Local Map Versus Histogram Shifting for PredictionError Expansion Reversible Watermarking

Adrian Tudoroiu, Dinu ColtucElectrical Engineering Dept.

Valahia University of Targoviste, RomaniaEmail: {tudoroiu,coltuc}@valahia.ro

Abstract—This paper continues our research on high capacityprediction error expansion reversible watermarking. Three pre-diction error expansion (PEE) schemes are considered, namelyhistogram shifting (HS), location map (LM) and block map (BM)schemes. Their performances for embedding capacities greaterthan 1 bit per pixel are analyzed. For embedding capacity lessthan 1 bit per pixel, it is known that the PEE-HS schemesoutperform the PEE-LM and PEE-BM schemes. The paper showsthat as the capacity increases, the location map schemes andnotably the block map schemes outperform the histogram shiftingones. Experimental results are provided.

I. INTRODUCTION

Reversible watermarking is the process of hiding a messagein a digital media allowing the exact recovery of both thehidden message and the digital media. The most efficientapproach for reversible watermarking is difference expansion(DE). DE creates the space for data insertion by expandingsome differences. The first DE algorithms considered the dif-ference between adjacent pixels [1]–[3], etc. In order to reducethe difference and consequently, the embedding distortion, thedifference between pixels was replaced by the prediction-error[4]– [12], etc.

The classical algorithms, that expand two times the predic-tion error, provide up to 1 bpp embedding bit-rates. For higherembedding bit-rates, either one repeats the embedding untilthe required capacity is obtained (multilevel embedding), orone expands more the prediction error (multibit embedding).We remind that by multibit embedding, the prediction error isexpanded n times, n ≥ 2, in order to embed up to log2(n+1)bpp [10]–[12]. The scheme of [12] clearly outperform the onesof [10], [11].

This paper continues our research on high capacity DEreversible watermarking of [12], [13]. For embedding bit-rates less than 1 bpp, it is well-known that the predictionerror expansion schemes with histogram shifting (HS) largelyoutperforms the location map (LM) ones. In [12], we haveshown that multibit prediction error expansion outperformsthe multilevel implementation. A simple comparison betweenLM and HS prediction error expansion schemes shows that HSdistorts all the pixels, while LM only the embedded pixels. Onthe other side, HS schemes need a larger amount of additionalinformation than LM. In [13], we investigated the reductionof the size of the additional information by considering theembedding on blocks (BM). Thus, instead of a bit for eachpixel, one needs a bit for a block of pixels. The BM clearly

outperforms the simple LM schemes and provides results closeto the HS schemes.

This paper considers the multibit prediction-error expansionand investigates the behavior of PEE-HS and PEE-LM. Up to 1bpp, the PEE-HS outperforms the PEE-LM. As the embeddingcapacity increases, the results of the PEE-LM improve andoutperform the PEE-HS. At high capacity, the best results areprovided by the PEE-BM schemes. The outline of the paper isas follows. The basic principle of the multibit prediction errorexpansion and the typical implementations, HS, LM and BM,are discussed in Section II. Experimental results are providedin Section III and the conclusions are drawn in Section IV.

II. MULTIBIT PREDICTION ERROR EXPANSIONREVERSIBLE WATERMARKING

We shall first introduce the basic principle of the multibitprediction error expansion. Then, the histogram shifting, thelocation map and block map versions of PEE schemes arebriefly investigated.

A. Multibit PEE

We introduce the basic principle of the multibit prediction-error expansion reversible watermarking. Let x be thegraylevel of the current pixel and let x̂ be the predicted value.The prediction error is:

e = x− x̂ (1)

Let further n, n ≥ 2, be a fixed integer and let w be aninteger code in [0, n − 1]. The prediction error is expandedn-times and the integer data code w is added to the expandederror:

ew = ne+ w (2)

The new value of the pixel is:

x′ = x̂+ ew = x+ (n− 1)e+ w (3)

