(2R−1)
W1: W2:
W(R)
(11)
Mark-carrying sequences: N sequences in R subsets. Each subset contains M sequences of N bits.
Watermark: LM bits in 2R sections. Each section contains m bits.
Fig. 1. Embedding scheme: Organization of watermark-carrying sequences and watermark bits, and the mapping
Finally, the watermarked data are obtained:
I' = I + α M
R −1
∑ Sˆ i ,
(12)
i =0
where αM is the watermarking strength, which is different from αS.
3.2
Watermark Extraction
Cross-correlations between the received data and the known sequences Si,0, Si,1, … , and Si,M−1, respectively, are calculated. If positive and negative peaks occur when correlated respectively with, say, Si,A and Si,B, and the magnitude of correlation with Si,B is no less than that both with Si,A+1 and with Si,A−1, a decision can be made that W(i) is A, and W(i+R) is B. Otherwise, W(i+R) = A if the magnitude of correlation with Si,A+1 is greater than that with Si, A−1, and W(i+R) = A−1 if the reverse is true. In this way, the entire watermark can be extracted from the received data. Figure 2 shows the correlation outputs between a subset of 128 orthogonal sequences and a simulated received data. Two distinct peaks, one positive and the other negative, are present. These 7 bit binary codes can represent any characters drawn from the 128 alphanumeric-character set. In this example, the extracted ASCII characters are ‘c’
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and ‘5’, corresponding to W(i)=99 and W(i+R)=53, respectively. Additive white Gaussian noise has been added to the data with SNR = 30 dB. There is considerable undulation in the correlation output because of the effects of the host data as well as the noise. In this example the noise interference has not destroyed the watermark detection, meaning that the method has certain noise resisting capability. 10 8 6 4 2 0 -2 -4 -6 -8 -10
0
20
40
60
80
100
120
140
Fig. 2. Cross-correlation between a set of 128 sequences and received data. The data are contaminated by noise with SNR=30dB. The positive and negative peaks show that the two embedded characters are ‘c’ and ‘5’
4
Performance Analysis
Suppose that ρ0,W(0) is the cross-correlation between the detected data and S0,W(0). According to the central limit theorem,
ρ 0,W ( 0 ) =
1 N
∑ [I ’’( j ) S
N −1 j =0
2 2 α , σ I + σ N ( ) ~ j N 0, w ( 0 ) M N
]
,
(13)
while the cross-correlations between the detected data and other sequences in S0 are
σ 2 + σ N2 ρ 0,other ~ N 0, I N
.
(14)
Thus, the probability density function of (ρ0,W(0) − ρ0,other) is
(ρ
0 ,W ( 0 )
2 2 2(σ I + σ N ) . − ρ 0,other ~ N α M , N
)
Therefore, the probability of ρ0,W(0) being greater than one ρ0,other can be obtained:
(15)
Multi-bit Watermarking Scheme Based on Addition of Orthogonal Sequences
N . P ρ 0,W ( 0 ) − ρ 0,other > 0 = Φ α M 2 2 σ σ 2 ( + ) I N
[(
) ]
413
(16)
In extraction, W(0) will be judged correctly if 0,W(0) is greater than all 0,other. Because the probability given by Equation (16) is very close to 1 and the effect of embedding W(R) on ρ0,W(0) can be neglected, the probability of 0,W(0) being greater than all 0,other approximately equals
N P0 = 1 − M 1 − Φ α M . 2 2 2(σ I + σ N )
(17)
Here the situation W(0)=W(R) has been ignored as the probability of its happening is rather small. If the decision made for W(0) is in error, the average number of bits in error is m/2 as W(0) contains m mark bits. Therefore, the bit error rate in extraction of W(0) is
BER M =
M 2
N . 1 − Φ α M 2 2 2(σ I + σ N )
(18)
This is a general expression for the BER in extraction of any W(i) and W(i+R). Similar to the method based on addition of ordinary PN sequences, the energy in the embedded watermark is
E M, mark = 2 R N α M = 2
5
1 2 LM N α M . m
(19)
Experimental Results and Performance Studies
As a multi-bit embedding scheme, the technique introduced in this paper can be used in conjunction with various public watermarking frameworks, irrespective of the types of digital media such as image, audio, and video. Also, it is not restricted to any specific operating domain (whether time/space or transform domain), transform used and embedding locations chosen. In our performance study, nonetheless, experiments were carried out on still images using a DCT technique to embed watermark into a middle band in the transform domain. 5.1
Description of the Experiment
A 256×256 test image Lena was segmented into 32×32=1024 blocks, each sized 8×8. Two-dimensional DCT was then performed on the blocks resulting in a total of 64 data groups, each sized 32×32 and composed of coefficients taken from one of 64 positions in all 1024 blocks. The coefficients in these groups were shuffled pseudo-
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randomly prior to a second-layer DCT. The purpose of data shuffling, as stated above, was to remove correlation between coefficients and make the second-layer DCT coefficients in each group to possess a uniform expected energy, that is, to achieve spectral equalization. Incidentally, the particular mapping corresponding to the shuffling may be used as part of the key for prevention of unauthorized watermark extraction. As a result of data shuffling, the second-layer DCT coefficients, except the DC component, within each group are i.i.d. Gaussian with a zero mean and a standard deviation associated to the rank of the group inherited from the index of the first layer 2 DCT. This was confirmed by a χ test with a level of significance 0.10. In Table 1, standard deviation values of the spectrum-equalized second-layer DCT coefficients of the test image corresponding to the eight diagonal indices are listed. Table 1. Standard deviation of the spectrum-equalized second-layer DCT coefficients of Lena at diagonal frequency locations Data group index
(1,1)
(2,2)
(3,3)
(4,4)
(5,5)
(6,6)
(7,7)
(8,8)
σI
368.9
57.0
25.4
14.2
10.2
6.4
4.6
4.3
