https://doi.org/10.31449/inf.v44i1.2042 Informatica 44 (2020) 75–84 75 A Robust Image Watermarking Scheme Based on the Laplacian Pyramid Transform Nguyen Chi Sy, Ha Hoang Kha Faculty of Electrical & Electronics Engineering, Ho Chi Minh City University of Technology, VNU-HCM, Vietnam E-mail: chisy.nguyen@gmail.com, hhkha@hcmut.edu.vn Nguyen Minh Hoang Saigon Institute of Information Communication Technology E-mail: nmhoang@gmail.com Keywords: robust watermarking, Laplacian pyramid, framing pyramids Received: November 20, 2017 This paper is concerned with the digital image watermarking techniques to protect intellectual property and to authenticate digital images. Different from the most conventional methods using the discrete co- sine transforms (DCT) and discrete-wavelet transforms (DWTs), this paper exploits the improved Lapla- cian pyramid transform to develop a new image watermarking scheme in which the improved Laplacian pyramid transform is used to decompose and reconstruct the host image. Then, to select an appropriate watermarking solution, we investigate the various frequency sub-band regions with different the levels and strength factors to perform the watermark embedding. Finally, we conduct experiments to investigate the invisibility and robustness of the proposed algorithm in terms the peak signal-to-noise ratio (PSNR), normalized correlation (NC), and structural similarity index (SSIM). Experimental results showed that our proposed scheme offers good robustness and invisibility. As compared to the watermarking schemes using the curvelets, our watermarking scheme is more robust for the lossy JPEG compression and Gaussian low pass filtering attacks. In addition, our method is also efficient in terms of computational time. Povzetek: ˇ Clanek predstavlja novo obliko zašˇ cite slik s pomoˇ cjo Laplacove piramidne transformacije. 1 Introduction Since the rapid development of communication networks and advances in digital signal processing have lead to the multimedia piracy issues, copyright protection of multime- dia products has become an extensive research topic. To protect content of the multimedia data from the modifi- cation and to provide content authentication, watermark- ing methods have been used [1, 2, 3]. The watermarking method is to embed or hide digital information, known as watermark, into a multimedia product. Then, one can ex- tract the watermark data when necessary for verifying the authenticity or the integrity of the carrier signals, identify- ing its owners, or tracing copyright infringements. The dig- ital watermarking schemes can be applied to various digital multimedia data such as audio, image and video. In this pa- per, we focus on the digital watermarking for digital image. 1.1 Related works Watermarking methods for digital images can be imple- mented in spatial domain or in transform domains. Wa- termarking schemes in spatial domain directly modify the gray level values of pixels. It has been known that the wa- termarking methods in spatial domain are ineffective since the watermarks can be easily destroyed by common sig- nal processing operations [4]. To overcome this drawback, transform domain based watermarking schemes have been actively studied [5]. With regards to transform domain based watermarking schemes, two typical transforms that have been widely used are discrete cosine transform (DCT) and discrete wavelet transform (DWT) (see, for example, [3, 6, 7, 8, 9], and references therein). In general, the de- sired properties of watermarking schemes are the robust- ness, the invisibility and the capacity [10]. However, there are tradeoffs between these desirable properties. Reference [3] showed that the DCT based watermarking techniques are superior to ones based on spatial domain in terms of ro- bustness. In addition, reference [6] demonstrated that DCT based watermarking schemes are robust against such the common signal processing attacks as low-pass filtering, re- ducing image quality (blurring), and adjusting contrast and brightness. However, DCT based watermarking techniques are unsustainable with the geometric transform attacks, for example, rotation, rescaling, and cutting operations [9]. Al- ternatively, by using the wavelet transform into watermark- ing schemes, the authors in [3] showed that watermarking schemes based on wavelet transform outperform those on DCT approaches. It should be noted that in compression and denoising applications, the coefficients in the transform domain are quantized or performed thresholding operations and, thus, there exist errors in reconstructed images. 