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Reversible Watermarking Techniq…

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Hindawi Publishing Corporation EURASIP Journal on Information Security Volume 2010, Article ID 134546, 19 pages doi:10.1155/2010/134546 Review Article Reversible Watermarking Techniques: An Overview and a Classification Roberto Caldelli, Francesco Filippini, and Rudy Becarelli MICC, University of Florence, Viale Morgagni 65, 50134 Florence, Italy Correspondence should be addressed to Roberto Caldelli, roberto.caldelli@unifi.it Received 23 December 2009; Accepted 17 May 2010 Academic Editor: Jiwu W. Huang Copyright 2010 Roberto Caldelli et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. An overview of reversible watermarking techniques appeared in literature during the last five years approximately is presented in this paper. In addition to this a general classification of algorithms on the basis of their characteristics and of the embedding domain is given in order to provide a structured presentation simply accessible for an interested reader. Algorithms are set in a category and discussed trying to supply themain information regarding embedding and decoding procedures. Basic considerations on achieved results are made as well. 1. Introduction Digital watermarking techniques have been indicated so far as a possible solution when, in a specific application scenario (authentication, copyright protection, fingerprinting, etc.), there is the need to embed an informative message in a digital document in an imperceptible way. Such a goal is basically achieved by performing a slight modification to the original data trying to, at the same time, satisfy other bindings such as capacity and robustness. What is important to highlight, beyond the way all these issues are achieved, it is that this “slight modification” is irreversible: the watermarked content is different from the original one. This means that any successive assertion, usage, and evaluation must happen on a, though weakly, corrupted version, if original data have not been stored and are not readily available. It is now clear that in dependence of the application scenario, this cannot always be acceptable. Usually when dealing with sensitive imagery such as deep space exploration, military investigation, and recognition, and medical diagnosis, the end-user cannot tolerate to risk to get a distorted information from what he is watching at. One example above all: a radiologist who is checking a radiographic image to establish if a certain pathology is present or not. It cannot be accepted that his diagnosis is wrong both, firstly, to safeguard the patient’s health and, secondly, to protect the work of the radiologist himself. In such cases, irreversible watermarking algorithms clearly appear not to be feasible; due to this strict requirement, another category of watermarking techniques have been introduced in literature which are catalogued as reversible, where, with this term, it is to be intended that the original content, other than the watermark signal, is recovered from the watermarked document such that any evaluation can be performed on the unmodified data. Thus doing, the watermarking process is zero-impact but allows, at the same time, to convey an informative message. Reversible watermarking techniques are also named as invertible or lossless and were born to be applied mainly in scenarios where the authenticity of a digital image has to be granted and the original content is peremptorily needed at the decoding side. It is important to point out that, initially, a high perceptual quality of the watermarked image was not a requirement due to the fact that the original one was recoverable and simple problems of overflow and underflow caused by the watermarking process were not taken into account too. Successively also, this aspect has been considered as basic to permit to the end user to operate on the watermarked image and to possibly decide to resort to the uncorrupted version in a second time if needed. 2 EURASIP Journal on Information Security Semi-fragile Robust Fragile Reversible Figure 1: Categorization of reversible watermarking techniques. Reversible algorithms can be subdivided into two main categories, as evidenced in Figure 1: fragile and semifragile. Most of the developed techniques belong to the family of fragile that means that the inserted watermark disappears when amodification has occurred to the watermarked image, thus revealing that data integrity has been compromised. An inferior number, in percentage, are grouped in the second category of semi-fragile where with this term it is intended that the watermark is able to survive to a possible unintentional process the image may undergo, for instance, a slight JPEG compression. Such feature could be interesting in applications where a certain degree of lossy compression