1 Introduction

The fast development of the Internet and multimedia technologies has enabled the ease of multimedia content distribution, communication and reproduction. However, some very crucial issues for multimedia such as illegal copying, distribution, editing and copyright protection have arisen due to these technological advancements [8, 41]. To tackle these problems, digital watermarking has emerged as an obvious solution [8, 11, 12, 33, 44]. The first technology of copyright protection is cryptography where the content is encrypted prior to delivery and a decryption key is provided only to those who have purchased legitimate copies of the content. In addition, cryptography can protect content from manipulation only in encrypted form but once decrypted, the content has no further protection from illegal duplication. Watermarking schemes can be introduced as a standard solution to tackle these increasing requirements. It is a technique that attempts to guard digital content from illegal copying and manipulation even after decryption [13]. Digital watermarks could have a wide range of applications like copyright protection, content authentication, broadcast monitoring, transaction tracking, owner identification, copy control and media forensics [44, 55].

Digital watermarking can be defined as the practice of embedding secret imperceptible piece of information into the multimedia data (i.e., images, videos and audios).The secret imperceptible piece of information is called watermark and the multimedia data in which watermark gets embedded is called cover or host signal [13, 59]. A variety of watermarking schemes have been proposed in literature. Digital watermarking techniques can be categorized in various ways on the basis of criteria like embedding method, visibility, attack resistance etc. Based on attack resistance, digital watermarking is categorized into three classes: robust watermarking, semi-fragile watermarking and fragile watermarking. In these days, the robust digital watermarking has received a great attention. In this type of watermarking, watermark is designed to resist intentional or unintentional manipulations in the host signal [9, 58]. In the fragile watermarking, watermark is intended to be destroyed even after the minor unintentional or intentional manipulation in the host signal [29, 52–54]. In the semi-fragile watermarking, watermarks have the ability to resist unintentional manipulations caused by common image processing operations like JPEG compression and are fragile against intentional manipulations [43, 46]. The main purpose of the robust watermarking is to protect copyright and ownership of the digital data, whereas the fragile watermarking and semi-fragile watermarking are employed to ensure the integrity and content authentication of the digital data [55, 57].

Digital watermarking is categorized into blind, semi-blind and non-blind watermarking, based on the requirements for watermark detection or extraction. The non-blind (or private) watermarking techniques require both the original host image and the secret key(s) to identify the watermark. Semi-blind watermarking techniques require the presence of the secret key(s) and the watermark for watermark extraction. On the other hand, the blind (or public) watermarking schemes require only the secret key(s) for extraction [15].

The watermark techniques can also be broadly classified into two major classes based on the embedding domain: spatial domain techniques and transform domain techniques [20, 57]. Spatial domain techniques are the simplest and in these techniques, the watermark directly applies on pixel intensities of the host signal [20, 31, 51, 52]. On the other hand, transform domain techniques perform the watermarking by changing the transformed domain coefficients of the host signal [20]. The transform domain coefficients can be Discrete Wavelet Transform (DWT) [17, 60], Redundant Discrete Wavelet Transform (RDWT) [14, 16, 36], Discrete Fourier Transform (DFT) [45, 56], Discrete Cosine Transforms (DCT) [6, 22], Singular Value Decomposition(SVD) [35, 39] and Divisive Normalization Transform (DNT) [28, 42] coefficients etc. Typically, the transform domain techniques are more robust in various attacks than the spatial domain techniques [12, 37, 48]. The performance of transform domain techniques can be further improved by joining two or more transform coefficients.

Most of the current literature focus on the performance measures like imperceptibility, robustness and capacity. Inclusion of security along with performance measures is an essential issue in many critical watermarking applications, such as medical image watermarking, authentication of legal documents, fingerprinting and data monitoring. In [31], Lin et al. proposed a lossless watermarking scheme for copyright protection based on 1/T rate forward error correction. This scheme is blind and based on spatial domain. In this scheme, watermark logo was fused with noise bits to improve the security, and later XORed with the feature value of the image by 1/T rate FEC. In [33], Lin et al. proposed a wavelet-tree-based watermarking scheme for copyright protection, using distance vector of binary cluster. In this scheme, wavelet trees were classified into two clusters using the distance vector to denote binary watermark bits so that they exhibit a sufficiently large statistical difference based on the distance vector. This difference is utilized for subsequent watermark extraction. In [32, 34], Lin et al. proposed two blind watermarking scheme for copyright protection based on wavelet coefficient quantization. In the first scheme, the significant difference between the maximum wavelet coefficient and the second maximum wavelet coefficient was utilized for embedding. In the second scheme, watermark was embedded in the local maximum coefficient using different sub-bands.

