Robust image watermarking based on
multiple description vector quantisation
J.-S. Pan, Y.-C. Hsin, H.-C. Huang and K.-C. Huang
An innovative scheme for watermarking based on vector quantisation for transmitting over noisy channels is proposed. By modifying multiple description vector quantisation for watermark embedding and extraction, simulation results not only demonstrate effective transmission of the watermarked image, but reveal the robustness of the extracted watermark.
Introduction: Digital watermarking is one of the useful solutions for copyright protection. It embeds secret information into digital con-tents to protect intellectual properties. In this Letter, we propose an innovative algorithm concentrating on vector quantisation (VQ) based image watermarking, suitable for error-resilient transmission over noisy channels. By incorporating a watermarking algorithm with multiple description coding (MDC), our proposed scheme can effi-ciently overcome channel impairments while retaining the capability for copyright protection.
Design of MDVQ with watermarking: In multiple description (MD) coders, the same source material is coded into several strings, called descriptions, such that each description can be decoded independently to obtain a minimum fidelity; while combining with other descriptions to achieve better quality. Applications of MDC focus on error concealment. For transmission, MDC is suitable for noisy channels with long bursts of errors.
Information-theoretic issues of MDC have been studied extensively since the early 1980. Practical designs of multiple description scalar quantisers ( MDSQs) [1] and multiple description vector quantisers ( MDVQs)[2]emerged in the 1990s. The descriptions of the MDSQs can be interpreted as the row and column indices of a matrix, in which the codewords, or respectively, their indices, are placed. The dimension of the matrix is denoted by K; it equals the number of descriptions, or the number of channels for transmission. We set K ¼ 2 in this Letter.
We demonstrate the structure of our watermarking system with MDVQ inFig. 1, by modifying that in [2]. Our goal is to focus on using MDVQ to incorporate with robust watermarking techniques to provide both the error-resilient transmission of the watermarked image over different channels with independent breakdown probabilities, and the capability for copyright protection.
Fig. 1 Structure for MDVQ-based watermarking with two descriptions
Let the input image be X with size M N. We perform the VQ operation first[1]to train the codebook for X, and obtain the codebook with length L, C ¼ {c0, c1, . . . , cL1,}. Each index in C is represented by a dlog2Le-bit binary string, where de means a ceiling function. X is divided into non-overlapping blocks xbwith size (M=Mw) (N=NW), 0 b < MwNW, then each xb finds its nearest codeword ci in the codebook C, and the index i is assigned to xb. Let the watermark for embedding be W ¼ {W0, W1, . . . , WMWNW1}, having size MWNW.
Each element in W, Wb, 0 b < MWNW, represents one watermark bit to be embedded into xb. For watermarking purposes, the new index iW for representing xbis generated from two parts: to shift the original index i to the left by one bit, and to tag watermark bit Wbto the end of the shifted index, i.e.
iW ¼ ði 1Þ þ Wb ð1Þ Next, we make use of the MDSQ algorithms in[1]for index assign-ment. The index assignments inFig. 1, i1¼a1(iW) and i2¼a2(iW), map
the quantiser output index iWto two descriptions i1and i2. Then, i1 and i2are transmitted over two memoryless and mutually independent channels with erasure probabilities p1for channel 1, and p2for channel 2, respectively.
At the decoder side inFig. 1, it first shifts received binary indices i1 0
and i2 0
to the right by one bit to smooth away the effects from watermark embedding, and determines the outcome i0 from received indices with the MDSQ decoder. Next, it performs a table look-up process on the determined i0 to obtain ci
0
and then obtains the watermarked reconstruction X0.
In watermark extraction, we carry out the estimation criterion from received indices for determining the value of the watermark bits. With MDC, if both descriptions for one block xb are received, then the resulting index decoded by MDSQ can be determined uniquely, and the watermark bit is extracted by taking out the last bit. Besides, because of the error concealment capability for index assignment, when only one description is received, the block can be partly reconstructed, and the watermark bit needs to be determined from several possible indices assigned in the MDSQ row or column matrix [1]. We first use a majority vote to determine the watermark bit. However, if there are equal numbers of 0’s and 1’s obtained, we assign the watermark bit randomly. Furthermore, if none of the descriptions are received, the watermark bit is randomly assigned. By gathering all the extracted watermark bits Wb
0
, we obtain the extracted watermark W0.
Simulation results: In our simulations, we take the test image, Lena, with size 512 512, as the original source. We have the embedded watermark with size 128 128. The original source is divided into 4 4 blocks for VQ compression, which also meets the number of bits for watermark embedding. The codebook size is L ¼ 512, and indices therein are represented by 9-bit strings.
We employ the bit error rate (BER), of the extracted watermark for evaluating the robustness of our algorithm. In addition, the water-marked image quality after transmitting over two erasure channels is also considered, measured by peak signal-to-noise ratio (PSNR) between X0 and X. Simulations show the practicality and usefulness of our method.
0% 11.82% 26.66% 19.45%
a b c d
Fig. 2 Extracted watermarks under different channel erasure probabilities p1, p2 in Fig. 1. Corresponding percentage values represent BER in extracted watermarks
a p1¼p2¼0 b p1¼p2¼0.25 c p1¼0, p2¼1 d p1¼1, p2¼0
Table 1: Simulation results with different erasure probabilities
Erasure probabilities
PSNR of watermarked reconstruction (dB)
Bit error rate of extracted watermark [%] Channel 1 Channel 2 0.0 0.0 32.53 0.00 0.05 0.05 30.69 2.44 0.1 0.1 28.90 4.86 0.25 0.25 24.59 11.82 0.5 0.5 19.98 23.75 1.0 0.0 26.09 19.45 0.0 1.0 26.18 26.66
Simulations with different channel erasure probabilities are presented in Fig. 2 and Table 1. In Fig. 2, p1 and p2 denote the erasure probabilities with channel 1 and channel 2, respectively. Fig. 2a
shows the extracted watermark under error-free transmission that is identical with the embedded one. Fig. 2b represents the result for transmitting over the lightly erased channels with p1¼p2¼0.25. BER is low and the extracted watermark is recognisable. Figs. 2cand d
illustrate extracted watermarks under heavily erased channels, for which data transmitting over channel 1 or channel 2 are totally lost,
respectively. Although BER values get somewhat higher, extracted watermarks are still recognisable. InTable 1, PSNR and BER values under different erasure probabilities are indicated. PSNR values in
Table 1show error-resilient capabilities with MDVQ under severely erased channels. Also, BER values are not high even under severely erased channels, and their corresponding watermarks can all be recog-nised subjectively.
To sum up, under a wide range of channel erasure probabilities, results with our proposed algorithm demonstrate both the effective transmission of watermarked images, and the robustness of the extracted watermarks.
Conclusion: We propose an innovative scheme for VQ-based image watermarking with multiple description coding, which is suitable for transmitting over noisy channels. We modified the MDVQ and MDSQ index assignments for watermark embedding and extraction. By incorporating with MDC, simulation results also present both the better robustness of the watermarking algorithm, and the more resilience to combat channel noise under lightly to heavily erased channels.
#IEE 2004 2 August 2004
Electronics Letters online no: 20046454 doi: 10.1049/el:20046454
J.-S. Pan and Y.-C. Hsin (Department of Electronic Engineering, National Kaohsiung University of Applied Sciences, Kaohsiung, Taiwan, Republic of China)
H.-C. Huang (Department of Electronics Engineering, National Chiao Tung University, Hsinchu, Taiwan, Republic of China) K.-C. Huang (Department of Electronics Engineering, Cheng Shiu University, Kaohsiung, Taiwan, Republic of China)
References
1 Vaishampayan, V.A.: ‘Design of multiple description scalar quantizers’, IEEE Trans. Inf. Theory, 1993, 39, (3), pp. 821–834
2 Go¨rtz, N., and Leelapornchai, P.: ‘Optimization of the index assignments for multiple description vector quantizers’, IEEE Trans. Commun., 2003, 51, (3), pp. 336–340