76 Informatica 44 (2020) 75–84 S.C. Nguyen et al. Recently, the directional transforms have been exploited in the watermarking schemes. In [11], the authors in- troduced a digital image watermarking scheme using the curvelet transform domain. By using the scale distribution, Human Visual System (HVS) and curvelet coefficients, they selected the appropriate positions to insert the water- mark. In their method, the binary watermark of21 21 was used. By experimental results, they showed that the embed- ding watermark in the curvelet domain ensures robustness and invisibility. In addition, they also indicated that water- marking in the curvelet domain offers the improved robust- ness and invisibility as compared to those in the ridgelet domain. On the other hand, reference [12] proposed a digi- tal image watermarking algorithm operating in the fast curvelet transform in which they selected the medium fre- quency coefficients to embed the binary watermark image of32 32 pixels. In [12], the authors illustrated that their proposed watermarking scheme is good at both invisibil- ity and security. In addition, experiment results therein showed that their watermarking scheme offers good robust- ness against noise, cropping, filtering, JPEG compression and other attacks. Reference [13] proposed a blind water- marking based on the curvelet transform domain. In or- der to achieve both invisibility and robustness, many dif- ferent scales of curvelet transform domain have been in- vestigated to choose the appropriate scales to embed the watermark. Experimental results showed the advantages of their method as compared to a watermarking scheme in the DCT-DWT combined domain for the lossy JPEG compression attacks, speckle and Gaussian noise. Alter- natively, the authors in [14] proposed Laplacian pyramid (LP) scheme to represent multi-resolution for images. The advantages of the LP scheme are its simplicity and low computation complexity. However, there exists some draw- backs in the LP schemes, such as implicit oversampling [15]. The authors in [15] proposed an improved Lapla- cian pyramid (LP) scheme by exploiting an efficient filter bank (FB). This approach is proved to be more efficient than the conventional methods for the signal reconstruction degraded by noise. 1.2 Motivation and contributions Motivated from the advantages of an improved Laplacian pyramid (LP) scheme in [15] and inspired by the works in [11, 12, 16], we develop a blind watermarking algorithm in improved LP domain in which the symmetric bi-orthogonal and the new reconstruction methods are used. More specifi- cally, we propose a blind watermarking using the improved Laplacian Pyramid transform. To balance the invisibility and the robustness, we exploit the low frequency and the mid frequency regions to embed the watermark. We in- vestigate the various levels and strength factors to choose the appropriate values. The watermark is a binary image whose size is 32 32. To evaluate the performance of the watermarking schemes, we use the performance met- rics as the peak signal-to-noise ratio (PSNR), normalized correlation (NC) and the structural similarity index (SSIM) to measure the invisibility and the robustness of the algo- rithms. Our experimental results showed that the proposed watermarking scheme offers high invisibility and robust- ness. As compared to the watermarking schemes based on curvelets, the proposed algorithm has better invisibility and robustness for the lossy JPEG compression attack. The rest of the paper is organized as follows. In Sec- tion 2, we introduce a proposed watermarking scheme in which the improved Laplacian pyramid and a new recon- struction using projection are used. Then, watermark em- bedding and extracting schemes with selective levels and strength factors are introduced as well. Section 3 presents experimental results and discussions. Finally, the conclud- ing remarks are presented in Section 4. The contributions in this paper have been partly pre- sented in the 2017 International Conference on Recent Ad- vances in Signal Processing, Telecommunications & Com- puting [17]. 2 Proposed watermarking scheme using Laplacian pyramid transform In this section, we present a blind watermarking scheme. The embedding and extracting watermark algorithms are shown in Figure 1 and Figure 2, respectively. In our blind watermarking scheme, the host image is firstly analyzed into improved LP coefficients by Laplacian pyramid tool- box. We present the improved LP transform in detail in 2.1. To enhance the security for the watermark, we use the Arnold transform on the watermarks which shall be described in 2.2. The embedding scheme in detail is ex- plained in 2.3 and the extracting scheme in detail is de- scribed in 2.4. 