An IWT based blind and robust image watermarking scheme using secret key matrix

Abstract

In this paper, the authors have proposed a binary watermark embedding approach for protecting the copyright ownership of the gray-scale images. The proposed watermark embedding process is realized in integer wavelet transform (IWT) domain to defend the robustness property. Instead of inserting the watermark bits directly in the coefficients of cover media, an indirect embedding mechanism is proposed with the reference to a logistic map based secret key matrix which enhance the secrecy of the proposed embedding approach. Initially, the approximate sub band of the IWT transformed cover image is selected with the intention to embed the watermark. Later, a secret key matrix of size corresponding to the approximate sub band of the cover image is formed using the logistic map with secret parameters. During the watermark embedding process, the approximate sub band is modified indirectly with reference to the secret key matrix and a proposed division table. The scheme is tested on a set of standard images and satisfactory results are achieved. In addition, the proposed schemes is also able to extract the watermark information in blind manner. Also, the scheme is comparable with some other related schemes. Finally, the proposed watermarking scheme is able to survive the watermark even after performing certain types of image manipulation attacks.

1 Introduction

The extensive evolution of digital technology facilitates the multimedia data to be transmitted and distributed in digital format over the Internet. As digital data are easily exposed to illegal possession, duplication and dissemination over the Internet, it has become an essential to think about the copyright protection, ownership verification, and tamper-resistance of digital data during their applications. Digital watermarking method is one of the widely used solution for detecting the illegal manipulation occurred in digital data. In digital watermarking method, the information related to the digital data is embedded or hidden in the digital data itself such that the authenticity and integrity can be verified by extracting or detecting the embedded information. The embedded information is termed as watermark. The digital data that contain watermark is termed as cover media. Depending upon the cover media, the watermarking schemes are classified as image, video or audio watermarking.

Depending upon the specific goal, the watermarking method can be categorized into robust, semi-fragile and fragile watermarking. The robust watermarking method is generally considered for copyright protection of the digital data [17, 18]. In robust watermarking scheme, the existence of secret information can be known but it is hard to remove/manipulate the secret information [8]. So in copy right protection scheme robust watermarking is preferred.

Depending upon the embedding domain, again the robust watermarking schemes can be divided into two categories, i.e., spatial-domain schemes and frequency-domain schemes. In Spatial domain, watermark is added directly by modifying pixel values of the cover image. Several robust watermarking scheme in spatial domain have been devised by researchers [10, 15,16,17, 21]. Embedding the watermark into the cover image in spatial domain is a straight forward method, which has the advantages of low computational complexity and easy implementation. However, the most serious problem of spatial domains is the weakness of robustness i.e. spatial domain watermarking algorithms is able to resist some limited number of attacks. In transform domain, the watermark is embedded by modulating the coefficients of the transformed cover image. However in case of frequency-domain scheme, the computational cost is higher than the ones based on spatial domain, more information can be embedded and better robustness against the common image processing attacks can be survived. The main advantages of using the frequency domain methods are that they can easily be adapted to lossy compression systems, which have the ability to embed data in the compressed representations, and have ability to reveal the watermark even from the modified watermarked image [9, 20]. The transform domain based watermarking schemes can be implemented through various transformation tools such as discrete cosine transform (DCT) [22], discrete wavelet transform (DWT) [23], Discrete Fourier transform(DFT) [12], Integer wavelet transform(IWT) [4], Singular Value Decomposition(SVD) [11] etc.

Various robust image watermarking schemes based on transform domain have shown their effectiveness in image data protection. In [24], Thabit et al. proposed another watermarking scheme based on Slantlet transform matrix to transform small blocks of the original image and hiding the watermark bits by modifying the mean values of the carrier subbands. Fazli et al. [7] proposed a robust watermarking based on a combination of DWT, DCT, and SVD domains. This paper mainly focuses on the geometric attacks. To address this goal, the host image is divided into four non overlapping rectangular segments called sub-images and then watermark is independently embedded into each of them, using the hybrid scheme. The redundancy reduces effect of cropping attack. Moreover, in order to correct main geometric attacks, such as rotation, translation, and affine translation, an inventional synchronization technique is utilized to recover the geometrically attacked image via detection of desired image corners. A binary image in the first experiment and some 1D binary random sequences with different lengths in the next experiments are used as watermarks. Weng et al. proposed another method based on integer Haar wavelet transform (IHWT), which utilizes block selection and difference expansion (DE) (or histogram shifting (HS)) [28]. IHWT has the characteristic that the average of a block remains unchanged before and after watermark embedding. Hence, this invariability can be used for determining whether a block is located in a smooth region or not. In [19], Pal et al. proposed a robust and blind watermarking scheme based on Discrete Cosine Transform (DCT) for protecting the copyright ownership of the digital images. In this work a binary watermark is embedded into the block based DCT transformed cover image by modifying the middle significant AC coefficients using repetition code. The proposed approach ensures the protection of copyright information even in compressed form of the watermarked image. In [13], Kumsawat et al., the watermark has been embeded into the DMT coefficients using multiwavelet tree techniques. Digital watermarking algorithm using integer wavelet transform(IWT) have received wide range of attention in the recent years due to the property that it can map integer to integer without the rounding error, and can obtain good imperceptibility . There are many IWT-based watermarking schemes that have been proposed in recent years. In [25], Verma et al. designed robust digital watermarking scheme using 3-level lifting wavelet transform (LWT) with a block selection procedure. Non-overlapping coefficient blocks from the low pass subband are selected after applying LWT and using certain criterion based on minimum coefficient difference and a threshold value. Ansari et al. proposed another watermarking scheme using IWT and SVD (singular value decomposition) based to address false positive problem that are suffered in SVD based watermarking techniques [3]. The properties of IWT and SVD help in achieving high value of robustness. Singular values are used for the watermark embedding. In order to further improve the quality of watermarking, the optimization of scaling factor (mixing ratio) is performed with the help of artificial bee colony (ABC) algorithm. In [26], Wang et al. proposed an efficient integer transform based reversible watermarking scheme. In this paper, Tian’s difference expansion (DE) technique can be reformulated as an integer transform. Then, a generalized integer transform and a payload-dependent location map are constructed to extend the DE technique to the pixel blocks of arbitrary length. In [5], Bohra et al. proposed a technique for robust watermarking of images based on lifting-based integer wavelet transform. The proposed scheme, along with its robustness has got the capability of blind self–authentication of the watermarked images. This paper also utilizes histogram modification to avoid overflow/underflow problem. In [6], the 2-level IWT based watermarking scheme for embedding the compressed version of the binary watermark logo has been developed for robust watermarking. In this paper, the source document image is divided into empty and non-empty segments depending on the absence or presence of the information. Watermarking is applied for non-empty segments. A binary watermark logo is compressed using binary block coding technique of appropriate block-size. IWT is applied on the non-empty segment of the source document image. LL-sub–band of the transformed image is subdivided into blocks of uniform size and compressed watermark bit stream is embedded into it. In [14], Lingamgunta et al. proposed a reversible watermarking based on IWT. The proposed algorithm hides the data and the bookkeeping information in the high frequency subbands of CDF (2,2) integer wavelet coefficients whose magnitudes are similar to a certain predefined threshold. Histogram modification is applied as a preprocessing to prevent overflow/underflow. The embedding technique is based on the parent–child structure of the transformed coefficients called “quadruple wavelet tree” (QWT). In this paper, we develop an invisible robust watermarking scheme based on 1–level IWT domain. Robustness and imperceptibility are strongly achieved in the proposed method through the characteristics of IWT. