Color Image Hiding Using Neural Networks with Grey Relation Based on Interpolative Vector Quantization

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(1)Color Image Hiding Using Neural Networks with Grey Relation Based on Interpolative Vector Quantization Chi-Yuan Lin1,2 and Chin-Hsing Chen1 1. Department of Electrical Engineering, National Cheng Kung University, Tainan, 70101 Taiwan, R.O.C. 2 Department of Electronic Engineering, National Chin-Yi Institute of Technology, Taichung, 41111 Taiwan, R.O.C. E-mail: [email protected] Abstract. information. security. [1].. However,. most. In this paper, a novel color image hiding. traditional cryptosystems were only designed to. technique using spread grey-based competitive. protect text data. They are not suitable to encrypt. Hopfield. and. image directly. Recently there have been several. Hadamard Transform (HT) digital watermarking. cryptosystems proposed for gray image security. is proposed. The goal is to offer secure. [2-5]. In this paper, we focus on the subject of. communications. through. joint color image compression and color image. compress the original color image and embedded. watermarking to protect color image information. into another disguise color image. Our method. for secure communications in the internet.. neural. network. in. the. (SGHNN). internet. competitive. In our presented color image hiding. Hopfield neural network with grey relational. approach, we employ a disguise color image to. analysis for color image compression based on. camouflage our original color image to be an. interpolative vector quantization (IVQ). Then we. embedded color image. The embedded color. embedded. sorted. image is one that can be made public. In addition,. codebooks of original color image information. for the purpose of reducing massive hiding color. into a disguise color image by HT-based. image information, the interpolative color Vector. watermarking so that design a security color. Quantization (VQ) is adopted.. includes. a. spread-unsupervised. color. IVQ. indices. and. Neural networks with competitive learning. image hiding is feasible. Keywords: interpolative vector quantization,. have been demonstrated by the authors capable. grey theory, neural networks, and Hadamard. of performing vector quatization [6-8]. In this. transform.. paper, we presented a Spread Grey-based. 1. Introduction Color images are widely used in our daily lives. The major issue of compression and security for color image has seen an explosive growth in computers, networks, communications and multimedia applications. A cryptosystem is a useful tool for. competitive Hopfield Neural Network (SGHNN) for. color. image. compression. based. on. Interpolative VQ (IVQ). Furthermore, based on the presented scheme, we developed digital watermarking software to hid color image information. The original color image is first compressed by the SGHNN based on interpolative VQ into the.

(2) color IVQ indices and sorted codebooks which is. 2.2 Digital Watermarking. then embedded into the Hadamard transform domain of the original color image.. embed a secret data in a digital image or video sequence that allows ownership to be identified.. 2. Background. The earlier watermarking techniques were spatial domain [11-12]. Spatial domain method. 2.1 Competitive Hopfield Neural Network For Q training vectors and F classes, the discrete Hopfield neural network with competitive learning (called CHNN) [9-10] Q ×F. consists of. vector is iteratively trained to update the weight of the neurons by using the nearest neighbor rule. In a 2-D Hopfield neural network, let 9 \ , M be. ( \ , M )WK. the output state of the. neuron and. : [ , L ; \ , M represents the interconnected weight neuron. ([ , L ). ([ , L ). and neuron. (\ , M ) .. A. in the network receives weighted. inputs : [ , L ; \ , M. analyzes the original data in spatial domain and manipulates Least Significant Bit (LSB) to embed watermark data. Most. neurons, which can be. conceived as a two-dimensional array. Each. between neuron. Digital watermarking is a technique to. from each neuron. 1HW [ , L =. ∑∑ W. [ , L ; \ , M9 \ , M. domain. Transform (DFT) [16] and Discrete Wavelet Transform (DWT) [17-18]. Frequency domain method converts the original data and watermark data. into. frequency. domain. and. then. manipulates the coefficients to embed watermark data into the original multimedia data.. 3. Color Image Hiding In this paper, the proposed scheme is a combination between color image compression based. F. transform. Transform (DCT) [13-15], Discrete Fourier. and a bias , [ , L from outside. The total input to. Q. current. watermarking techniques use Discrete Cosine. (\ , M ). neuron ([ , L ) is computed as. of. + I [ ,L. (1). \ =1 M =1. on. interpolative. VQ. and. digital. watermarking techniques. The goal of color image compression based on interpolative VQ is. and the Lyapunov energy function of the two-dimensional Hopfield neural network is. to reduce massive hiding data in the digital representation of a color image. In order to achieve high compression ratio with less. given by [10]. distortion, we presented a spread grey-based competitive Hopfield neural network for color ( =−. −. 1 2 Q. Q. Q. F. F. ∑ ∑∑∑9. [ ,L. image compression scheme.. : [ , L ; \ , M9 \ , M. [ =1 \ =1 L =1 M =1 F. ∑∑ ,. [ , L9 [ , L. Consider an original color image that we (2). [ =1 L =1. want to offer secure communications in the internet by our proposed scheme. We must first choose. The network reaches a stable state when the Lyapunov energy function is minimal.. another. disguise. color. image. to. camouflage it. Since our scheme is based on interpolative VQ, two data items need to be hided. One is the sorted codebook. The other is a set of indices on the sorted codebook. The.