Many of the existing SVD-based digital watermarking schemes suffer from the false positive detection problem which is referred as the ability to extract an un-embedded watermark from the digital host image. Several authors have conducted experiments on SVD-based watermarking to find the robust watermarking scheme. In literature listed in Table 1, only the singular values of watermark(or singular values of host image and watermark) are embedded into the host image. These approaches cause the false positive detection problem because the SVD subspaces (left and right singular vectors) represent the detailed information about the image whereas singular values only determine the luminance of the image layers produced by left and right singular vectors [3, 23, 62]. These schemes mainly deal with robustness and imperceptibility issues. Jain et al. [23] proposed a reliable SVD-based digital watermarking scheme which was capable to handle the false positive detection problem. In this scheme the principal component of watermark is embedded into the host image rather than singular values of the watermark. Gupta and Raval [16] proposed a DWT-SVD based scheme which was also capable to handle the false positive detection problem. This scheme handles such problem by incorporating signature-based authentication mechanism. Further Bhatnagar et al. [10] proposed a logo image watermarking scheme based on Wavelet Frame Transform, SVD and automatic thresholding. The core idea of this scheme is using reversible random extension transform, to randomly upscale the size of cover image followed by the embedding of logo watermark in the Wavelet Frame domain. After embedding logo watermark, a verification phase is performed with the help of a binary watermark and Toral Automorphism. Second critical problem of digital watermarking scheme is the problem of multiple claims of ownership. If an attacker embeds another illegal watermark to the already watermarked image, proofing the ownership becomes a serious problem. Mohammad et al. [39] suggested a solution to deal with this problem by ensuring to reach the maximum allowable amount of embedded information to prevent the attacker from adding any extra information to the image. However, this solution is not applicable in that watermarking scheme where it requires multiple number of watermarks to be embedded. Further, Run et al. [49] proposed a digital watermarking scheme that solves the ambiguities and false positive detection problem but at the same time it is poor with respect to imperceptibility and robustness of host image. Third common security challenge that watermarking techniques face is keeping the secret message unreadable for unauthorized persons. Cryptography techniques like Arnold transformation [4], chaotic encryption [24] can be used to deals with this problem.

Table 1 SVD based watermarking schemes which are suffering from false positive detection problems
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An important issue related to the efficiency and feasibility of watermarking schemes is blind watermarking. The blind watermarking scheme has a great significance and practical value in many applications where keeping the original image without security is not practical.

In this DWT-SVD based blind watermarking scheme, an effective solution for these challenging problems is proposed and evaluated using gray image watermark. The false positive detection problem is tackled by embedding complete watermark into host image. To tackle the unauthorized reading issue, an attempt is made to encode the watermark using Arnold transformation. Scaling factor plays an important role to control the transparency and robustness of the watermarked image. There is no exact algorithm to choose the value of scaling factor. Most of the existing algorithms are based on trial-and-error method. In our scheme, there is no requirement for choosing scaling factor as it makes the addition of other watermarks harder. To maintain the transparency we split the watermark into two parts as MSBs and LSBs planes. The DCT coefficients of MSBs and LSBs planes are embedded into singular values of LH and HL sub-bands in block-wise manner.

The rest of this paper is organized as follows: Section 2 gives brief backgrounds of DWT, SVD, DCT and Arnold Cat Map transformation. Section 3 describes the details of the proposed watermarking scheme. Sections 4 discusses experimental results. Finally, Section 5 draws the Conclusion.

2 Background

2.1 Discrete wavelet transform (DWT)

The small waves of varying frequency and limited duration are wavelet [1, 18, 40]. Wavelet transform has become an important tool in watermarking and image processing due to its excellent space and frequency energy compaction properties. At each level, DWT decomposes an image into four sub-bands i.e. a lower resolution approximation component (LL) and three other spatial direction components corresponding to horizontal (HL), vertical (LH) and diagonal (HH) detail components. The LL sub-band is obtained by low-pass filtering in both horizontal and vertical directions. It contains an approximate description of the image. The HH sub-band is obtained by applying high-pass filter in both horizontal and vertical directions. It contains the high-frequency components along the diagonals. The HL and LH sub-bands are obtained by low-pass filtering in one direction and high-pass filtering in another direction. HL contains the horizontal detail information while LH represents the vertical detail information. At each level of decomposition the magnitude of the DWT coefficients is larger in the approximation sub band (LL), and smaller for other high resolution sub bands (HL, LH and HH). The high resolution sub bands help in locating the edge and texture patterns of any image. DWT-based watermarking techniques enable good spatial localization and have multi-resolution characteristics, which are similar to the human visual system (HVS).