2.1 Laplacian pyramid and novel reconstruction method 2.1.1 Burt and Adelson’s Laplacian Pyramid The block diagram for analysis and synthesis of the LP is shown in Figure 3 in which x is the input signal, output c is a coarse approximation while output d is a difference between the original signal and the prediction p [14, 15]. First, using low-pass filtering and down sampling yields a coarse approximation of the original. The coarse approxi- mation signal is given by c[n] = X k2Z d x[k]h[Mn k] = D x; e h[: Mn] E (1) wheren;k2 Z d ;h[n] = h[ n]. The coarse components are up-sampled and filtered to yield the prediction compo- A Robust Image Watermarking Scheme. . . Informatica 44 (2020) 75–84 77 nent which is given by p[n]= X k2Z d c[k]g[n Mk]: (2) In terms of matrices and vectors, the coarse and prediction components are expressed as c = Hx and p = Gc where x = (x[n]:n2Z d ),G andH correspond toG("M) and H(# M), respectively. Then, the difference between the Figure 1: The proposed watermark embedding scheme original signal and this predicted counterpart, known as the prediction error, is defined by d = x p = x GHx = (I GH)x: (3) Accordingly, we can rewrite the analysis operator of LP as c d y = H I GH A x: (4) Figure 2: The proposed watermark extracting scheme. The inverse transform of the LP is shown Figure 3(b) in which^ x =Gc+ d and, thus, one has ^ x = G I c d : (5) It has been shown in [15] that LP can be perfectly recon- structed with any pair of filtersH andG. 2.1.2 Reconstruction using projection A new reconstruction method is shown in Figure 4 [15]. From Figure 4, the improved inverse transform of LP can be written as ^ x = G I GH c d : (6) LetS 2 = G I GH be a transform matrix for the reconstruction algorithm. From Equations (4) and (6), we haveS 2 A =I GH +(GH) 2 . Thus,S 2 is a left inverse ofA if and only ifGH = (GH) 2 , i.e.,GH is a projector. The projection condition is HG =I (7) 78 Informatica 44 (2020) 75–84 S.C. Nguyen et al. Figure 3: The typical Laplacian pyramid transform: (a) Analysis scheme: (b) Synthesis diagram. or D e h[: Mk];g[: Ml] E = [k l]8k;l2Z d : (8) Any filters H and G are called bi-orthogonal filters if they satisfy condition (8). The reconstruction scheme in Fig- ure 4 is equivalent to an inverse transform of the LP if and only if two filters H and G are bi-orthogonal with given sampling latticeM. That is, the prediction operator of the LP(GH) is a projector. In this paper, we use the9 7 bi- orthogonal filters whose coefficients are shown in Table 1. It is important to evaluate the reconstruction performance of the two methods in Figure 3(b) (namely, REC-1) and Figure 4 (REC-2). Suppose that one wants to approximate x given^ y = Ax+ . Without information about the error , ^ x is chosen such that the residualkA^ x ^ yk is minimized. Using this measurement to evaluate the reconstruction per- formance, reference [15] showed that REC 2 outper- formsREC 1. Figure 4: New reconstruction diagram for the LP scheme [14]. 2.2 The Arnold transform To provide a improved security for the watermark, the Arnold transform is adopted to make the watermark uncer- tain. With the Arnold transform, the watermark cannot be defined even when it is detected. This transform also im- proves the robustness of the watermark. The Arnold trans- form function is given by [12] x 0 y 0 = 1 1 1 2 x y modN (9) whereN is the watermark image size and the point(x 0 ;y 0 ) is a shifted version of point(x;y). 2.3 The watermark embedding scheme To embed the watermark into the LP transform domain, the improved LP decomposes the host image into multi- scale images. Since the Human Vision System (HVS) is very sensible to the low frequency coefficients, the wa- termark should be embedded into the high frequency co- efficients in order to increase invisibility. However, the common image processing attacks normally affect the high frequencies of the image signals. Thus, robustness is im- proved if the watermark is inserted into the low frequen- cies. It is worth noting that robustness plays an important role for applications of protecting digital image copyrights. Thus, to increase the embedded watermark size and to en- hance the robustness of the proposed algorithm, we have investigated the embedding of watermark into the predic- tion error coefficients d at both low and middle frequencies from level number 5(d 5 ) (from low frequency to high fre- quency: 5;4;3;2;1) as shown in Figure 5. The scheme for embedding watermark is described in detail in Algo- rithm 2 in which ‘ is the decomposed level; d ‘ is image of the prediction error at level ‘; p 1 and p 2 are position parameters of d l ; k is position parameter of watermark. FunctionmoveNext(d(‘;p 1 ;p 2 )) returns the next coeffi- cient ofd(‘;p 1 ;p 2 ), is a metric of embedment strength, max(d ‘ ) is the largest coefficient of prediction error of level ‘. Each bit of binary watermark is embedded in an improved LP coefficient. This coefficient is determined as follows. In each level (‘) selected to embed the watermark, we calculate a threshold value T ‘ = max(d ‘ ). The value ofT ‘ affects on the invisibility and robustness of wa- termarking schemes [11]. If the value of T ‘ is large, ro- bustness will be strong, vice versa. The value of belongs to 0 < 1. Because the low frequency coefficients are used to embed the watermark in the