Spread Spectrum Watermarking Method for Image Databases Mihai P. Mitreaa , Françoise J. Prêteuxb , Adriana Vlada , and Nicolas F. Rougonb a
Faculty of Electronics and Telecommunications, POLITEHNICA University of Bucharest, Romania b
ARTEMIS Project Unit, Institut National des Télécommunications, Evry, France e-mail address:
[email protected],
[email protected]
ABSTRACT By means of the Internet, the image distribution may be easily and quickly done. However, a lot of scepticism may be found in this respect: an unlimited number of unauthorised copies can be obtained with quite banal equipment. This paper aims at presenting a new watermarking method which is able to afford ownership and track down copy maker. Our main contribution consists in the way in which we embed a very low power SS-CDMA (Spread Spectrum - Code Division Multiple Access) signal in the most significant DCT coefficients. In contrast to other SS–based approaches mentioned in the literature, our method complies with the StirMark robustness requirements. Note that we embed a 64 bits message, thus making it possible to identify a copy maker or, at least, a group of copy makers, depending on the targeted application. Although the most of the experimental results reported in the present paper correspond to grey level still image databases, the method may be extended to any sequence of images; for instance, we obtained very good results when watermarking some grey level video sequences.
Keywords: oblivious image databases watermarking; DCT; SS-CDMA; StirMark robustness.
1. INTRODUCTION Since ever, methods and techniques belonging to cryptography, steganography and watermarking have been of utmost importance: from Herodotus’ Histories up to Shannon’s works [1], from the XVIIth century books (see [2] and the references therein) up to nowadays papers, solutions to secrecy communications have been searched for. Moreover, the today applications are not only devoted to the traditional fields of army and diplomacy but to day by day use, as well [3]–[6]. In this context, image databases ownership in Internet is an emerging application. No matter the field to which the databases belong (art, science, journalism), the owners are quite afraid of loosing their property rights: any number of unauthorised exact copies may be quickly done with common devices. Here is the very role of watermarking: to ensure the ownership by tracking down unauthorised copies. When approaching watermarking, several sound surveys can be found [3]–[7]. Moreover, in the
last years, some truly theoretical papers [8]–[11] defined watermarking as a science per se. At a glance, to watermark means to embed some extra information into host data. This information is to be later used for several purposes such as: ownership proving, image/video indexing and retrieval, broadcast monitoring, etc. The embedded extra information is called watermark or mark. The host data is a natural signal, such as text, audio, image or video. Watermarked data stand for (host) data which have a mark embedded. The first requirement for a common watermarking technique is to be transparent; i.e., when embedding the mark, the host data should not be perceptually altered. The second watermarking requirement is related to robustness; i.e., the mark should be detectable after any processing of watermarked data which does not change their meaning (e.g. after JPEG compression, resampling, rescaling). Depending on the targeted application, there is always a trade–off to be reached between transparency and robustness (generally, the greater the robustness, the worst the transparency).
A watermarking method is referred to as nonoblivious when it requires the original (unmarked) data to be present at the detector and as oblivious when the original data may not be present. The general framework [9] for nowadays watermarking methods may be represented as in Fig. 1.