2.2 Discrete cosine transformation (DCT)

The DCT has distinct property that most of the significant information of the image is concentrated in just a few low frequency coefficients of the DCT. It is referred as energy compaction property. DCT is often used in image and signal processing due to its strong energy compaction property [30]. The two-dimensional DCT transform formula is given in (1).

$$ F(u,v)= c(u)c(v)\frac{2}{N}\sum\limits_{x=0}^{N-1}\sum\limits_{y=0}^{N-1} f(x,y)cos\left( \frac{2x+1}{2N}u\pi\right)cos\left( \frac{2y+1}{2N}v\pi\right) $$
(1)

where x, y, u, v = 0, 1, 2, . . . , N − 1, and

$$c(u) =c(v) = \left\{ \begin{array}{ll} \frac{1}{\sqrt{2}}& u=0,v=0;\\ 1 & otherwise. \end{array} \right. $$

The inverse transform (IDCT) formula is given in (2).

$$ f(x,y)= \frac{2}{N}\sum\limits_{u=0}^{N-1}\sum\limits_{v=0}^{N-1}c(u)c(v) F(u,v)cos\left( \frac{2x+1}{2N}u\pi\right)cos\left( \frac{2y+1}{2N}v\pi\right) $$
(2)

where f(x, y) is the gray value of a pixel and F(u, v) is the DCT coefficient. The top left corner coefficient of the frequency domain matrix represent the DC value, and the remaining coefficients represent the AC values of the image.

2.3 Singular value decomposition (SVD)

SVD is a well-known factorizing technique for real or complex rectangular matrix in numerical analysis. If I is an image, it is indicated as I ∈ R M × N, where R represents the real number domain. The SVD of I is defined as follows [10, 41]:

$$ I =U S V^{t} $$
(3)

where U ∈ R M × M and V ∈ R N × N are unitary matrices and S ∈ R N × N is a diagonal matrix with diagonal entries \(s_{i}^{,s} \) satisfying s 1 ≥ s 2 ≥ s 3... ≥ s N ≥ 0 and the superscript t denotes matrix transposition. The U and V are left and right singular vectors and S is a singular value matrix. The main properties of the SVD in terms of image processing applications is the singular values of the image have very good stability to know when a small perturbation is made in the image of the singular value does not change significantly [19, 35]. It is worth noting that, the singular vectors of an image specify the image geometry while the singular values specify the luminance (energy) of the image. It is found that slight variations in the singular values do not affect the visual perception of the quality of the image. The property based on psycho-visual effect allows one to embed the watermark bits in the original image through minor modification of the singular values of the original image.

2.4 Arnold cat map

To enhance the security of the watermarking scheme watermark should be randomized before embedding into cover image. Among the various ways for scrambling, we are using Arnold Cat Map (or Arnold transform) [61] which is an iterative process to move the pixel position. We assume the dimension of the original grayscale image I is N × N which have pixels S = {(x, y)|x, y = 0, 1, 2, ... , N − 1}. The generalized 2D Arnold transform is defined as:

$$ \left[\begin{array}{lllllll} x_{k}\\ y_{k} \end{array}\right] = \left\{\left[\begin{array}{lllllll}1 & p \\q& pq +1 \end{array}\right]\left[\begin{array}{lllllll} x\\ y \end{array}\right](mod N)\right\}^{K} $$
(4)

where x k and y k are transformed coordinates corresponding to coordinates x and y after K iterations; N is the height or width of the square image processed; p and q are positive integers. It is an iterative process, if the location (x, y) is transformed several times then it returns to its original position after T iterations. This T is called the period of the transformation and depends on parameters p, q and N. These parameters can be used as secret keys. Periodicity is required to get back the image. If the scrambling is done by performing K iterations, one can get back the original image by performing (T − K) iterations.

Let us consider, an image of size 128 × 128, when parameters p =1, q =1 are given, then it recovers the original pixel positions after being iterated 96 times. By varying the size of the image and parameters p, q, the image can be recovered after a different number of iterations. In other words, periodicity (T) of the image depends on the size of the image and choosing the parameters p and q value. So the size of the image and the parameters of the Arnold cat map may be treated as secret keys for image encryption. For the parameters p = 1, q = 1 of an image of size 256 × 256, total 192 iterations is required to recover the original pixel positions. For the parameters p = 10, q = 8 of an image of size 256 × 256, total 128 iterations is required to recover the original pixel positions.

3 Proposed methodology

Proposed DWT-SVD and DCT based watermarking scheme is presented in this section. The scheme can be divided into two stages: first stage discuses watermark embedding procedure where as second stage consists of watermark extraction procedure. Overview of these procedures can be seen in Figs. 1 and 2 respectively. The detailed procedures are discussed in the following subsections.

Fig. 1
figure 1

Block diagram of proposed watermark embedding procedure

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Fig. 2
figure 2

Block diagram of proposed watermark extraction procedure

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3.1 Watermark embedding procedure

The procedure to embed gray scale watermark image W into cover image I is formulated as follows.