has to be tolerated; that is, the image has to be declared as authentic even if slightly compressed. Within this last category can also be included a restricted set of techniques that can be defined as robust which are able to cope with intentional attacks such as filtering, partial cropping, JPEG compression with relatively low quality factors, and so on. The rationale behind this paper is to provide an overview, as complete as possible, and a classification of reversible watermarking techniques, while trying to focus on their main features in a manner to provide to the readers basic information to understand if a certain algorithm matches with what they were looking for. In particular, our attention has been dedicated to papers appeared approximately from years 2004-2005 till 2008-2009; in fact, due to the huge amount of works in this field, we have decided to restrict our watch to the last important techniques. Anyway we could not forget some “old” techniques that are consid- ered as reference throughout the paper, such as [1–3], though they are not discussed in detail. The paper tries to categorize these techniques according to the classifi- cation pictured in Figure 1 and by adding an interesting distinction regarding the embedding domain they work on: spatial domain (pixel) or transformed domain (DFT, DWT, etc.). The paper is structured as follows: in Section 2, fragile algorithms are introduced and subdivided into two sub- classes on the basis of the adopted domain; in Section 3, techniques which provide features of semi-fragileness and/or robustness are presented and classified again according to the watermarking domain. Section 4 concludes the paper. 2. Fragile Algorithms Fragile algorithms cover the majority of the published works in the field of reversible. With the term fragile a watermarking technique which embeds a code in an image that is not readable anymore if the content is altered. Consequently the original data are not recoverable too. 2.1. Spatial Domain. This subsection is dedicated to present some of the main works implementing fragile reversible watermarking by operating in the spatial domain. One of the most important works in such a field has been presented by Tian [4, 5]. It presents a high-capacity, high visual quality, and reversible data embedding method for grayscale digital images. This method calculates the difference of neighboring pixel values and then selects some of such differences to perform a difference expansion (DE). In such different values, a payload B made by the following parts will be embedded: (i) a JBIG compressed location map, (ii) the original LSB values, and (iii) the net authentication payload which contains an image hash. To embed the payload, the procedure starts to define two amounts, the average l and the difference h (see (1)). Given a pair of pixel values (x, y) in a grayscale image, with x, y Z, 0 x, y 255, l = x + y 2 h = x y, (1) and given l and h, the inverse transform can be respectively computed according to(2) x = l + h + 1 2 ; y = l h 2 . (2) The method defines different kinds of pixel couples according to the characteristics of the corresponding h and behaves slightly different for each of them during embedding. Two are the main categories: changeable and expandable differences, let us see below for their definitions, respectively. Definition 1. For a grayscale-valued pair (x, y) a difference number h is changeable if 2 h 2 + b min(2(255 l), 2l + 1). (3) Definition 2. For a grayscale-valued pair (x, y) a difference number h is expandable if |2 h + b| min(2(255 l), 2l + 1). (4) This is imposed to prevent overflow/underflow problems for the watermarked pixels (x′, y′). To embed a bit b = (0, 1) of the payload, it is necessary to modify the amount h obtaining h′ which is called DE EURASIP Journal on Information Security 3 Table 1: Payload size versus PSNR of Lena image. Payload Size (bits) 39566 63676 84066 101089 120619 141493 175984 222042 260018 377869 516794 Bit Rate (bpp) 0.1509 0.2429 0.3207 0.3856 0.4601 0.5398 0.6713 0.8470 0.9919 1.4415 1.9714 PSNR (dB) 44.20 42.86 41.55 40.06 37.66 36.15 34.80 32.54 29.43 23.99 16.47 (Difference Expansion) according to (5) for expandable differences h′ = 2 h + b, b = LSB(h′), (5) and (6) for changeable ones h′ = 2 h 2 + b, b = LSB(h′), (6) by replacing h with h′ within (2), the watermarked pixel values x′ and y′ are got. The basic feature which distinguishes expandable differences from changeable ones is that the first ones can carry a bit without asking for saving the original LSB. That yields to a reduced total payload B. A location map takes into account of the diverse disjoint categories of differences. To extract the embedded data and recover the original values, the decoder uses the same pattern adopted during embedding and applies (1) to each pair. Then two sets of differences are created: C for changeable h and NC for not changeable h. By taking all LSBs of differences belonging to C set, a bit stream B is created. Firstly, the location map is recovered and used together with B to restore the original h values; secondly, by using (2) the original image is obtained, lastly, the embedded payload (the remaining part of B) is used for authentication check by resorting to the embedded hash. Tian applies the algorithm to “Lena” (512 512), 8 bpp grayscale image. The experimental results are shown in Table 1, where the embedded payload size, the corresponding bitrate, and PSNRs of the watermarked image are listed. As DE increases, the watermark has the effect similar to mild sharpening in the mid tone regions. Applying the DE method on “Lena,” the experimental results show that the capacity versus distortion is better in comparison with the G- LSB method proposed in [2], and the RS method proposed in [1]. The previous method has been taken and extended by Alattar in [6]. Instead of using difference expansion applied to pairs of pixels to embed one bit, in this case difference expansion is computed on spatial and cross-spectral triplets of pixels in order to increase hiding capacity; the algorithm embeds two bits in each triplet. With the term triplet a 1 3 vector containing the pixel values of a colored image is intended; in particular, there are two kinds of triplets. (i) Spatial Triplet: three pixel values of the image chosen from the same color component within the image according to a predetermined order. (ii) Cross-spectral Triplet: three pixel values of the image chosen from different color components (RGB). The forward transform for the triplet t = (u0,u1,u2) is defined as v0 = u0 +wu1 + u2 N , v1 = u2 u1, v2 = u0 u1, (7) where N and w are constant. For spatial triplets, N = 3 and w = 1, while in cross-spectral triplets, N = 4 and w = 2. On the other side, the inverse transform, f 1(), for the transformed triplets t′ = (v0, v1, v2) is defined as u1 = v0 v1 + v2 N , u0 = v2 + u1, u2 = v1 + u1. (8) The value v1 and v2 are considered for watermarking according to (9) v′1 = 2 v1 + b1, v′2 = 2 v2 + b2, (9) for all the expandable triplets, where expandable means that (v′1 + v ′ 2) satisfies a limitation similarly to what has been proposed in the previous paper to avoid overflow/underflow. In case of only changeable triplets, v′1 = 2 v1/2 + b1 (v′2 changes correspondingly), but the same bound for the sum of these two amounts has to be verified again. According to the above definition, the algorithm classifies the triplets in the following groups. (1) S1: contains all expandable triplets whose v1 T1 and v2 T2 (T1, T2 predefined threshold). (2) S2: contains all changeable triplets that are not in S1. (3) S3: contains the not changeable triplets. (4) S4 = S1 S2 contains all changeable triplets In the embedding process, the triplets are transformed using (7) and then divided into S1, S2 and S3. S1, and S2 are transformed in Sw1 and S w 2 (watermarked) and the pixel values of the original image I(i, j, k) are replaced with the corresponding watermarked triplets in Sw1 and S w 2 to produce the watermarked image Iw(i, j, and k). The algorithm uses a binary JBIG compressed location map M, to identify the location of the triplets in S1, S2, and S3 which becomes part of the payload together with the LSB of changeable triplets. In the reading and restoring process, the system simply follows the inverse steps of the encoding phase. Alattar 4 EURASIP Journal on Information Security Table 2: Embedded payload size versus PSNR for colored images. Lena Baboon Fruits Payload (bits) PSNR (dB) Payload (bits) PSNR (dB) Payload (bits) PSNR (dB) 305,194 35.80 115,050 30.14 299,302 35.36 420,956 34.28 187,248 28.54 497,034 33.00 516,364 33.12 256,334 27.20 582,758 32.45 660,618 31.44 320,070 26.10 737,066 31.14 755,096 30.28 408,840 24.73 824,760 30.06 837,768 29.10 505,150 23.34 853,846 29.49 941,420 27.01 656,456 21.20 888,850 28.52 Table 3: Comparison results between Tian’s and Alattar’s algorithm. Gray-scale Lena Gray-scale Barbara Tian’s Alg. Alattar’s Alg. Tian’s Alg. Alattar’s Alg. PSNR (dB) Payload (bits) Payload (bits) PSNR (dB) Payload (bits) Payload (bits) 29.4 260.018 298.872 23.6 247.629 279.756 32.5 222.042 236.318 31.2 159.000 202.120 34.8 175.984 189.468 32.8 138.621 187.288 36.2 141.493 131.588 34.1 120.997 167.986 37.7 120.619 107.416 37.4 81.219 108.608 40.1 101.089 49.588 40.2 60.577 45.500 41.6 84.066 19.108 42.8 39.941 19.384 w h Quad q = (u0,u1,u2,u3) Figure 2: Quads configuration in an image. tested the algorithm with three 512 512 RGB images, Lena, Baboon, and Fruits. The algorithm is applied recursively to columns and rows of each color component. The watermark is generated by a random binary sequence and T1 = T2 in all experiments. In Table 2, PSNRs of the watermarked images are shown. In general, the quality level is about 27 dB with a bitrate of 3.5 bits/colored