For 8 bit graylevel images, x ∈ [0, 255]. Obviously, oneshould also have x′ ∈ [0, 255], i.e., 0 ≤ x+(n−1)e+w ≤ 255.In order to avoid overflow or underflow regardless the valueof w, the following condition should be fulfilled:

0 ≤ x+ (n− 1)e < 255− n (4)

At the decoding stage, the embedded integer code can beextracted as

w = (x′ − x̂) mod n (5)

978-1-4673-6143-9/13/$31.00 ©2013 IEEE

Then, the original pixel is recovered as:

x =x′ + (n− 1)x̂− w

n(6)

The equations (5) and (6) show that the transform defined bythe equation (3) is reversible. Obviously, one should recover atdetection the same predicted value for x. This is obtained byusing, for instance, anticausal predictors and by consideringopposite scanning directions for marking and detection. Thus,if the marking is performed in raster-scan starting with theupper left corner, the detection is performed in oppositedirection starting with the last embedded pixel from lowerright corner. Obviously, the context of the last embedded pixelremains unchanged and the same predicted value is computed.Once the original value of the last embedded pixel is restored,the context of the last but one embedded pixel is recoveredand so on. Before going any further a comment should bemade. While the great majority of the DE schemes rely onrecovering the prediction context of each pixel, in fact notthe predicted value should be recovered at detection, but theprediction error itself. Recently novel schemes based on thisobservation have been proposed [8], [9]. Such schemes aimat improving the embedding distortion by embedding data notonly into the pixel itself, but also into the prediction context.

It should be noticed that in order to extract the embeddeddata one should know if a pixel was embedded or not. Thereare two basic schemes for embedded pixel detection. Thestraightforward scheme uses a location map (LM). A moreelaborate approach is the histogram shifting (HS) one.

B. Location mapA binary map is used to indicate if a pixel is embedded or

not. The map has the size of the image. For the embeddedpixels, the corresponding bit of the map is set to ”1”. Themap is lossless compressed and embedded into the imageas additional information. An efficient strategy for additionalinformation embedding is discussed in [12]. The map issubstituted into the LSBs of pixels from the beginning ofthe image and the substituted bits are concatenated with thepayload and embedded into the remaining of the image.

C. Histogram shiftingThe idea of HS is to translate the graylevel of the pixels that

cannot be embedded in order to provide, at detection, a greaterprediction error than the one of the embedded pixels [4]. Atdetection, the expanded prediction error of an embedded pixelis ne + w. Since the prediction error before data embeddingis bounded by T and w ∈ [0, n−1], one immediately gets theupper and lower limits of the prediction error at detection:

−nT < ne+ w < nT + n− 1 (7)

Let us consider that pixel x was not embedded because theprediction error exceeds the threshold condition, |e| < T .In order to be located at detection, the pixel x should betransformed as follows:

xHS =

{x+ (n− 1)T, if e ≤ −T,x− (n− 1)T + n− 1, if e ≥ T

(8)

(a) Barbara (b) House

(c) Cameraman (d) Tiffany

(e) Boat (f) Mandrill

Fig. 1. Test images.

The pixels that cannot be shifted because of overflow orunderflow are left unchanged. They are identified by usingan overflow/underflow map that can be hidden as discussed inthe previous section.

D. Block map

The LM approach introduces distortion only into the pixelswhere data is embedded. By the contrary, the HS approachdistorts the entire image. While the embedded pixels aredistorted in order to insert information, the non-embeddedpixels are distorted in order to provide, at detection, a largeprediction error. In fact, the non-embedded pixels are moredistorted than the embedded ones. For both approaches, acompressed location map should be hidden into the image.The overflow/underflow map of HS needs considerably lessspace than the one of LM. This is the reason why the PEE-HS schemes perform better than the LM ones.

The extra distortion introduced by the HS approach is aserious drawback. This made us investigate the reduction ofthe size of the location map used in LM approaches [13]. Weconsidered a block map (BM) approach. The image is split

Fig. 2. Experimental results for reversible watermarking

in blocks. Furthermore, a block is embedded if all the pixelsof the block can be embedded. On the other side, if a singlepixel cannot be embedded, the embedding of the block fails.

For k × k blocks, the size of the initial location mapis reduced by k2 times. An important size reduction alsoappears after the lossless compression. We have tested the BMapproach. The 8 × 8 block size appeared as an optimum forembedding capacities up to 1 bpp. We found that the BMschemes considerably outperform the LM ones and performclose to the HS ones. While in [13] the results are providedfor fixed size of the block, in this paper we consider theoptimization of the block size together with n.

III. EXPERIMENTAL RESULTS

The high capacity multibit prediction error expansion re-versible watermarking schemes have been tested on standardgraylevel test images. Next we present the experimental resultsobtained on 6 graylevel images of sizes 512 × 512, namely

Barbara, House, Cameraman, Tiffany, Boat and Mandrill (Fig.1).

The anticausal Median Edge Detector (MED) predictor wasused in all the experiments. We remind that the estimate pro-vided by the MED predictor is computed on a neighborhoodcomposed of three pixels, namely the pixels located on south(xs), east (xe) and south-east (xse).

x̂ =

max(xs, xe), if xse ≤ min(xs, xe)

min(xs, xe), if xse ≥ max(xs, xe)

xs + xe − xse, otherwise(9)

The results for the 6 test images are plotted in Fig. 2. Theplots for PEE-HS and PEE-LM are obtained by optimizing,for each capacity, the embedding distortion in function of nand T . The plots for PEE-BM, take into account not only thethreshold and the modulus of expansion, but also the size ofthe block. Opposite to the results of [13] where the size of theblock was fixed, the results for PEE-BM of Fig. 2 consider

also the variation of k, the block size.While for a capacity of less than 1 bpp, the results of the

PEE-HS clearly outperforms the ones of the PEE-LM, our testsshow that, as soon as the capacity increases, both schemesgive rather similar results or, generally, the PEE-LM slightlyoutperforms the PEE-HS one. The best results are obtainedfor Barbara. The only exception appears for Mandrill, wherePEE-HS appears to provide the best results. For Mandrill, itshould be observed that, for all the reversible watermarkingschemes, the embedding capacity remains very low (in therange 1.25-1.32 bpp).

The PEE-BM outperforms both PEE-HS and PEE-LM.The best results are obtained on Barbara. Compared withthe results of PEE-HS, the improvement is of about 2 dB.Quite similar results are obtained for Cameraman. It shouldbe observed that the Cameraman test image has very largeuniform areas. It provides a very high embedding capacity,about 3.25 bpp. The improvement of PEE-BM with respect toPEE-HS can be also seen for House and Tiffany. For Boats,PEE-BM slightly outperforms PEE-HS.

The results of Fig. 2 have been obtained by using the MEDpredictor. The same results hold for other predictors, as well.See, for instance, in Fig. 3, the results obtained for the testimage Barbara by using two other predictors, namely GAPand SGAP.

IV. CONCLUSIONS

The performances of histogram shifting and location mapprediction error expansion reversible watermarking schemesfor high embedding bit-rates have been analyzed. While forembedding bitrates of up to 1 bpp, the histogram shiftingprediction error expansion schemes clearly outperform the lo-cation map ones, the situation changes as soon as the embedingbit-rate increases. Thus, it appears that the histogram shiftingPEE and the standard location map PEE provide rather similarresults. In fact, in most cases, PEE-LM outperforms PEE-HS.Furthermore, the block map prediction-error expansion (whichis an improved LM) outperforms the PEE-HS. To conclude, iffor embedding bit-rates lower than 1 bpp one should select aPEE-HS scheme, for embedding capacities greater than 1 bpp,a good strategy is to select a PEE-LM or a PEE-BM scheme.

ACKNOWLEDGMENT

This work was supported by UEFISCDI, PN-II-PT-PCCA-2011-3.2-1162 project and by POSDRUCPP107/DMI1.5/S/77497 Predex.

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