Input[ Host Image: I, Watermark Image: W ]

  • Step 1. On the basis of MSBs and LSBs plane, split the input watermark W into two parts W 1 and W 2 as follows:

    $$ {b_{n,m}} = \lfloor\frac{w_{n}}{2^{m-1}}\rfloor \bmod 2, m=1,2,...,8 $$
    (5)
    $$ W_{1} = bin2dec([b_{n,1}, b_{n,2}, b_{n,3}, b_{n,4}]) $$
    (6)
    $$ W_{2} = bin2dec([ b_{n,5}, b_{n,6}, b_{n,7}, b_{n,8}]) $$
    (7)

    where w n represents the n th pixel of watermark image, b n, m represents eight bits binary values of w n and bin2dec() is used to convert binary number string to decimal number.

  • Step 2. Apply DCT followed by Arnold Cat Map (K) times on the entire Generated Watermarks W 1 and W 2. The resultant outputs are called as scrambled watermarks W 1s and W 2s .

    $$ D_{k}=DCT2(W_{k}), k=1,2 $$
    (8)
    $$ W_{ks}=ACM(D_{k}, K), k=1,2 $$
    (9)

    where ACM () represents the Arnold Cat Map function.

  • Step 3. Apply one-level Haar DWT on the host image I to decompose it into four sub-bands LL, LH, HL and HH.

  • Step 4. Divide the LH and HL sub-bands into non-overlapping blocks of size 4 × 4.

  • Step 5. Perform SVD operation on all blocks of LH and HL sub-bands.

    $$ [U_{k,i} S_{k,i} V_{k,i}]= SVD(B_{k,i}) , i=1,2, ..., N; k=1,2 $$
    (10)

    where k represents one of two sub–bands, B k, i is the i th block of corresponding sub-band and N is the total number of blocks in LH (or HL) sub-band.

  • Step 6. Modify the middle singular values S k, i of block B k, i with the help of absolute values of Scrambled Watermarks W 1s and W 2s in the following ways:

    $$ \delta_{k,i}= S_{k,i}(2,2) - S_{k,i}(3,3), i=1,2, ..., N; k=1,2; $$
    (11)
    $$ {\Delta}_{k,i}= abs(W_{ks}(i)) - \delta_{k,i}, i=1,2, ..., N; k=1,2 $$
    (12)
    $$ S_{k,i}(2,2)= S_{k,i}(2,2) +{\Delta}_{k,i}, i=1,2, ..., N; k=1,2 $$
    (13)

  • Step 7. Obtain two non-zero binary sequences and call them as Generated Keys i.e. K e y 1 and K e y 2with the help of S k, i (1,1) and modified S k, i (2, 2) by using (12).

    $$ Key_{k}(i) = \left\{ \begin{array}{ll} 1 & \text{if \(S_{k,i}(1,1) \geq S_{k,i}(2,2)\)}\\ -1 & \text{if \(S_{k,i}(1,1) < S_{k,i}(2,2)\)} \end{array} \right. , i=1,2, ..., N; k=1,2 $$
    (14)

  • Step 8. Obtain another two non-zero Generated Keys i.e. K e y 3 and K e y 4 using the Scrambled Watermarks W 1s and W 2s as follows:

    $$ Key_{p}(i,j) \,=\, \left\{ \begin{array}{ll} 1 & \text{if \(W_{ks}(i,j) \geq 0\)}\\ -1 & \text{Otherwise} \end{array} \right. , i\,=\,1,2, ..., X; j\,=\, 1,2,..,Y; k\,=\,1,2; p\,=\,3, 4 $$
    (15)

    where X and Y are the height and width of Scrambled watermarks.

  • Step 9. Apply inverse SVD to all blocks to construct modified LH and HL sub-band..

    $$ B_{k,i}^{w}= U_{k,i} S_{k,i} V_{k,i}^{t} , i=1,2, ..., N; k=1,2 $$
    (16)

  • Step 10. Apply one- level inverse Haar DWT to get the desired watermarked image, denoted by I w .

Output [ Watermarked Image: I w , Generated Keys: K e y 1, K e y 2, K e y 3, K e y 4 ]

3.2 Watermark extraction procedure

In the watermark extraction procedure, our objective is to obtain the original watermark. For watermark extraction, only generated Keys (K e y 1, K e y 2, K e y 3, K e y 4) are required. Hence, the watermark extraction is blind procedure. The extraction process can be done by the following steps.

Input [ Suspected watermarked image: \({I^{*}_{w}}\), Generated Keys: K e y 1, K e y 2, K e y 3, K e y 4, Arnold Cat Map parameters: p, q, K, T ]

  • Step 1. Apply one-level Haar DWT on the suspected watermarked image \({I^{*}_{w}}\) (possibly distorted) to decompose it into four sub-bands L L ∗, L H ∗, H L ∗, H H ∗.