(3) distinguished coefficient.. relative illustrations are described as follows.. 3.1. Color Image Compression SGHNN Based on VQ. Using. The spread grey-based competitive Hopfield neural network has the same. Suppose an image is divided into Q. architecture as the competitive Hopfield. blocks (vectors of pixels) and each block. neural network [9-10]. In order to update. occupies l × l pixels. A vector quantizer is a. the training performance, the grey relation. technique. theory. that. maps. the. Euclidean. l × l -dimensional space. 5 l×l. into a set. {ωM , M = 1,2,..., F } of points in 5 l×l , called a codebook. It looks for a codebook such that each. Grey-based. codebook. A codebook is optimal if the average distortion is at the minimum value. The average distortion. ( [G ([ \ , ωM )] between an input. sequence. of. {[ \ , \ = 1,2,..., Q } output. training and. sequence. its. of. competitive. into. a. Spread. Hopfield. Neural. simplified object function for the SGHNN can be modified as Q. 3. ( =. Q. F. F. ∑∑∑∑∑9 S =1 [ =1 \ =1 L =1 M =1. [ , L ; S γ \ , M ; S9 \ , M ; S. (5). and 1HW [ , L ; S =. Q. F. ∑∑ γ \ =1 M =1. vectors. \ , M ; S9 \ , M ; S. (6). is. grey. corresponding code. vectors. {ωM , M = 1,2,..., F } is defined as 1 ' = ( [G (x \ , ω M )] = Q. embedded. Network (named SGHNN). Therefore the. training vector is approximated as close as possible by one of the code vectors in the. was. the. modified. relational grade between training samples. [\. Q. ∑ G (x. γ \ ,M;S. where. \. ,ω M ). (3). \ =1. and codevector Z. M. at the pth plane. and , [ , L ; S = 0 . We then map R, G, and B plane training. The grey relational theory proposed in. vectors of a color image to the SGHNN neuron. theory. array, and using Eqs. (5) and (6), the proposed. demonstrates the measurement of similarity. spread competitive Hopfield neural network in. between training vectors and codevectors based. each plane can be used for color vector. on the grey relational space. Let [ \. quantization in a parallel manner are given as. 1982. [19-20].. Grey. relational. be a. training vector and ωM be the codevector j, then. follows.. the grey relational coefficient is defined as. Step. γ. \ ,M. (. ≡γ [. \. , ωM. )=. ∆ PLQ . + ξ ∆ PD[ . ∆ \M + ξ ∆ PD[ .. 1:. Input. {. set. training. ; S = [ 1; S , [ 2; S , L , [ Q ; S (4). },. vector and the. number of class c. Step 2: Compute the grey relational grade matrix. where. {. 5= γ ∆ PLQ. = PLQ[ \ − ωM , ∆ PD[. = PD[[ \ − ωM. a. ,. }. Q ,F ;3. \ ,M ;S. \ =1, M =1; S =1. with. training. samples and codevectors at each plane. ∆ \M = [ \ − ωM. ,. and. 0 < ξ <1. is. the. Step 3: Set the initial number of the vectors to be n. Each class contains at least one vector..