proposed method, to balance between the invisibility and the robustness, the value of is set to0:2 [16] for all levels. The selected co- efficient to embed a bit of watermark depends on the value of embedded bit and the value of examining coefficient as compared withT ‘ . If it is not the case where the coefficient do not satisfies the predefined conditions, the next coeffi- cient will be considered. The positions of the selected co- efficients are recorded in order to reuse in the watermark extracting scheme. The watermark embedding scheme is summarized in Algorithm 2. A Robust Image Watermarking Scheme. . . Informatica 44 (2020) 75–84 79 Table 1: The9 7 bi-orthogonal filters with coefficients. n 0 1 2 3 4 h[n] 0:852699 0:377403 0:110624 0:023894 0:037828 g[n] 0:788486 0:418092 0:040689 0:064539 2.4 An algorithm for extracting watermarks To extract the watermarks, the watermarked image firstly is transformed into the improved LP domain. Based on the information recorded in Algorithm 2 about the positions selected to embed the binary watermark, we calculate and determine whether the bit at this position is bit 0 or bit 1. Second, as similar as in the scheme for embedding water- mark, the threshold value is calculated by Equation (11). Third, we obtain sequently the positions recorded in the scheme for embedding watermark to seek the coefficient selected to embed a bit watermark. Finally, each coefficient will be processed and compared to the parameterT ‘ 0 to de- cide whether the bit embedded in this coefficient is bit0 or bit 1. The description in detail of the extracting algorithm is represented in Algorithm 3 in which‘ is the decomposed level; d ‘ 0 is image of the prediction error at level‘;p 1 and p 2 are position parameters of d ‘ ;k is position parameter of watermark. 2.5 Performance metrics of an image watermarking algorithm To measure the invisibility and robustness of the water- marking scheme, four parameters, namely the ratio of peak signal to noise (PSNR), the normalized correlation (NC), the structural similarity index (SSIM) and the execution time for embedding watermark and extracting watermark are typically considered [11, 12]. To assess the difference between the original image and the processed or attacked one, we can use three first metrics. Assume that the dimen- sion of the images isM N and the pixels of the original image and of the watermarked images areX ij andW ij , re- spectively. To measure the invisibility between the original gray image and the watermarked one, we can use the PSNR defined by PSNR = 10log 10 (255) 2 MSE dB (12) where the mean square error (MSE) is given by MSE = 1 M N M X i=1 N X j=1 (X ij W ij ) 2 (13) On the other hand, the NC can measure the difference be- tween original watermark and extracted watermark. Thus, to assess the robustness between the original watermark Figure 5: The results of decomposition host image by using the improved LP transform with 5 levels, and images of improved LP. and recovered watermark, the NC can be used. The for- mula of NC is defined by NC = M P i=1 N P j=1 W oij W rij s M P i=1 N P j=1 W 2 oij s M P i=1 N P j=1 W 2 rij (14) where the pixels of the original watermark and the ex- tracted watermark image of M N dimension are W oij andW rij , respectively. It is obvious that NC has the values from0 to1, and NC value of1 reveals the best robustness. The robustness of watermarking schemes is also reflected by the NC when watermarked image is attacked on. Structural Similarity index (SSIM) is commonly used to measure the similarity between two images [18]. Three components including luminance, contrast and structures are compared to compute SSIM. The value of SSIM is be- tween 0 and 1, where 1 means two image identical and 0 means two image totally different. At each step, the local window is used to calculate the local statistics and SSIM index. Final local SSIM measure is the product of three 80 Informatica 44 (2020) 75–84 S.C. Nguyen et al. Algorithm 2 : The proposed scheme for embedding water- mark 1: Analyze the host image by using the improved Lapla- cian pyramid transform toolbox [15] as shown in Fig- ure 5 (decomposed level = 5). The binary watermark is embedded into the prediction error from level num- ber5 until the last bit of watermark is processed; 2: Scramble the watermark by the Arnold transform. 3: In each level(‘ = 5;4;3;2;1), we calculate the thresh- old by using the following equation: T ‘ = max(d ‘ ) (10) wheremax(d ‘ ) is the largest Laplacian pyramid coef- ficients of level‘ and is a strength parameter. 4: Set ‘ = 5, k = 1, W(1) is the first bit of the binary watermark 5: while‘> 0 andk<= size of(W) do 6: ifW(k) == 0 then 7: while NOT (0 < d(‘;p 1 ;p 2 ) < T ‘ 2 or T ‘ < d(‘;p 1 ;p 2 )< 3T ‘ 2 ) do 8: moveNext(d(‘;p 1 ;p 2 )); 9: end while 10: Set d(‘;p 1 ;p 2 ) = d(‘;p 1 ;p 2 ) mod(d(‘;p 1 ;p 2 );T ‘ )+ T ‘ 4 ; 11: else 12: while NOT( T ‘ 2