  • Step 2. Divide L H ∗ and H L ∗ sub-bands into blocks of size 4 × 4.

  • Step 3. Perform SVD operation on all blocks of L H ∗ and H L ∗ sub-bands.

    $$ [U_{k,i } S_{k,i} V_{k,i}]= SVD(B^{*}_{k,i}) , i=1,2, ..., N; k=1,2 $$
    (17)

    where k represents one of two sub–bands, \({B^{*}_{k,i}}\) is the i th block of corresponding sub-band and N is the total number of blocks in L H ∗ (or H L ∗) sub-band.

  • Step 4. Extract the scrambled watermarks W 1s and W 2s using K e y 1 and K e y 2 as

    $$ W_{ks}(i) = \left\{ \begin{array}{ll} S_{k,i }(2,2) - S_{k,i }(3,3) & \text{if \(Key_{k}(i) =1 \)}\\ S_{k,i }(1,1) - S_{k,i }(3,3) & \text{if \(Key_{k}(i) = -1 \)} \end{array} \right. , i=1,2,...,N; k=1,2 $$
    (18)

  • Step 5. Apply Arnold Cat Map (T- K) times on extracted W 1s and W 2s to get absolute values of DCT coefficients (W 1D and W 2D ) of Generated watermark \({W^{*}_{1}}\) and \({W^{*}_{2}}\). Here T is the time period of Generated watermarks and K is the number of iterations are used in Arnold Cat Map at the time of watermark embedding.

  • Step 6. Using Keys, K e y 3 and K e y 4 , the DCT coefficients of Generated watermark \({W^{*}_{1}}\) and \({W^{*}_{2}}\) are obtained by (19) and further apply Inverse DCT2 to get the generated watermarks \({W^{*}_{1}}\) and \({W^{*}_{2}}\).

    $$ W^{*}_{kD}(i) = \left\{ \begin{array}{ll} W_{kD} & \text{if \(Key_{j}(i) =1 \)}\\ - W_{kD}& \text{if \(Key_{j}(i) = -1 \)} \end{array} \right. , i=1,2,...,N; k=1,2; j=3,4 $$
    (19)
    $$ W^{*}_{k}=IDCT2(W^{*}_{kD}), k=1,2 $$
    (20)

    where IDCT2 () represents the Inverse DCT2 function.

  • Step 7. Finally, extracted watermark W ∗ is constructed by appending the \({W^{*}_{1}}\) (i.e. MSBs plane values)with \({W^{*}_{2}}\) (i.e. corresponding LSBs plane values ) which makes 8 bits plane.

Output [ Extracted watermark W ∗ ]

4 Experimental results and discussions

The proposed DWT–SVD based scheme was implemented in MATLAB 13 b. The computational platform was a Core i7-3770 processor having clock frequency of 3.40 GHz with 2 GB of RAM. To evaluate the performance of the proposed methodology, cover images and watermark images of size 1024 × 1024 and 128 × 128 were used. The performance of the proposed scheme is examined with various experiments in terms of imperceptibility and robustness against various attacks. Many performance evaluation criteria are suggested in literature to estimate the imperceptibility and the robustness. The most widely used performance evaluation criteria are the Peak Signal-to-Noise Ratio (PSNR) and the Normalized Correlation (NC), which are employed consecutively. The PSNR is utilized to estimate the imperceptibility; a term used to evaluate the similarity between a host image and a watermarked image, and can be defined as follows [41]:

$$ PSNR= 10log_{10}\frac{(255)^{2}}{MSE} $$
(21)

where MSE is Mean Square Error defined as

$$ MSE=\frac{1}{M \times N}\sum\limits_{m=0}^{M-1}\sum\limits_{n=0}^{N-1}\left( f(m,n)-\hat{f}(m,n)\right)^{2} $$
(22)

where f and \({\hat {f}}\) are the two gray scale images of size M × N in which first one is the original cover image and second one is the corresponding watermarked image. A good imperceptibility means that the watermarked image looks nearly identical to the original image, and thus, the host image is barely affected by the embedding process.