(4) Step4: Calculate the input to each neuron (x,i) by. least computation overhead since its basis. Eq. (6). Step 5: Apply the equation below to update the. {. 1HW[ ,L ;S =PD[1HW[ ,1;S,1HW[ ,2;S,L1HW[ ,F;S . RWKHUZLVH. vectors. content. only. +1. and. –1.. No. multiplication is necessary and only fixed point. output states for each neuron in a row. 1 LI 9[ ,L ; S = 0. Hadamard Transform (HT) [22-23] takes the. }. Step 6: Repeat Steps 4 and 5 for all rows, and count the number of neurons for the new. arithmetic. is required. for. computing the. transformation. The forward and inverse 2-D Hadamard transform for an 1 × 1. image can. be define as: Forward:. state. If no neuron is changed go to step 7, otherwise go to step 4. Step 7: Complete the codebook design in the pth. 1 ) (X ,Y ) = 1. 1 −1 1 −1. ∑∑ I ( M , N )(− 1). l −1 ∑ [E L (X )E L ( M )+E L (Y )E L (N )] L =0. M =0 N =0. plane (p = 1,2,3). (7). 3.2 Interpolative Vector Quantization. Inverse:. Interpolative vector quantization has been devised to alleviate the visible block structure of coded images and lessen the sensitive codebook. 1 ) (M , N )= 1. 1 −1 1 −1. ∑∑ I (X ,Y )(− 1). l −1 ∑ [E L (X )E L ( M )+E L (Y )E L ( N )] L =0. X =0 Y =0. problems produced by a simple vector quantizer. (8). [21]. In a VQ system, the complexity of the. where ) (X ,Y. encoders is often depending up on the size of the. coefficients, I ( M , N ) are the pixel value at. codebook used. In this paper, for the purpose of. ( M , N ) , 1 = 2 l for some l , and E L (X ) is. reducing massive hiding data, the. 1 ×1. original image was down-sampled into. 1 ×1 2. size image. Therefore, just only. 1 ×1 2. pixels. ). are the Hadamard transform. the ith bit of u in the binary form. In our scheme, a 256 × 256 disguise color image is divided into non-overlapped 4096 blocks. (4 × 4). , which are transformed to. frequency domain by the HT. The bit stream of. of each plane in the original image was. indices and sorted codebooks of 256 × 256. processed using the proposed SGHNN approach.. original color image compression based on IVQ. Then the interpolative method was used to. is embedded into eight coefficients in lower. rebuild the empty pixels using the average of. band of each block [15]. The embedded process. their neighbor pixels in each plane. That is to say,. each plane is described as follows. the Interpolative method must do an extra work. Step 1: Sequentially extract out every 8 bits data. for interpolating pixels and little rebuilt quality. from bit stream of IVQ indices and. maybe reduced but can reduce massive hiding. sorted codebooks.. data.. Step 2: Obtain a random number, generated by. 3.3 Color Image Hiding Through Hadamard Transform Among various popular image transforms,. pseudo random number system, which points to one of 4096 blocks of disguise color image..

(5) Step 3: Embed extracted the 8 bits data into the 8. Quantization. (VQ).. In. this. paper,. the. lower band coefficients in the block. × original color image was separated. pointed by Step 2.. into RGB 3-plane. Then each plane were divided. Step 4: Repeat Step 1 to Step 3, until all bit. 4×4. into. blocks. to. generate. 4096. stream of IVQ indices and sorted. non-overlapping 16-D training vectors, and were. codebooks is run out.. trained using the proposed spread GHNN. Step 5: The employee replace bit was hidden at. (SGHNN) method to generated better codebook. position bit 3 in the selected 8 bits. based on VQ. To show the reconstruction. coefficient.. performance,. The extraction step of original color image from embedded color image is similar to the. evaluated. the. by. resulting. the. average. images PSNR. were among. three-color planes is. process of the embedded algorithm. The extraction step is described below.. 3615. $. =. Step 1: Transform the embedded color image to frequency domain by HT. Step 2: Use the same set of random numbers, which is applied in the embedding process. Step 3: Apply the random number to find the extract location of the HT block in the. 3615 5 + 3615 * + 3615 % 3. (9). where 3615 5 , 3615 * , and 3615 % are the for. PSNR. red,. green,. and. blue. planes,. respectively, and the resulting images were evaluated subjectively by the Peak Signal to Noise Ratio (PSNR) that is defined for images of size N×N as. original disguise color image. Step 4: Extract 8 bits data from each HT block by inverse embedded bit stream of IVQ. 3615 = 10 ORJ10. indices and codebooks. Step 5: Rearrange IVQ indices and codebooks to original color image. Step 6: Rebuilt original color image.. 4. Experimental Results Based on the proposed color image hiding method, we developed a SGHNN algorithm to compress color image and HT-based digital watermarking software to color image hiding. The relative compression efficiency and hiding empirical test are shown as follows.. 4.1 Compression Efficiency The codebook design is the primary problem in image compression based on Vector. where. H2. 255 × 255 H2. (10). is the mean squared of the. reconstructed image error and 255 is the peak gray level, respectively. Table 1 shows the PSNRs of the “House”, “Girl”, and “couple” images reconstructed from the codebook of size 128 designed by the spread GHNN method each plane. From the simulated results, the proposed SGHNN method can produce good reconstructed color image quality.. 4.2 Hiding Empirical Test To show the feasibility of the proposed color image hiding method, we employed the 256 × 256 “Couple” color image as our original color image. To camouflage this original color.

(6) image, we employed the 256 × 256 “Tree” color image as the disguise color image. Figure 1. 1983. [2] N. Bourbakis and C. Alexopoulos, “Picture. displays the experimental results. Pictures in the. data. encryption using scan patterns,”. Figure 1 (a) is the “Couple” original color image,. Pattern Recognition, vol. 25, pp. 567-581,. Figure 1 (b) is the “Tree” disguise color image,. 1992.. Figure 1 (c) is embedded “Tree” color image. [3] T. S. Chen, C. C. Chang, and M. S. Hwang,. whose average PSNR is 38.8602 dB, and Figure. “A Virtual Image Cryptosystem Based upon. 1 (d) is extracted and reconstructed “Couple”. Vector Quantization,” IEEE Trans. On. original color image whose average PSNR is. Image Processing, vol. 7, no. 10, pp.. 29.0931 dB. Experimental results show that the. 1485-1488, 1998.. embedded color image is unobtrusiveness and. [4] P. P. Dang and P. M. Chau, “Image. the extracted and reconstructed color image has. Encryption for Secure Internet Multimedia. acceptable quality.. Applications,”. 5. Conclusions and Future Work In this paper, we present a novel color image hiding technique based on interpolative VQ through a spread grey-based competitive Hopfield neural network and HT-based digital image watermarking embedded process. The goal is to offer secure communication in the internet through compress the original color image into another disguise color image. The presented approach allows color image can be compressed with high compression ratio, and the security of transmission process in the internet is enhanced. Experimental results show that the embedded color image is unobtrusiveness and the extracted and reconstructed original color image has acceptance quality. However, the timing measurements, there is a need to build a hardware. system,. which. exploits. parallel. processing to speed up the color image hiding. The hardware implementation of SGHNN algorithm will be our future work.. IEEE. Transactions. on. Consumer Electronics, vol. 46, no. 3, pp. 395-403, 2000. [5] C. C. Chang, M. S. Hwang, and T. S. Chen, “A New Encryption Algorithm for Image Cryptosystems,” Journal of Systems and Software, pp. 83-91, 2001. [6] C. Y. Lin, C. H. Chen, and J. S. Lin, “VQ Codebook. Design. Using. a. Genetic. Competitive Learning Network,” The 13th IPPR. Coferenceon. Graphics. and. Computer Image. Vision,. Processing,. pp.362-369, 2000. [7] C. Y. Lin, and C. H. Chen, “Image Compression using Grey-Based Neural Networks Domain,”. In. the. 2001. Wavelet. Transform. National. Computer. Symposium, vol. 4, pp. D083-D090, 2001. [8] C. Y. Lin, ”Color Image Compression Using Frequency-Sensitive Neural Networks with Wavelet Decomposition,” Chin-Yi Journal, vol. 20, no. 1, pp. 153-163, 2002. [9] P. C. Chung, C. T. Tsai, E. L. Chen, and Y. N. Sun, “Polygonal approximation using a. References [1] D. E. R. Denning, Cryptography and Data Security. Reading, MA: Addison-Wesley,. competitive Hopfield neural network,” Pattern. Recognition,. vol.. 27,. pp..

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(8) (a) Original color image. (b) Disguise color image. (c) Embedded color image. (d) Extracted & rebuilt original color image. Fig. 1 Experimental test for the proposed color image hiding. Color Image Hiding Using Neural Networks with Grey Relation Based on Interpolative Vector Quantization 應用插補向量量化之灰關聯神經網路於彩色影像藏密技術 Chi-Yuan Lin1,2 (林基源) and Chin-Hsing Chen1 (陳進興) 1. Department of Electrical Engineering, National Cheng Kung University, Tainan, 70101 Taiwan, R.O.C. (國立成功大學電機工程系) 2 Department of Electronic Engineering, National Chin-Yi Institute of Technology, Taichung, 41111 Taiwan, R.O.C. (國立勤益技術學院電子工程系) E-mail: [email protected]. 摘要本篇論文提出㆒個應用灰關聯競爭式霍普神經網路與 Hadamard 域數位浮水印技術於彩色影像藏密。目的是使用壓縮原始彩色影像並嵌入另㆒張偽裝彩色影像以提供安全的網際網路通信。我們的方法包括使用㆒個植基於插補向量量化之灰關聯競爭式霍普神經網路之彩色影像壓縮技術，然後再利用 Hadamard 域浮水印技術嵌入原始彩色影像插補向量量化之索引值與排序之編碼簿進㆒張偽裝彩色影像，以至於設計出㆒套安全可行的彩色影像藏密技術。. 關鍵字：插補向量量化 (Interpolative vector quantization) ，灰色理論 (Grey theory)，神經網路 (Neural networks)，Hadamard 轉換 (Hadamard transform)。.

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