reported in the literature may survive a StirMark attack. The present paper proposes an oblivious method designed for the robust image databases watermarking, see Fig. [2]. Note that it also holds for robust video watermarking. Key
Noise A t t a c k
Logo
Key
Noise A t t a c k Key
Key
Watermark
Logo
Channel with side information (Image)
Watermark Detector
Watermark
Recovered Logo
Image
Channel T
Watermark Detector
Recovered Logo
oblivious watermark
Fig. 2. The watermarking scheme we propose
oblivious watermark
Fig. 1. Watermarking framework
The watermark is generated according to a secret information (referred to as key) and is in an one–to–one correspondence with a message (a logo, serial number, etc.). The embedding procedure may be adapted according to the original image; that is, the unmarked image may stand for a channel with side information, [9], [16]. The marked image is subject to two types of alterations. First, there are the perturbations which come across with any processing of the image; these perturbations are referred to as noise. Second, an unauthorised user might try to make the mark undetectable at the detection side; these perturbations are referred to as attack . Note that in the nowadays applications, the channel capacity should be increased: there is no longer a problem of transmitting a single bit of information as in the early watermarking methods, but of recovering a message represented on 60 to 70 bits, see [3]. Moreover, another requirement is compulsory for a modern watermarking scheme: the original (unmarked) data should not be required at the detection. That is, the modern techniques deal only with oblivious watermarking. In order to benchmark the watermarking methods, Peticolas has developed, [14], a procedure called StirMark. This procedure brings into evidence some transformations which are designed in order to make it impossible for the detector to find out the mark while preserving the watermarked image unaltered from the HVS (Human Visual System) point of view. It consists of several small transformations, successively applied: resampling, geometric (stretching, shearing, shifting, rotating) and a global bending on the image (a slight deviation of each pixel, depending on the position in image). It was found out that very few methods
Our method relies both on Cox, [12], and Ó Ruanaidh, [13], non–oblivious methods. These two methods are devoted to individual still images and do not survive the StirMark attack, [14]. Besides, Cox method, [12], allows only a single bit to be recovered: at the detection side a marked/unmarked answer is obtained. The method we propose allows a 64 bit message to be checked out at the detector. The message is coded according to the Spread Spectrum - Code Division Multiple Access (SS-CDMA) technique, [15],[13], and embedded into the most significant DCT coefficients (except for the DC – the direct component). Note that our method can afford the requirements in Fig. 1 and the StirMark robustness without taking any advantage on the side information. We applied our method on 1000 sequences of 32 still images and on 100 grey levels video sequences: the output of video surveying cameras, scientific video products elaborated at ARTEMIS project units, art video, etc. The present paper has the following structure. Section 2 focuses on the application we propose. Section 3 is devoted to the experimental results while Section 4 presents the concluding remarks.
2. METHOD PRESENTATION The watermarking method we propose is devoted to grey level still image databases; experimentally we found out that it also works for grey level video sequences. It will be further presented, considering a sequence of 32 images of 512 × 512 pixels and 256 grey levels. Note that all the numerical values presented below were those involved in our experiments. Depending on the targeted application, they may be adapted, without altering the method quality.
The embedding procedure starts by computing the DCT for each and every image in the sequence. For each image, the coefficients are sorted in a decreasing order and the largest 1024 (except for the DC) are recorded. Consequently, a vector of N = 1024 × 32 coefficients is obtained; be it denoted by v . The mark is generated starting from the Ó Ruanaidh suggestions, [13]. Be there s1 , s 2 , ..., s16 the message to be embedded (a logo, a serial number, etc.), represented as 16 digits in hexadecimal (that is, 64 bits). The msequence obtained as the output of an LFSR (linear feedback shift register), see [17] and Fig. 3, is divided into 16 sequences, each of them having an N + 15 length: ni = [ ni,1 , ni, 2 , ..., ni, N +15 ] , i = {1, 2 ... , 16 } (1) Note that the use of a LFSR afford a bipolar noise sequence characterised by a delta–like autocorrelation function. In Fig. 3, g 0 , g 1, ... , g m stand for the coefficients of a g (x) m degree primitive polynomial over GF(2) – Galois Field of second order, [17]. SET/RESET
D1
Q1
g 0 =1
D2
+
g1
Q2
Dm Qm
+
+
Output
g m =1
g2
Each s i symbol in the message is modulated by means of an N length ri sequence, cut out from the n i sequence: (2)
In order to obtain the x mark, the ri sequences are summed–up: 16
x=
∑ ri .
(3)
i =1
Note that in Eq. (3) x stands for an N = 1024 × 32 length vector. Consequently, the msequence we used must be longer than
16 × N = 1019 and the corresponding LFSR must be characterised by a primitive polynomial with a degree larger than 19; in our experiment, we used 20 degree primitive polynomials. Further, the power of the x mark was adjusted to 1 6 (the experiments guided us to this
In Eq. (4), v' represents the vector of the watermarked coefficients while α is a coefficient [12] set α = 0. 4 . In order to obtain the watermarked sequence, the v coefficients are replaced by the v' and 32 inverse DCTs are computed. At the detector side, the DCTs are computed on the (possible) corrupted sequence, the largest 1024 coefficients (except for the DC) are recorded for each and every image in the sequence. The vector obtained by concatenating these coefficients is denoted by v' ' . The message is recovered by means of crosscorrelation functions, computed between v' ' and each ni , i = 1,16 . When watermarking video data, the still images are replaced by successive frames. Note that at 25 frames/s, our method is applied on about 1s of video, thus complying with the requirement for video watermarking, [3].
