Contribution of neural networks in image steganography, watermarking and encryption

IET Image ProcessingVolume 17, Issue 2 p. 463-479 ORIGINAL RESEARCHOpen Access Contribution of neural networks in image steganography, watermarking and encryption Maminiaina Alphonse Rafidison, Corresponding Author Maminiaina Alphonse Rafidison [email protected] orcid.org/0000-0001-7734-4563 Telecommunication-Automatic-Signal-Image-Research, Laboratory/Doctoral School in Science and Technology of Engineering and Innovation, University of Antananarivo, Antananarivo, Madagascar Correspondence Maminiaina Alphonse Rafidison, LOT II H 46 BIS Ground Floor Ambatokary Faravohitra, Antananarivo 101, Madagascar. Email: [email protected]Search for more papers by this authorSabine Harisoa Jacques Rafanantenana, Sabine Harisoa Jacques Rafanantenana Telecommunication-Automatic-Signal-Image-Research, Laboratory/Doctoral School in Science and Technology of Engineering and Innovation, University of Antananarivo, Antananarivo, MadagascarSearch for more papers by this authorAndry Harivony Rakotomihamina, Andry Harivony Rakotomihamina Telecommunication-Automatic-Signal-Image-Research, Laboratory/Doctoral School in Science and Technology of Engineering and Innovation, University of Antananarivo, Antananarivo, MadagascarSearch for more papers by this authorRajaonarison Faniriharisoa Maxime Toky, Rajaonarison Faniriharisoa Maxime Toky Telecommunication-Automatic-Signal-Image-Research, Laboratory/Doctoral School in Science and Technology of Engineering and Innovation, University of Antananarivo, Antananarivo, MadagascarSearch for more papers by this authorHajasoa Malalatiana Ramafiarisona, Hajasoa Malalatiana Ramafiarisona Telecommunication-Automatic-Signal-Image-Research, Laboratory/Doctoral School in Science and Technology of Engineering and Innovation, University of Antananarivo, Antananarivo, MadagascarSearch for more papers by this author Maminiaina Alphonse Rafidison, Corresponding Author Maminiaina Alphonse Rafidison [email protected] orcid.org/0000-0001-7734-4563 Telecommunication-Automatic-Signal-Image-Research, Laboratory/Doctoral School in Science and Technology of Engineering and Innovation, University of Antananarivo, Antananarivo, Madagascar Correspondence Maminiaina Alphonse Rafidison, LOT II H 46 BIS Ground Floor Ambatokary Faravohitra, Antananarivo 101, Madagascar. Email: [email protected]Search for more papers by this authorSabine Harisoa Jacques Rafanantenana, Sabine Harisoa Jacques Rafanantenana Telecommunication-Automatic-Signal-Image-Research, Laboratory/Doctoral School in Science and Technology of Engineering and Innovation, University of Antananarivo, Antananarivo, MadagascarSearch for more papers by this authorAndry Harivony Rakotomihamina, Andry Harivony Rakotomihamina Telecommunication-Automatic-Signal-Image-Research, Laboratory/Doctoral School in Science and Technology of Engineering and Innovation, University of Antananarivo, Antananarivo, MadagascarSearch for more papers by this authorRajaonarison Faniriharisoa Maxime Toky, Rajaonarison Faniriharisoa Maxime Toky Telecommunication-Automatic-Signal-Image-Research, Laboratory/Doctoral School in Science and Technology of Engineering and Innovation, University of Antananarivo, Antananarivo, MadagascarSearch for more papers by this authorHajasoa Malalatiana Ramafiarisona, Hajasoa Malalatiana Ramafiarisona Telecommunication-Automatic-Signal-Image-Research, Laboratory/Doctoral School in Science and Technology of Engineering and Innovation, University of Antananarivo, Antananarivo, MadagascarSearch for more papers by this author First published: 06 October 2022 https://doi.org/10.1049/ipr2.12646AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract In front of information fishing, it is necessary to protect the information to be circulated over public channel. The goal of this paper is to propose an approach which inserts a logo inside of cover image and having three different possible results according to user's needs. The algorithm can perform steganography, watermarking or host encryption. This technique is based on singular value decomposition (SVD) and discrete wavelet transform (DWT) composed by three steps: pre-processing, embedding and extraction/decryption. Reference matrix and reference parameter are the two factors deciding the operation and the intervention of neural networks makes the choice of their parameters easier according to the desired result. For measuring the steganography performance, the authors adopt the structural similarity index measure (SSIM) which calculates the similarity between original and watermarked image and peak signal-to-noise ratio. For watermarking, the normalized correlation (NC) coefficient investigates the correlation between the original watermark and the extracted watermark. Attacking the watermarked image with common attacks used by previous publication searchers, the value of SSIM and NC coefficient are closed to one. Regarding peak signal-to-noise ratio, the overall score is around 61.73 dB. The performance score is not negligible also for the encryption method. 1 INTRODUCTION Steganography is from the Greek words: 'stegos' meaning 'cover' and 'grafia' meaning 'writing' defining it as 'covered writing' [1]. Initially, in order to communicate secretly, two warlords used slaves. They tattooed the message on their skulls and then the hair grew back. The slave was then sent to the correspondent thus deceiving the enemy. Once shaved the message was perfectly legible. Although very rudimentary, this method is a fairly good symbol of what steganography is. Over time, steganography has been used very often and has opened up to a large number of forms. The image steganography is inspired by this statement; then the logic is to insert a secret information in host image without arousing suspicion [2]. Watermarking or tattoo is a technique including data authentication, protection of ownership. Mainly, it can easily be defined as the process of embedding watermarks in digital image using an appropriate algorithm. The objective purpose of watermark is large including the identification of work and discourages its unauthorized use [3]. The definition of image encryption here is an encryption of medium with hidden information. It means that the original can be reconstructed even encrypted is facing a different attack. We are talking about algorithm robustness capability. In this paper, we will propose an efficient approach able to perform image steganography, watermarking or encryption based on Singular Value Decomposition (SVD), Discrete Wavelet Transform (DWT) and neural networks. To accomplish this, we introduce the notion of reference parameter α and reference matrix A w ${A}_w$ which define the type of operation to be done. Choosing these parameters seems not evident, so the Pulse Couple Neural Networks (PCNN) and perceptron must intervene. PCNN role extracts the pertinent information present in image to form the image signature and from this, the perceptron fully connected calculates the value of reference parameter. To validate our method, we applied it to Lena, Peppers, Barbara, Baboon, Boat, Tunnel, Jet, House, Cameraman, Fruits and Cat. They are taken by the related works cited in the next paragraph as experimental images; then we must keep them for performance comparison. The main contributions of this work are the following: The simplicity of the method because there are just a few parameters required by embedding and extraction modules and for this reason, it allows us to have an optimal time response. Such kind of solution may be supported by embedded systems. The neural networks know in advance the appropriate reference parameter ensuring the best performance of the operation according to the characteristics of host image. This one approach has an ability to handle three operations: steganography, watermarking or encryption image. It is up to the user to command the neural networks module by choosing the operation type in neural input layer. Comparing with related existing studies performance, we have a slight improvement. The rest of the paper is organized as follows: The second paragraph describes the state of art of steganography, watermarking and encryption followed by the methodology and test/performance comparison. The motivation and discussion are the object of paragraph 5 and finally, paragraph 6 concludes this paper. To ensure a good understanding of this research, Table 1 presents the list of abbreviations and definitions. TABLE 1. Table of abbreviations Abbreviation Definition DCT-SVD Discrete cosine transform–singular value decomposition DWT Discrete wavelet transform HH High high HL High low JPEG Joint photographic experts group LH Low high LL Low low LSB Least significant bit LWT-DCT-SVD Lifting wavelet transform–DCT-SVD MSE Mean squared error NC Normalized correlation NPCR Number of pixels change rate PCNN Pulse couple neural networks PSNR Peak signal-to-noise ratio SIPI Signal and image processing institute SNR Signal-to-noise ratio SSIM Structural similarity index measure SVD Singular value decomposition UACI Unified average changing intensity 2 LITERATURE SURVEY A digital image steganography research was done by Pan et al. [4] in 2022 with title 'Double-Matrix Decomposition Image Steganography Scheme Based on Wavelet Transform with Multi-Region Coverage' and the experimental results demonstrate that the proposed technique has a good performance in imperceptibility of medium and best quality of extracted secret image after some attacks such as Gaussian noise, salt and pepper noise, speckle noise, JPEG compression, JPEG2000 compression, sharpening attack, histogram, equalization and motion blur. The method consists by transforming the host image by multi-wavelet transform and the non-sensible or hidden regions selected in the wavelet domain are exploited for mark insertion. These regions undergo Arnold transform, Hessenberg decomposition, singular-value decomposition and the embedding is done by intensity factor. Authors did the experience with Lena, Baboon, Peppers and the result will be detailed in test and performance paragraph. Zaidan [5] in 2020 proposed a new approach of steganography in paper entitled 'Digital Image Steganography Scheme Based on DWT and SVD'. In this scheme, the cover image is going through two successive DWT to obtain the high frequency band HL2. To embed the greyscale secret image, the technique used SVD which is applied on the HL2 band. The method has a good robustness and imperceptibility even passing in different known attacks such as JPEG compression, filtering, cropping and noise addition. The test validation was done with Cameraman, House, Boats and Peppers. Singh in 2019 wrote a paper entitled `High PSNR based Image Steganography', the approach is similar as ours in terms of mathematic tools [6]. The results are showing comparison in between Discrete Cosine Transform (DCT)-SVD- and Lifting Wavelet Transform (LWT)-DCT-SVD. PSNR of proposed methodology is high as compared to DCT-SVD. Tejal and Rao [7] in 2017 published a paper entitled 'Advanced Image Steganography Technique using DWT and SVD with High PSNR' and the work consists of hiding within cover image. This cover image is transformed to Red Green Blue (RGB) and each channel passes through DWT to obtain four frequencies low low (LL), low high (LH), high low (HL) and high high (HH) frequencies components. HH is not sensible on human vision; then they apply SVD transform to increase the security level before inserting the mark using LSB update. The PSNR average was around 84 tested with Baboon, Lena, Peppers, Sail Boat and Tunnel. Nevriyanto et al. [8] in 2017 presented a steganography technique combining DWT and SVD. The text message is converted into binary image first and processed by Haar transform, and the same operation is done for cover image; then the HH of both images are decomposed to SVD. The second step consists of combining the three components of