pixel. In Table 3, it is reported also the performance comparison in terms of capacity between the Tian’s algorithm and this one, by using grayscale images Lena and Barbara. From the results of Table 3, the algorithm proposed outperforms the Tian’s technique at lower PSNRs. At higher PSNRs instead, the Tian’smethod outperforms the proposed. Alattar proposed in [7] an extension of such a technique, to hide triplets of bits in the difference expansion of quads of adjacent pixels. With the term quads a 14 vector containing the pixel values (2 2 adjacent pixel values) from different locations within the same color component of the image is intended (see Figure 2). The difference expansion transform, f (), for the quad q = (u0,u1,u2,u3) is defined as in (10) v0 = a0u0 + a1u1 + a2u2 + a3u3 a0 + a1 + a2 + a3 , v1 = u1 u0, v2 = u2 u1, v3 = u3 u2. (10) The inverse difference expansion transform, f 1(), for the transformed quad q′ = (v0, v1, v2, v3) is correspondingly defined as in (11) u0 = v0 (a1+a2+a3)v1+(a2+a3)v2+a3v3 a0 + a1 + a2 + a3 , u1 = v1 + u0, u2 = v2 + u1, u3 = v3 + u2. (11) Similarly to the approach previously adopted, quads are categorized in expandable or changeable and differently treated during watermarking; then they are grouped as follows. (1) S1: contains all expandable quads whose v1 T1, v2 T2, v3 T3 with v1, v2, v3 transformed values and T1,T2, and T3 predefined threshold. (2) S2: contains all changeable quads that are not in S1. (3) S3: contains the rest of quads (not changeable). (4) S4: contains all changeable quads (S4 = S1 S2). EURASIP Journal on Information Security 5 In the embedding process the quads are transformed by using (10) and then divided into the sets S1, S2, and S3. S1 and S2 are modified in Sw1 and S w 2 (the watermarked versions) and the pixel values of the original image I(i, j, and k) are replaced with the corresponding watermarked quads in Sw1 and S w 2 to produce the watermarked image Iw(i, j, k). Watermark extraction and restoring process proceeds inversely as usual. In the presented experimental results, the algorithm is applied to each color component of three 512 512 RGB images, Baboon, Lena, and Fruits setting T1 = T2 = T3 in all experiments. The embedding capacity depends on the nature of the image itself. In this case, the images with a lot of low frequencies contents and high correlation, like Lena and Fruits, produce more expandable triplets with lower distortion than high frequency images such as Baboon. In particular with Fruits, the algorithm is able to embed 867 kbits with a PSNR 33.59 dB, but with only 321 kbits image quality increases at 43.58 dB. It is interesting to verify that with Baboon the algorithm is able to embed 802 kbits or 148 kbits achieving a PSNR of 24.73 dB and of 36.6 dB, respectively. The proposed method is compared with Tian’s algo- rithm, using grayscale images, Lena and Barbara. At PSNR higher than 35 dB, quad-based technique outperforms Tian, while at lower PSNR Tian outperforms (marginally) the proposed techniques. The quad-based algorithm is also com- pared with [2] method using grayscale images like Lena and Barbara. Also, in this case the proposed method outperforms Celik [2] at almost all PSNRs. The proposed algorithm is also compared with the previous work of Alattar described in [6]. The results reveal that the achievable payload size for the quad-based algorithm is about 300,000 bits higher than for the spatial triplets-based algorithm at the same PSNR; furthermore, the PSNR is about 5 dB higher for the quad- based algorithm than for the spatial triplet-based algorithm at the same payload size. Finally, in [8], Alattar has proposed a further gener- alization of his algorithm, by using difference expansion of vectors composed by adjacent pixels. This new method increases the hiding capacity and the computation efficiency and allows to embed into the image several bits, in every vector, in a single pass. A vector is defined as u = (u0,u1, . . . ,uN1), where N is the number of pixel values chosen from N different locations within the same color component, taken, according to a secret key, from a pixel set of a b size. In this case, the forward difference expansion transform, f (), for the vector u = (u0,u1, . . . ,uN1) is defined as v0 = N1 i=0 aiuiN1 i=0 ai , v1 = u1 u0, ... vN1 = uN1 u0, (12) where ai is a constant integer, 1 a h, 1 b w and a + b /= 2, (w and h are the image width and height, resp.) The inverse difference expansion transform, f 1(), for the transformed vector v = (v0, v1, . . . , vN1), is defined as u0 = v0 N1 i=1 aiviN1 i=0 ai , u1 = v1 + u0, ... uN1 = vN1 + u0. (13) Similarly to what was done before, the vector u = (u0,u1, . . . ,uN1) can be defined expandable if, for all (b1, b2, . . . , bN1) 0, 1, v = f (u) can be modified to produce v = (v0, v1, . . . , vN1) without causing overflow and

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