4. EXPERIMENTAL RESULTS
Fig. 3. A linear feedback shift register
si ↔ ri = [ ni, si +1, ni ,si +2 , ...,ni ,si + N ]
value which reaches the trade–off between robustness and transparency). As embedding procedure, we use Cox suggestions [12]: the watermarked coefficients are obtained by means of a weighted addition between the v unmarked coefficients and the x mark, see Eq. (4): v ' = v ⋅ (1 + α x ) (4)
1 6 numerical
We started our experimental work by watermarking sequences of 32 still images. In order to illustrate our results, we select the images in Fig. 4. Fig. 4 displays several kind of images: naturals, frames from a scientific video product elaborated at ARTEMIS project unit and computer simulated images, obeying different probability laws and autocorrelation functions [18]. Note that this figure provides information about the way in which our method works in the most difficult situations: images with large background areas and a lot of details. By comparing Fig. 4 to Fig. 5, a very good transparency of the method may be noticed. This was obtained by the low power of the mark, namely 1 6 . As regards the robustness, very good results were also obtained: the watermark was detected after print-and-scan, noise addition, and JPEG compression at a very low Q quality factor, namely Q = 10 (Fig. 6). All these alterations were independently performed on each image in the sequence. The method also proves a good resistance against multiplicative noise. As
regards the rotation, the method holds only for small θ angles: θ∈ ( − 2 .5 o ; 2 .5 o ) ; for a larger θ angle, a registration procedure before detection would be recommendable. A search in the angle space, with a resolution of 5o may also be a
solution to the rotation problem. The StirMark [14] attack was independently applied on each image in the sequence. Note that our method is robust to all attacks in the StirMark software (at the standard parameters [14]).
Fig. 4. Original still images in a sequence
Fig. 5. Still images in a marked sequence
Fig. 6. Still images in a marked sequence, corrupted by print–and –scan, noise addition and JPEG compression
Fig. 7. Frames in an unmarked video surveying sequence
Fig. 8. Frames in a marked video surveying sequence
Fig. 9. Frames in a heavily marked video surveying sequence
The method was applied on 1000 sequences of 32 images. We have considered various types of images: natural, computer simulated, test images, etc. The probability of false alarm was experimentally evaluated as being lower than
5 ×10−9 . When applying the method on video frames, Figs. 7–9, some problems may arise. Note that successive frames in video are quite identical. Hence, the HVS may identify some differences among watermarked frames. For instance, the background areas in Fig. 8 are the same while those in Fig. 9 are slightly different. However, when watermarking the output of a video surveying system or a scientific video product, these differences do not mean disturbing artefacts.. Note that when watermarking a video surveying sequence, the problem may no longer be to afford ownership but to provide data integrity (the video should not be maliciously modified). If the mark is not detected, the
respective video sequence is suppose to be fake. When watermarking art video, the artefacts may be considered disturbing. Concerning the robustness, the above–reported properties were preserved. As an additional remark, note the good robustness against temporal cropping: the detection also works when disposing only of 24 out of the 32 marked frames.
4. CONCLUDING REMARKS This paper present a new robust watermarking method which is devoted to any kind of grey level image databases (natural, medical, computer simulated, etc.). From the experimental study it was found out that this method is also suitable for several types of video sequences: video surveying, scientific products, etc. The method here proposed features a very good robustness against JPEG compression, additive and multiplicative noise, linear transformation,
Gaussian and median filtering, rescaling and FMLR [14]. As regards spatial cropping and rotation, a registration method prior to detection would be recommended. The resistance against the StirMark attack, [14], was here obtained by the very embedding procedure, i.e. by dividing the mark among several images/frames; note that there was no need for the special StirMark counterattack, [19]. However, for a practical application, the hints in [19] should not be skipped over (e.g. the averaging counterattack). On the other hand, an inversion attack, [20] may be prevented by means of either a hash function, [20], or a cryptographic mixing transformation, [21], [22]. The robustness may be improved by applying error correcting codes; we already tried the BCH and the turbo codes and we got quite relevant improvements (these two classes of codes have been already used in watermarking, [14], [21]). The extension toward colour images and video is straightforward. On the other hand, by adapting the embedding strategy, improvements in art video watermarking are to be obtained. 5. REFERENCES 1.
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