The NC is a criterion that measures robustness by evaluating the similarities between the original and extracted watermark. The NC can be estimated as follows [10, 41]:

$$ NC(w,\hat{w}) = \frac{{\sum}_{m=0}^{M-1}{\sum}_{n=0}^{N-1}\left( \left( w(m,n)- \mu_{1}\right)(\hat{w}(m,n)-\mu_{2})\right)} {\sqrt{\left( {\sum}_{m=0}^{M-1}{\sum}_{n=0}^{N-1}\left( w(m,n)- \mu_{1}\right)^{2}\right)\left( {\sum}_{m=0}^{M-1}{\sum}_{n=0}^{N-1}\left( \hat{w}(m,n)- \mu_{2}\right)^{2}\right) }} $$
(23)

where μ 1 and μ 2 are the mean value of images w and \({\hat {w}}\) respectively. The correlation coefficient has the value \(NC(w,\hat {w})=1\), if two images are absolutely identical, \(NC(w,\hat {w})=0\) if they are completely uncorrelated, and \(NC(w,\hat {w})= -1\) if they are completely anti-correlated. When the NC value is closer to 1 under applicable attacks, the scheme is robust against those attacks. In general, an NC value is acceptable if it is 0.75 or higher. Figure 3 shows some of the original covers, original watermark, watermarked and extracted watermark (without any attacks). Table 2 shows the PSNR and NCC values of watermarked image relative to the original test images and NC values of original watermark with extracted watermark. As the embedding PSNR and NC values are very high, so it is highly difficult to differentiate between the watermarked and the original image in vision.

Fig. 3
figure 3

a,e,i,m,q,s Cover Images, (b,f,j,n,r,v) Original Watermark, (c,g,k,o,s,w) Watermarked Images, (d,h,l,p,t,x) Extracted Watermark images

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Table 2 Essential information observed during watermark embedding and extraction without attacks
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The imperceptibility of the proposed scheme has also been compared with Gupta & Raval, 2012 [16] and Lai and Tsai, 2010 [27], shown in Table 3. In this comparison, L e n a, P h o t o, P i r a t e and W o m a n image are taken as host image. The P h o t o image of size 128 × 128 is chosen as the watermark. The PSNR value of proposed scheme is better than [16] and [27].

Table 3 Comparison of Peak Signal to Noise ratio (in dB) for each host image
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The robustness of the proposed scheme has been demonstrated by considering a variety of attacks namely Salt & Pepper noise, Speckle noise and Gaussian noise addition, Averaging and Median Filtering, JPEG Compression, Cropping, Resizing, Histogram Equalization, Motion Blur, Gamma Correction, Log Transformation and Sharpen attacks on the watermarked image. The resultant Normalized Correlation Coefficient (NC) values for all extracted watermark of test images are given in Table 4. It demonstrates the enhanced performance of proposed scheme in terms of robustness against different kinds of attacks. The visual results are shown in Figs. 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 and 16 after considering different kinds of attacks on watermarked P h o t o and L e n a images.

Table 4 Normalized correlation coefficient of extracted watermarks from test images
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Fig. 4
figure 4

a, c Watermarked of P h o t o and L e n a Images after adding additive Salt & Pepper noise of density 1.0; b, d Extracted watermarks

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Fig. 5
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a, c Watermarked of P h o t o and L e n a Images after adding additive Gaussian noise of density 0.1; b, d Extracted watermarks

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Fig. 6
figure 6

a, c Watermarked of P h o t o and L e n a Images after adding Speckle noise of density 0.1; (b, d) Extracted watermarks

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Fig. 7
figure 7

a, c Watermarked of P h o t o and L e n a Images after resizing attack(1024→512→1024); (b, d) Extracted watermarks

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Fig. 8
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a, c Watermarked of P h o t o and L e n a Images after cropping attack; b, d Extracted watermarks

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Fig. 9
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a, c Watermarked of P h o t o and L e n a Images after Histogram Equalization; (b, d) Extracted watermarks

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Fig. 10
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a, c Watermarked of P h o t o and L e n a Images after JPEG Compression(Q=30)(b, d) Extracted watermarks

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Fig. 11
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a, c Watermarked of P h o t o and L e n a Images after Motion Blur; (b, d) Extracted watermarks

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Fig. 12
figure 12

a, c Watermarked of P h o t o and L e n a Images after Median Filtering 9 × 9; (b, d) Extracted watermarks

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Fig. 13
figure 13

a, c Watermarked of P h o t o and L e n a Images after Average Filtering 13 × 13; (b, d) Extracted watermarks

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Fig. 14
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a, c Watermarked of P h o t o and L e n a Images after Gamma Correction(γ = 0.6); (b, d) Extracted watermarks

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Fig. 15
figure 15

a, c Watermarked of P h o t o and L e n a Images after Log Transformation (b, d) Extracted watermarks

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Fig. 16
figure 16

a, c Watermarked of P h o t o and L e n a Images after Sharpen Attack; (b, d) Extracted watermarks

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The noise addition is most common attack on an image. Digital image is degraded and distorted by noise. Robustness against noise addition attack is estimated by Salt & Pepper noise(100 %),Gaussian noise (γ = 0.1) and Speckle noise (γ = 0.1) as shown in Figs. 4, 5 and 6. Figures (4a & c, 5a &c, 6a &c) show the watermarked of P h o t o and L e n a image after addition of Salt & Pepper, Gaussian and Speckle noise respectively. Figures 4b, d, 5b, d, 6b and d consequently represent the extracted watermark.