the matrix SVD and inserting the secret image into the cover image to form the stegano image. To extract the mark, they just apply IDWT. The result of PSNR obtained from DWT and SVD is 57.0519 and 56.9520, while the result of mean squared error (MSE) is 0.1282 and 0.1311. They conclude that the performance of the combination of DWT and SVD is better than the LSB, DCT and DWT methods. Yasmeen and Uddin in 2021 [9] published an efficient watermarking approach based on the LL and HH edges of DWT–SVD. For watermark embedding, DWT transform level 4 was applied to host image and level 3 for watermark image. The respective result is going through first- and second-level SVD on LL4 and HH4 sub-bands and then combine the first and second levels of SVD. They add an embedding process module to insert the mark and apply SVD, DWT inverse to obtain the watermarked image. The extraction algorithm is the same but the watermarked and host image pass via DWT transform level 4. The proposed method got 43.8362 as PSNR for Lena greyscale watermarked image and 34.7266 for colour. Regarding the normalized correlation (NC), it was 0.9934 and 0.9822, respectively, for extracted watermark. A similar conception work was done by Wang and Zhao [10] in 2020 in which the cover image is divided by first-level Haar DWT and the SVD is added to the LH and HL sub-bands. Besides, the watermark is split into equal halves and LH and HL are modified before being inserted in the host image. The watermark is extracted from the reverse process. It is noted that this approach only demonstrates robustness for histogram equalization. Another image watermarking research was published by Kusumaningrum et al. [11] in 2020 entitled 'DWT-SVD Combination Method for Copyrights Protection'. The technique remains around the combination of DWT and SVD and it resists Gaussian filters, JPEG compression and noise. The PSNR value with watermark image size 32 × 32 and 64 × 64 which is 59.2656 and 54.7414 dB, respectively. The embedding scheme consists of converting the RGB host image to greyscale, then decomposing it with DWT transform level 2. They are interested only on LL2 sub-band which undergoes SVD decomposition and the greyscale watermark image is inserted into the diagonal matrix. The watermarked image is obtained with DWT inverse transform levels 1 and 2. Pourasad Y, Ranjbarzadeh R, Mardani A [12] in 2021 published a paper in image encryption domain 'A new algorithm for digital image encryption based on chaos theory'. The work deals with a chaotic-based algorithm using characteristics of the chaotic map, SVD and wavelet transform. The encryption process in this algorithm includes two stages. At first, they performed the image diffusion operation. Moreover, by performing the wavelet transform and SVD decomposition, the calculation amount in confusion was considerably reduced by hyper-chaotic sequences. They have tested this method for Lena, Peppers, Barbara, Baboon, and Boat Images from benchmark MATLAB test images. Moreover, the histograms of both input images and encrypted images are depicted. In addition, the encryption performance analysis criteria such as PSNR, NC, Number of Pixels Change Rate (NPCR) and Unified Average Changing Intensity (UACI) are recorded. Based on the results, the correlation value for Lena, Peppers, Barbara, Baboon and Boat is 95.48%, 99.64%, 98.09%, 91.37% and 90.01%, respectively. To evaluate the proposed approach's robustness, the test images are tested against four types of image processing attacks: rotation, Gaussian noise, median filtration and histogram equalization. The results show that the proposed design is associated with higher robustness and NC. In this research, they compared the performance with [13-17]. Note that this literature survey paragraph does not describe all related works in detail, some are listed only as reference. We can remark also that there is no related work performing in the same time the steganography, watermarking and encryption so we will compare the result of these studies with our approach using the same experience materials separately. 