It is clear from the preceding analysis that the watermark performance is closely related to the choice of several parameters including N, M, and α. It is also related to the amplitude of host data and noise. In the experiments, N = 1024. Coefficients of group (4,4) were chosen as the host data for embedding, with σI =14.23. Let M = 128 so that 7 bits were carried by each orthogonal sequence, which can represent one character. Thus, a total of 16 alphanumeric characters were embedded into the host image. 5.2
Performance Comparison
In the experiments, the peak-signal-to-watermark power ratio (PSWR) was used to describe invisibility, while the character-extraction error rate (CER) under the attack of AWGN at PSNR=30 dB was used to represent robustness. From Equation (9), CER of the single-bit-per-sequence scheme is given by
N CER S = m BER S = m 1 − Φ α S 2 σ I +σ N2
,
(20)
while CER of the proposed method can be obtained from Equation (17):
N CER M = M 1 − Φ α M . 2 2 2(σ I + σ N )
(21)
PSWR can be calculated by the following equation:
PSWR = 10 log10
σ p2S , E mark
(22)
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where σP is the magnitude of peak signal and S is the size of host data. In the experiment, σP =255 and S =256×256. With the same amount of data embedded, robustness and imperceptibility were effectively increased by using the proposed approach compared to the original method as shown in Fig.3 where the embedded data are 16 alphanumeric characters. Alternatively, with the same robustness and imperceptibility, a larger embedding capacity can be achieved by using the proposed method. If robustness and imperceptibility of the original scheme are kept at the same level as shown by the solid line in Figure 3, both the numbers of bits and characters embedded using the old method can be calculated. The results are listed in Table 2, from which one can see that the new method provides a higher embedding capacity.
Character-extraction error rate (%)
25
20
15
10
5
0 44.5
45
45.5
46
46.5
Peak-signal-to-watermark power ratio (dB)
Fig. 3. Comparison of robustness and imperceptibility using original (dashed line) and proposed (solid line) approaches with 16 alphanumeric characters embedded Table 2. Embedding capacities with different imperceptibility and robustness CER (%)
2.50
1.11
0.46
0.16
0.045
0.011
0.0037
PSWR (dB)
46.0
45.5
45.0
44.5
44.0
43.5
43.0
Proposed method (KM)
16
16
16
16
16
16
16
Original method (KS)
8
7
7
6
6
5
5
2.00
2.29
2.29
2.67
2.67
3.20
3.20
Number of embedded characters
K = KM / KS
5.3
Simulation Results
A low rate of character extraction error is required in practical applications. In the experiment, αΜ = 2.72 was used to give a CER = 1.0% under AGWN interference at
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PSNR = 30 dB. In this case PSWR = 45.46dB, obtained from Figure 3. This was in good agreement with simulation results. Three common types of attack were tested in the experiment. They were low-pass filtering, noise interference, and JPEG compression. Table 3 gives character-extraction error rates at different noise levels. In the experiment, 50 tests were carried out with a total of 800 embedded characters to produce the statistical results. The experimental results are in line with the theoretical calculation based on Equations (21), as shown in Figure 4. Table 3. Character-extraction error rate at different noise levels PSNR (dB)
28
30
32
34
36
Character-extraction error rate (%)
2.62
1.13
0.75
0.50
0.38
5
Character-extraction error rate (%)
4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 26
28
30
32
34
36
38
PSNR caused by noise (dB)
Fig. 4. Character-extraction error rate: theoretical calculation (solid line) and simulation results (asterisks)
Blurring was implemented using a 3×3 Gaussian convolution mask. The strength of attack was characterized by the standard deviation σ. Table 4 shows the simulation results. Table 5 gives the character-extraction errors after JPEG compression. As expected, the measured error rates increased with increase of the strength of attacks. Table 4. Character-extraction error rate after low-pass filtering Standard deviation of Gaussian mask (σ)
0.7
0.6
0.5
0.4
0.3
Peak signal-to-distortion ratio (dB)
31.7
33.4
36.9
45.0
65.2
Character-extraction error rate (%)
2.88
1.25
0.75
0.25
0.13
Table 5. Character-extraction error rate after JPEG compression Quality factor (Q)
40
50
60
70
80
Compression ratio
9.82
8.60
7.61
6.45
5.16
Character-extraction error rate (%)
3.62
1.87
1.00
0.63
0.37
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Conclusion
In this paper, embedding schemes based upon addition of binary sequences and suitable for use in public watermarking frameworks are studied. It has been shown that some previous multi-bit embedding techniques are merely a simple extension of single-bit methods, in which each PN sequence only carries one bit of the watermark. In other words, these multi-bit watermarking schemes still use a one-bit-per-sequence technique. By introducing a set of orthogonal binary sequences, and by mapping more that one bit in the watermark to each of these sequences, an increase in the performance is achieved. The major difference between the two approaches is that, in the proposed method, the information carrying capacity of each sequence is effectively exploited. Therefore, by using the new method, the robustness and imperceptibility are improved, or a net increase in embedding capacity is achieved without sacrificing the other basic specifications. This has been confirmed in the experiments. The proposed embedding scheme is applicable to various watermarking frameworks, regardless of the type of host media, specific working domain and embedding strategy. Further improvement in performances may be obtained through a combination of different measures, among which incorporation of human perceptual system characteristics is the most important. This, however, can only be done individually for specific digital media and for the specific watermarking technique used.
Acknowledgments This work was supported by the National Natural Science Foundation of China (No. 60072030) and Key Disciplinary Development Program of Shanghai (2001-44).
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