Figures 7 and 8 demonstrate robustness against geometric attacks, resizing and cropping. Figures 7a and c show the watermarked of P h o t o and L e n a image after resizing (1024 → 512 → 1024). In Fig. 7b and d, extracted watermarks are shown. Similarly, Fig. 8a and c show the watermarked of P h o t o and L e n a image after cropping (50 %). Cropping attack is a lossy operation. The extracted watermarks are shown in Fig. 8b and d.

Figure 9 demonstrates the robustness the proposed scheme against histogram equalization. Figure 9a and c show the watermarked of P h o t o and L e n a image after histogram equalization. Histogram equalization is a common signal processing operation. In Figs. 9b and d, extracted watermarks are shown. To verify the robustness of our proposed scheme against Image Compression, the watermarked of P h o t o and L e n a image are tested with JPEG compression attack as shown in Fig. 10. Figure 10a and c show the watermarked of P h o t o and L e n a image after JPEG compression (Q F = 30). The extracted watermarks are shown in Fig. 10b and d, respectively.

The robustness of proposed scheme against filtering attack is shown in Figs. 11, 12 and 14. Filtering is a common signal processing operation which is capable to reduce noise and enhance smoothness. Robustness against filtering attack is estimated by motion blur, median and averaging filtering. Figures 11a, c, 12a, c, 13a and c, show the degraded watermarked of P h o t o and L e n a image after applying motion blur, median and averaging filtering, respectively. The corresponding extracted watermarks are depicted in Figs. 11b, d, 12b, d, and 13b, d.

The robustness of proposed scheme against image enhancement operations are shown in Figs. 14, 15 and 16. Figure 14 demonstrates the robustness against gamma correction. Figure 14a and c show the watermarked of P h o t o and L e n a image after gamma correction (γ = 0.6). Figure 14b and d, depicts the extracted watermarks. Figure 15 demonstrates the robustness against log transformation. Figure 15a and c show the watermarked of P h o t o and L e n a image after log transformation. The extracted watermarks are shown in Fig. 15b and d, respectively. Similarly Fig. 16 demonstrates the robustness against sharpen attack. Figure 16a and c show the degraded watermarked of P h o t o and L e n a image after sharpen attack. The extracted watermarks are shown in Fig. 16b and d, respectively.

The false positive detection problem normally occurs in most of the SVD-based image watermarking schemes. This occurs due to only singular values of watermark (or singular values of host and watermark image) are embedded into the host image. During extraction it is needed to provide some information which may give a fake watermark with an acceptable quality. The proposed scheme succeeds in tackling the false positive detection problem by embedding the whole original watermark into host image. Moreover the watermark extraction is a blind procedure. Figure 17 demonstrates this big issue. The valid four keys and parameters (p,q,K) of Arnold Cat Map enable the extraction of the correct watermark image shown in Fig. 17c, whereas, providing fake keys and parameters of Arnold Cat Map enable the extraction of an unrecognized image, shown in Fig. 17d.

Fig. 17
figure 17

a Watermarked Image; b Watermark Image; c Extracted watermark with entering valid Keys and parameters of Arnold Cat Map; d Extracted watermark with entering fake Keys and parameters of Arnold Cat Map

Full size image

Watermark, scrambled by Arnold Cat Map is unreadable. Only the legal receiver can reconstruct the watermark using four generated keys and three parameters (p,q,K) used in Arnold Cat Map. Even if the attacker identified the generated keys, it is difficult to reconstruct the watermark as it depends on the three parameters (p,q,K) of Arnold Cat Map.

The time complexity of the proposed watermarking scheme in a DWT-SVD domain has been computed by following equation

$$ T(M, N) = T_{1}(M,N) + O(MN)*(T_{2}(4, 4) + T_{3}(4, 4) + T_{4}(4, 4) )+ T_{5}(M,N) + T_{6}(X,Y) $$
(24)

where T 1(M, N) represents the complexity of DWT of size M × N, T 2(4,4) is the complexity of SVD of size 4 × 4, T 3(4,4) is the complexity of block-wise watermark embedding, T 4(4,4) is the complexity of Inverse SVD of a block, T 5(M, N) is the complexity of inverse DWT of size M × N and T 6(X, Y) is the time complexity of watermark generation. Suppose the size of Cover image is M × N and the size of watermark is X × Y, where X < M and Y < N. we obtain the following relations.

  • Time Complexity of DWT(M,N) = T 1(M, N) = O(M N)

  • Time Complexity of SVD(4, 4) = T 2(4, 4) = O(43) = C o n s t a n t = O(c)

  • Time Complexity of Watermark Embedding(4, 4) = T 3(4, 4) = C o n s t a n t = O(c)

  • Time Complexity of Inverse SVD(4,4) = T 4(4,4) = O(43) = C o n s t a n t = O(c)

  • Time Complexity of Inverse-DWT(M,N) = T 5(M, N) = O(M N)

  • Time Complexity of watermark generation = T 6(X, Y) = O(X Y)

After putting these values in (22), in general complexity of proposed watermarking scheme is

$$T(M, N) = O(MN) + O(MN)*(O(c) + O(c) + O(c))+ O(MN) +O(XY)</p><p class="noindent">$$
$$ =O(MN) $$
(25)

So the overall complexity of the proposed watermarking technique is approximated O(M N). Further if we consider the cover image of equal dimension(i.e. M = N) then by using (25), the overall complexity of the proposed scheme is O(N 2).

The significant performance of proposed watermarking scheme is compared with the comparable existing schemes proposed by Bhatnagar et al., 2012 [8], Ganic & Eskicioglu, 2005 [15], Gupta &Raval, 2012 [16], Lai & Tsai, 2010 [27] and Liu & Tan, 2002 [35]. Except Gupta & Raval [16], all other existing schemes [8, 15, 27] and [35] suffer from false positive detection problem. The comparative analysis is concluded using L e n a image as the cover and camera image as watermark image.

The existing and proposed schemes extract watermarks for Gaussian noise, Salt & Pepper noise, Speckle noise, Average Filtering, Median Filtering, Cropping, Histogram Equalization, Resizing, Sharpening, JPEG Compression, Motion Blur, Gamma Correction and Log Transformation attacks. Table 5 shows the result of detailed comparison. It is easily seen through Table 5, in most of the attacks performance of proposed scheme is better than the existing schemes. In the case of Gamma Correction, Log Transformation and Histogram Equalization, proposed scheme and all existing schemes except scheme proposed by Liu & Tan in [35] perform nearly similar. The performance of watermarking scheme proposed by Liu & Tan [35] gives very poor results for these attacks. In the case of cropping attack, watermarking scheme proposed by Bhatnagar et al. [8], gives poor result. In the case of rotation attacks, all the schemes perform almost equally except schemes proposed by Liu & Tan, 2002 [35] and Ganic & Eskicioglu [15]. In the case of JPEG and Resizing attacks, all the schemes perform almost equally except scheme proposed by Gupta & Raval [16]. The main reasons behind the better performance of the proposed watermarking scheme are:

  • Reason 1: In the proposed scheme, the whole watermark is embedded instead of singular values of watermark. So proposed scheme is free from false positive detection problem.

  • Reason 2: In the proposed scheme, DCT coefficients of watermark image are embedded instead of direct watermark value.

  • Reason 3: In the proposed scheme, it is not required to set scaling factor. Most of the existing schemes have drawback related to the computation time for finding scaling factors.

  • Reason 4: The proposed scheme is a blind watermarking scheme. So at the time of watermark extraction, there is no requirement for original watermark and cover image.

  • Reason 5: In the proposed scheme, the watermark is embedded in the middle singular value (i.e. second diagonal value). Since, the largest singular value is more significant for quality of the image, while the smallest singular values are more sensitive to the noise. Hence, the proposed scheme is more robust and imperceptible.

Table 5 Comparisons of normalized correlation coefficient with existing Schemes: Liu & Tan, 2002 [35], Bhatnagar et al., 2012 [8], Ganic & Eskicioglu, 2005[15], Gupta &Raval, 2012 [16] and Lai & Tsai, 2010 [27]
Full size table

5 Conclusions

In this paper, a new Discrete Wavelet Transform(DWT) and Singular Value Decomposition (SVD) based robust and blind watermarking scheme has been presented for copyright protection. The watermark is split in MSBs and LSBs planes. DCT coefficients of MSBs and LSBs planes of the watermark are embedded in the singular values of 4 × 4 block of LH and HL sub-bands of the cover image. The proposed scheme is free from false positive detection problem which normally occurs in the SVD-based watermarking schemes. Another major advantage of proposed scheme is that it is a blind scheme. So, there is no requirement of original watermark and cover image for watermark extraction. There is also no requirement to choose the scaling factor. Therefore, the proposed scheme is free from drawback related to the computation time for finding scaling factors. In consequence of this it has smaller time complexity i.e. O(N 2). The use of Arnold Cat Map on watermark successfully deals with the unauthorized reading problem. Further, the robustness of the proposed scheme is studied by a variety of attacks along with security and comparative analysis. The proposed watermarking scheme can be extended for video and audio multimedia processing.