On Stereo Embedding by Reversible WatermarkingDinu Coltuc

Electrical Engineering Dept.Valahia University Targoviste, Romania

Email: coltuc@valahia.ro

Abstract- This paper investigates the storage and bandwidth extracted. A similar application is the transmission of the audiorequirements reduction for stereo images by using reversible data hidden within the video sequence. For such applicationswatermarking. Given a pair of stereo images, the information (stereo embedding included), the stringent requirement isneeded to recover the right frame is embedded into the left watermarking capacity. On the contrary, robustness (usuallyframe. Thus, storage and bandwidth requirements are halved. watermark ing isnot antrary, sine hypothlThe proposed approach relies on the embedding capacity of the demanded in watermarking) is not an issue, since the hypoth-reversible watermarking. Compared with simple stereo image esis of a cooperative environment can be realistically accepted.pair compression, the proposed approach has the advantage that An original aspect of the proposed approach is the use ofthe content of the image remains available without additional reversible watermarking for data embedding. Compared withmanipulations. Furthermore, the use of reversible watermarkingallows the exact recovery of the left frame. If the reversible the classical watermarking, the reversible one introduces awatermarking provides enough data hiding bit-rate, the right challenging constraint, namely to recover at detection not onlyframe is exactly recovered, too. The validity of the proposed the embedded data but also the original image without anyapproach is investigated and experimental results are provided. error. In the context of the proposed approach, this means

that one of the stereo pair images is exactly recovered. If theI. INTRODUCTION data hiding capacity provided by the reversible watermarking

Stereo vision, a process naturally performed by humans is high enough to embed the entire information needed towith high accuracy is still not solved at a satisfactory level recover the second image, the stereo pair can be exactlyby computer vision and besides, it demands a doubling of recovered. Our objective is to ensure a high quality of thecomputational effort, of memory storage and of transmission recovered stereo pair and ideally, exact recovery. We mentionbandwidth. Obviously, in order to obtain stereo information, that the use of simple watermarking (even if it provides higha pair of images should be analyzed, transmitted or simply bit-rates) is not appropriate with respect to our objectives.stored. This is true even for the simple task of viewing images As it is known, by simple watermarking the cover image ison stereoscopic displays. irremediably destroyed, hence in no cases the stereo pair could

This paper focuses on the problem of reducing the size of be exactly recovered.the stereo data. A direct approach to this problem would be The outline of the paper is as follows. The reversiblethe simple data compression. Thus, the stereo pair could be watermarking used in our approach is discussed in Section II.(lossless or lossy) compressed and then, efficiently stored and The stereo embedding scenario and experimental results aretransmitted. The drawback of such an approach is the fact that presented in Section III and Section IV, respectively. Finally,once compressed, the content of the image is no more visible. the conclusions are drawn in Section V.Hence, for any simple task as the mere visualization stereoimage should be first uncompressed. This paper proposes II. REVERSIBLE WATERMARKINGa different approach that halves both the storage and the As discussed in Section I, the embedding capacity is thebandwidth requirements and meantime, keeps the content of main issue of the reversible watermarking scheme. The highestthe image directly accessible. capacity reversible watermarking schemes proposed so far are

Given a stereo image pair, the basic idea of the proposed lossless generalized LSB-embedding [2], difference expansionapproach is to embed by watermarking into one image the [3], [4], [5] or simple reversible schemes [6], [7], [8]. Weinformation needed to recover the other one. Thus, only one shall further consider the scheme recently proposed in [6].image instead of a pair is stored or, equivalently, transmitted. This scheme generalizes the ones of [7], [8] and introduces aSince no compression is used, the content of the image is different principle for marking/detection based on divisibility.directly accessible. Furthermore, when the stereo context is A parameter n is introduced providing, for a single embed-needed, the embedded data is extracted and the second image ding level, a theoretical maximum data hiding capacity ofof the pair is recovered. log2 (2n)/2 bits per pixel. For n > 2, bit-rates greater than

The idea of metadata embedding by watermarking is not 1 bpp can be obtained in a single iteration and without anynew [1]. For instance, chrominance information could be additional data compression. The spatial domain reversible wa-hidden into the luminance. Thus, only luminance is transmitted termarking based on such simple integer transforms providesand the graylevel image is directly available. Obviously, for higher bit-rates than the compression based schemes [2] andcolor displaying, the chrominance information should be prior almost similar results as the difference expansion ones [3], [4],

1-4244-0969-1/07/$25.OO ©C2007 IEEE.

but at a considerably lower mathematical complexity. In the With the above considerations, the basic principle of thesequel, we briefly introduce the basic principle of [6]. watermarking naturally follows. The watermark is embedded

The reversible watermarking scheme starts by partitioning into the transformed pixel pairs by using equation (6). Theimage into pairs of pixels. The pairs obeying some simple not transformed pixel pairs are modified by adding someconstraints are transformed in order to satisfy a congruence correction data in order to fulfill conditions (4). Since theequation. By adding some correction data, the not transformed watermark consists of integer codewords c $4 0, it followspixel pairs are enforced to obey the same equation, too. By that the transformed pairs (having embedded information)simple additions, the watermark together with the correction are immediately identified at detection as not obeying (4).data is embedded into the transformed pixels. After watermark Furthermore, by embedding the correction data together withinsertion, only the not transformed pixel pairs satisfy the the watermark, the original image can be completely restoredcongruence equation. Hence, at detection, the transformed with no loss of information. Obviously, the watermarkingpairs can be localized. Finally, the watermark and correction is possible if there are more transformed pairs than notdata can be extracted and the exact recovery of the original transformed ones. To prevent pixel underflow or overflow byimage follows by inverse transform. data insertion, supplementary constraints must be imposed:

The core of the reversible watermarking scheme is thetransform. Let [0,L] be image graylevel range (L = 255 0 < Yi-for 8 bit graylevel images), let x = (X, X2) be a pair of Yi + n < L (7)pixels and n > 1 be a fixed integer. The forward transform III. EMBEDDING STEREO INFORMATIONT :[0,L] x [0,L] -+ [0,L] x [0,L], y =T(x), whereTy [

X(L The proposed approach is as follows. Given a pair of stereoimages, one of the frames is selected as cover image. Since

Yi (n + 1)xi - nX2 usually the left frame is considered as reference frame, we

Y2 -nx, + (n + 1)X2 (1) shall consider it as cover image.Once a frame is selected, the information needed to recover

In order to avoid the overflow or underflow of transformed the other one should be prepared. Let s1 and 87 be the leftpixels, the following conditions should be fulfilled: and the right frames, respectively. Let r be the residual of the

O < (n + 1)xi - nX2 < L two frames:r=St - Sr (8)

0 <--nx, + (n +1)X2< L (2)For graylevels images represented on 8 bits (i.e., L = 255),

The inverse transform, x T1 (y) is: the pixels of d take values in the range [-L, L]. The residual

- (n+l)yl+nY2 is transformed to take values in the normal graylevel range.Xi- 2n+1 The residual normalization proceeds as follows:-2 nyl+(n+l)Y2 (3)LZ2= 2n+1 (3 L + r

Equation (3) exactly inverts (1). Since x1, X2, Yi, Y2 and n r [ (9)are integers, equations (3) show that 2n + 1 divide (n+ i)yi + It can be observed that because of the rounding, the normal-nY2 and ny1 + (n + 1)Y2, respectively. The divisibility can be ization of equation (9) is not exactly reversible. Meantime, thewritten as two congruence equations: error introduced by equation (9) is of maximum 1 graylevel.

(n + 1)yi + nY2 _ 0 mod (2n + 1) Such an error can be neglected without any loss of perfor-

ny,(n+1) - 0 mod (2n 1) (4\ mance.nYi + (n + uY82 - O mod (2n+ 1) ( ) The normalized residual is further compressed in orderStated in other words, this means that if a pair of pixels has to match the embedding bit-rate provided by the reversiblebeen transformed by equations (1), the transformed pair obeys watermarking scheme. Let cr be the compressed normalizedequations (4). residual. The best performances reported so far in the literatureAny transformed pair obeys equation (4). A not transformed for reversible watermarking are of around 2 bits per pixels. The

pixel pair, (X1, X2), does not necessarily fulfills (4). It can be performances depend on image statistics.easily shown (see [6]) that there is an unique integer a E The compressed normalized residual is further embedded[0, 2n] or, equivalently, a E [-n, n] such that the modified by reversible watermarking into the left frame, s1. The wa-pair: termarked left frame is further stored or transmitted instead

(Xl v X2) -+ (x1 + a, X2) (5) of the initial pair S1, Sr. As stated in Section I, the storagecapacity and the transmission bandwidth are halved. Since

obeys (4). Furthermore, if a codeword c E [-n,) fl], c $& 0 is the watermarked image is not compressed, it can be directlyembedded into a transformed pair: displayed.

The watermarked image contains the information neededYi, Y2)-(Yi+ C Y2) (6)to recover the stereo pair. The recovery proceeds as follows.

the transformed pair no longer obeys (4). The embedded information, i.e., the compressed normalized

Fig. 2. Normalized residual images.

Fig. 1. Test stereo images.

residual is first extracted and the original S1 is recovered. The Fig. 3. Compressed residual images.right frame is further recovered from s1 and the uncompressedresidual: IV. EXPERIMENTAL RESULTS

Sr = 2r' - -L (10) Let us consider the test stereo images shown in Fig. 1. The

corresponding normalized residuals are presented in Fig. 2.Since the watermarking is reversible, the left frame is The lossless compressed versions of the two residuals demand

exactly recovered. Regarding the right frame, the recovered a too higher bit-rate for the nowadays reversible watermarkingimage is distorted. As described above, very low distortions schemes. Therefore baseline JPEG compressed versions haveare introduced by the normalization procedure. More important been considered. Thus, for the upper image of Fig. 1, the bit-errors can be introduced by the residual image compression rate needed to embed the lossy compressed residual image isstage. Thus, if the embedding bit-rate provided by the re- 1.11 bpp. Quite similar results are obtained for the secondversible watermarking is high enough to allow the hiding of image, namely 0.89 bpp. Such bit-rates can be easily obtainedthe lossless compressed version of the residual, no errors are by using the reversible watermarking scheme of [6].introduced. If not, lossy compression should be performed to The watermarked left frames with the compressed residualmatch the embedding bit-rate. Both the embedding bit-rate and data embedded are shown in Fig. 4. As it can be seen inthe residual image compression ratio depend on the stereo Fig. 4, there are some artifacts, but the information contentimage content. For complex images with many details and of the two test images is clearly visible. The images of Fig.large textured regions it is expected to have low embedding 4 have an embedding capacity of 1.26 bpp and 1.37 bpp,bit-rates and low compression ratios and conversely, high bit- respectively. Thus, except the residuals, it is enough room forrates and high compression ratios for images with less details embedding some other information like some authenticationand large uniform regions. data. Furthermore, the limits of the embedding capacity are

not reached yet. The scheme of [6] can provide more than 2bpp for these two images, but at the cost of more distortions.

The left frames of the two test images are exactly recoveredafter watermark extraction. The compressed residuals areextracted with no loss of information, too. The recovered rightframes are shown in Fig. 5. Compared with the originals ofFig. 1, the PSNRs of the recovered versions are 31.56 dB and3 8.64 dB, respectively.

The results of Fig. 5 show a difference of quality betweenthe two recovered versions. This difference is explained bythe fact that the JPEG compression was tuned to providequite similar compression ratios. The less complex the image,the better the quality versus compression. Since the reversiblewatermarking provides a higher embedding bit-rate than theone used to produce the images of Fig. 4, a better qualitycompressed residual can be embedded in order to improve Fig. 4. Watered left frames.the quality of the recovered image. As said above, the costof improving the quality of the recovered right frame is theloss of quality for the watermarked image by increasing theembedding rate. This is not a major problem, since at detectionthe stereo pair is recovered at a good quality.

V. CONCLUSIONS AND FUTURE WORK

The problem of embedding stereo information by reversiblewatermarking has been investigated. Instead of image pairsmanipulation, only one watermarked frame is stored andtransmitted. The information needed to recover the otherimage frame is embedded into the marked frame by reversiblewatermarking. Thus storage and bandwidth requirements arehalved and besides, the image content is immediately avail-able. Compared with the simple compression of stereo pairs,the proposed approach has the advantage that image contentremains available during image manipulation. WUAhen stereoinformation is needed, the stereo pair is recovered. The wa- Fig. 5. Recovered right frames.termarked frame is exactly recovered and the second frameis restored at a quality which depends on the hiding bit-rateprovided by the reversible watermarking. The results obtained [2] M. U. Celik, G. Sharma, A. M. Tekalp, E. Saber, "Lossless Generalizedso far are promising. LSB Data Embedding", IEEE Trans. on Image Processing, vol. 14, no.

So far we have analyzed only the quality of the recovered [3] 12,pn. 2082-2090, 2005.J[]J. Tian, "Reversible Data Embedding Using a Difference Expansion",

stereo pair. Future work will be devoted to the validation of our IEEE Trans. on Circuits and Systems for Videotechnology, vol. 13, no. 8,approach by comparison between the disparity map computed pp. 890-896, 2003.

from he oiginlan the ecovred tere pair Furhermre, 4] A. M. Alattar, Reversible Watermark Using the Difference Expansion ofa Generalized Integer Transform, IEEE Trans. on Image Processing, vol.

instead of embedding the residual between the two frames, 13, no.8, pp. 1147-1156, 2004.the embedding of the disparity map will be considered, too. [5] L. Kamstra, H. J. A. M. Heijmans, "Reversible Data Embedding Into

More complex stereo images will be tested. This will demand Images Using Wavelet Techniques and Sorting", IEEE Trans. on ImageProcessing, vol. 14, no. 12, pp. 2082-2090, 2005.

higher embedding bit-rates. Research work to improve with [6] D. Coltuc, J-M. Chassery, "High Capacity Reversible Watermarking",more than 30% the capacity of the reversible watermarking Proceedings of the IEEE International Conference on Image Processing

scheme usedinour apprach is in pogress [9].ICIP '2006, Atlanta, GA SUA, Oct. 2006.scheme usediarni, ouBartol,Wapproac ing ss [ : Ea [7] D. Coltuc, A. Tremeau, "Simple Reversible Watermarking Schemes",

SPIE Proceedings, Security, Steganography and Watermarking of Multi-ACKNOWLEDGMENT media Contents - VII, vol. 5681, Editor(s): Delp, Edward J., Wong, Ping

W., USA, pp. 561-568, 2005.This work is supported by INFOSOC (CEEX 2006) Roma- [8] D. Coltuc, J-M. Chassery,, "Very Fast Watermarking by Reversible