3 METHODOLOGY The proposed method is shown in Figure 1. The watermark image must pass through pre-processing module which converts the mark in black and white image and then converts it in vector. This vector combined with host image are processed by embedding module in which the operator must choose between steganography, watermarking and host encryption. The operation key is the combination of matrix reference A w ${A}_w$ and reference parameter α. The determination of these parameters is done by neural networks: PCNN and fully connected neural networks. The training network is based on the prior calculation of performance metrics then select α which corresponds to the high performance. The input layer of fully connected neural networks is constituted by the value produced by PCNN and operation type. The output layer indicates the binary value of α. The output layer indicates the binary value of . We apply the embedding method to insert the secret image in the cover to obtain stegano/watermarked/encrypted image. The details of this algorithm will be shared in the next sub-paragraph. The image resultant may be attacked in the public communication channel; then the quality of extracted information judges the robustness of the method; the quality of medium ensures the imperceptibility in case of steganography and the restored host image for encryption. We should note that A w ${A}_w$ and α are required by extraction algorithm. FIGURE 1Open in figure viewerPowerPoint Proposed method Embedding algorithm First of all, the watermark image M ( l M × c M ) $M( {{l}_M \times {c}_M} )$ must be converted into binary. Once we have a binary image, we reshape it to vector M R ${M}_R$ (1, l M × c M ) ${l}_M \times {c}_M)$ . Concerning the medium image, conversion to RGB is required for image colour and we will exploit only the blue component. Note by I ( l I × c I ) $I\ ( {{l}_I \times {c}_I} )$ the image issued of this operation. It will be divided into ( l I / l M ) × ( c I / c M ) $( {{l}_I/{l}_M} ) \times ( {{c}_I/{c}_M} )$ block B k ${B}_k$ where k ∈ { 1 , 2 , … , ( l M × c M ) } $k \in \{ {1,\ 2,\ \ldots ,( {{l}_M \times {c}_M} )} \}$ . The next step is to apply DWT for each block. L L k , H L k , L H k , H H k = D W T B k $$\begin{equation}\left( {L{L}_k,H{L}_k,\ L{H}_k,H{H}_k} \right) = \ DWT\left( {{B}_k} \right)\end{equation}$$ (1)where L L k , H L k , L H k , H H k $L{L}_k,H{L}_k,\ L{H}_k,H{H}_k$ are respectively the approximate, horizontal, vertical and diagonal sub-bands. Our principal interest is with L L k $L{L}_k$ . We apply SVD on it as follows: U k , S k , V k = S V D L L k $$\begin{equation}\left( {{U}_k,{S}_k,{V}_k} \right) = \ SVD\left( {L{L}_k} \right)\end{equation}$$ (2) L L k = U k × S k × V k T $$\begin{equation}L{L}_k = {U}_k\ \times {S}_k \times \ V_k^T\end{equation}$$ (3)where S k ${S}_k$ is a diagonal matrix with a large singular value contained in its diagonal entries. V k T $V_k^T$ is a conjugate transpose of matrix V k ${V}_k$ . U k ${U}_k$ and V k ${V}_k$ are complex or real unitary matrices, such that U k × U k T ${U}_k \times U_k^T$ and V k × V k T ${V}_k \times V_k^T$ will result in identity matrix. Now, we insert the mark M R ${M}_R$ . No modification is needed when the bit equals 0 but with 1, we should consider the reference matrix A w ${A}_w$ same size as S k ${S}_k$ and reference parameter α. A w = α … 0 ⋮ ⋱ ⋮ 0 … α / 2 $$\begin{equation}{A}_w = \left[ { \def\eqcellsep{&}\begin{array}{@{}*{3}{c}@{}} \alpha &\quad \ldots &\quad 0\\[6pt] \vdots &\quad \ddots &\quad \vdots \\[6pt] 0&\quad \ldots &\quad {\alpha /2} \end{array} } \right]\ \end{equation}$$ (4) S w k = S k + α A w $$\begin{equation}{S}_{wk} = {S}_k\ + \alpha {A}_w\end{equation}$$ (5) L L w k = U k × S w k × V k T $$\begin{equation}L{L}_{wk} = {U}_k\ \times {S}_{wk} \times V_k^T\end{equation}$$ (6) B w k = I D W T L L w k , H L k , L H k , H H k $$\begin{equation}{B}_{wk} = \ IDWT\left( {L{L}_{wk},H{L}_k,\ L{H}_k,H{H}_k} \right)\end{equation}$$ (7) where S w k ${S}_{wk}$ , L L w k , $L{L}_{wk},$ B w k ${B}_{wk}$ are the singular value watermarked, approximate watermarked, block watermarked and I D W T $IDWT$ is the inverse DWT. Re-form the stegano/watermarked/encrypted image I w ${I}_w$ by assembling blocks. I w ${I}_w$ represents the blue component for colour image. According to our testing, a minimum value of α corresponds to steganography operation. Tattoo can be obtained by increasing this reference parameter and the watermark image becomes visible in host or medium image. The large value of α led us to medium encryption. However, finding the correct value of α does not matter because we have an appropriate method to define it based on medium image characteristics. Extraction algorithm The extraction algorithm is similar as the embedding algorithm. We decompose I w ${I}_w$ to ( l M × c M ) $( {{l}_M \times {c}_M} )$ block B k ${B}_k$ . w is the notation index indicating watermarked. We transform each block B w k ${B}_{wk}$ through DWT and the approximate matrix L L w k $L{L}_{wk}$ passes via SVD. L L w k , H L w k , L H w k , H H w k = D W T B w k $$\begin{equation}\left( {L{L}_{wk},H{L}_{wk},\ L{H}_{wk},H{H}_{wk}} \right) = \ DWT\left( {{B}_{wk}} \right)\end{equation}$$ (8) U w k , S w k , V w k = S V D L L w k $$\begin{equation}\left( {{U}_{wk},{S}_{wk},{V}_{wk}} \right) = \ SVD\left( {L{L}_{wk}} \right)\end{equation}$$ (9) To retrieve the watermark image, we have to calculate A w ${A}_w$ using (10) A w = ( S w k − S k ) / α $$\begin{equation}{A}_w = ({S}_{wk}\ - {S}_k)/\alpha \end{equation}$$ (10) To define if the component value of the extracted watermark M R ${M}_R\ $ is 0 or 1, we apply Equation (11); then we reshape M R ${M}_R$ with size l M × c M ${l}_M \times {c}_M$ to obtain the watermark/secret image. M R x = 1 i f det A w ≥ 1 0 o t h e r w i s e $$\begin{equation}{M}_R\ \left( x \right) = \left\{ \def\eqcellsep{&}\begin{array}{@{}*{1}{l}@{}} {1\quad if\det \left( {{A}_w} \right) \ge 1}\\[6pt] {0\quad otherwise} \end{array} \right. \end{equation}$$ (11) Host decryption algorithm When the MR(x) value in Equation (11) equals 0, we keep the value of Swk; otherwise Sk is calculated as follows: S k = S w k − α A w i f det A w ≥ 1 S w k o t h e r w i s e $$\begin{equation} {S}_k = \left\{ \def\eqcellsep{&}\begin{array}{@{}*{1}{l}@{}} {{S}_{wk} - \alpha {A}_w\quad i\!f\det \left( {{A}_w} \right) \ge 1}\\[6pt] {{S}_{wk}\qquad\qquad otherwise} \end{array} \right. \end{equation}$$ (12) Applying Equation (3), we have L L k $L{L}_k$ and then determinate the DWT inverse B k = D W T − 1 L L k , H L k , L H k , H H k $$\begin{equation}{B}_k = DW{T}^{ - 1}\ \left( {L{L}_k,H{L}_k,\ L{H}_k,H{H}_k} \right)\end{equation}$$ (13) Assembling all block B k ${B}_k$ is the last step to obtain the decrypted image. Pulse couple neural network PCNN is a model inspired from a neural mammal model. It has a great potential in image processing mainly for edge detection, segmentation, feature extraction and image filtering [18]. PCNN has receptive field, linking part or modulation and pulse generator. Its architecture is shown in Figure 2. FIGURE 2Open in figure viewerPowerPoint PCNN architecture Mathematically, the feeding and linking part are described in Equations (14) and (15). F i j n = S i j + F i j n − 1 . exp − α F + V F . M ∗ Y n − 1 i j $$\begin{eqnarray}{F}_{ij}\ \left( n \right) = {S}_{ij}\ + {F}_{ij}\left( {n - 1} \right).{\rm{exp}}\left( { - {\alpha }_F} \right) + {V}_F.{\left( {M{\rm{*}}Y\left( {n - 1} \right)} \right)}_{ij}\nonumber\\[-4pt]\end{eqnarray}$$ (14) L i j n = L i j n − 1 . exp − α L + V L . W ∗ Y n − 1 i j $$\begin{eqnarray}{L}_{ij}\ \left( n \right) = {L}_{ij}\ \left( {n - 1} \right).{\rm{exp}}\left( { - {\alpha }_L} \right) + {V}_L.{\left( {W*Y\left( {n - 1} \right)} \right)}_{ij}\nonumber\\[-4pt]\end{eqnarray}$$ (15)where F i j ${F}_{ij}$ is the Feeding compartment of the ( i , j ) $( {i,j} )$ neuron embedded in a 2D array of neurons, and L i j ${L}_{ij}$ is the corresponding linking compartment. Y i j $\ {Y}_{ij}$ 's are the outputs of neurons from a previous iteration [ n − 1 ] $[ {n - 1} ]$ . Both compartments have a memory of the previous state, which decays in time by the exponent term. The constants V F ${V}_F$ and V L ${V}_L$ are normalizing constants. If the receptive fields of M and W change, then these constants are used to scale the resultant correlation to prevent saturation [19]. The states of these two compartments are combined in a second-order fashion to create the internal state of the neuron, U. The combination is controlled by the linking strength, β. The internal activity is calculated by U i j n = F i j n . 1 + β . L i j n $$\begin{equation}{U}_{ij} \left( n \right) = {F}_{ij}\ \left( n \right).\left( {1 + \beta .{L}_{ij}\left( n \right)} \right)\end{equation}$$ (16) The internal state of the neuron is compared to a dynamic threshold, Θ, to produce the output, Y, by Y i j n = 1 , i f U i j n > Θ i j n 0 , e l s e $$\begin{equation}{Y}_{ij}\left( n \right)\ = \left\{ \def\eqcellsep{&}\begin{array}{@{}*{1}{l}@{}} {1,\quad if\ {U}_{ij}\left( n \right) > {\Theta }_{ij}\left( n \right)}\\[3pt] {0,\quad else\ } \end{array} \right. \end{equation}$$ (17) The threshold is dynamic in that when the neuron fires (Y > Θ) the threshold then significantly increases its value. This value then decays until the neuron fires again. This process is described by Θ i j n = Θ i j n − 1 . exp − α Θ + V Θ . Y i j n $$\begin{equation}{\Theta }_{ij} \left( n \right) = {\Theta }_{ij} \left( {n - 1} \right). {\rm exp}\left( { - {\alpha }_\Theta } \right) + {V}_\Theta .{Y}_{ij}\left( n \right)\end{equation}$$ (18)where V Θ ${V}_{{\Theta}}$ is a large constant that is generally more than an order of magnitude greater than the average value of U. The binary image Y may be a segmented image Y s ${Y}_s$ or edge detection Y e ${Y}_e$ as per the iteration. For each type of image, we calculate the entropy (E), energy entropy (EE), logarithm (L) and energy logarithm (EL) as shown in Equations (19) to (22) [20, 21]. E Y s , e = − P 1 l o g 2 P 1 − P 0 l o g 2 P 0 $$\begin{equation}{E}_{{Y}_{s,e}} = \ - {P}_1lo{g}_2\left( {{P}_1} \right) - {P}_0lo{g}_2\left( {{P}_0} \right)\end{equation}$$ (19) E E Y s , e = − P 1 2 l o g 2 P 1 2 − P 0 2 l o g 2 P 0 2 $$\begin{equation}E\ {E}_{{Y}_{s,\ e}} = \ - P_1^2lo{g}_2P_1^2 - P_0^2lo{g}_2P_0^2\end{equation}$$ (20) L Y s , e = − l o g 2 P 1 − l o g 2 P 0 $$\begin{equation}{L}_{{Y}_{s,\ e}} = \ - lo{g}_2{P}_1 - lo{g}_2{P}_0\end{equation}$$ (21) E L Y s , e = − l o g 2 P 1 2 − l o g 2 P 0 2 $$\begin{equation}E{L}_{{Y}_{s,\ e}} = \ - lo{g}_2P_1^2 - lo{g}_2P_0^2\end{equation}$$ (22)where P1 is the probability of 1's in a binary image, and P0 is that of 0's in the binary image. Reference parameter and reference matrix definition method To define the correct value of α and to ensure a best performance and robustness, we elaborate a neural network fully connected having 11 neurons on input layer with 12 neurons as output and 3 hidden layers. The input layer is composed by the operation type (neuron n°1: Steganography, neuron n°2: Watermarking, neuron n°3: host encryption) and the host image characteristics (neuron number 4 to 11) which are the output value of PCNN. The exact structure is presented in Table 2 and Figure 3 explains the processing mechanism of α determination. The hidden layers used sigmoid as an activation function and the initial weight was taken randomly. Concerning the activation function for the output layer, it is a binary step function with predefined threshold which decides if the output neuron is 0 or 1 [22]. The decimal conversion of all output neuron indicates the reference parameter α; then we get the reference matrix A w ${A}_w$ as per Equation (4). TABLE 2. Input layer structure Neuron n° Steganography Watermarking Encryption 1 1 0 0 2 0 1 0 3 0 0 1 4 E Y s ${E}_{{Y}_s}$ E Y s ${E}_{{Y}_s}$ E Y s ${E}_{{Y}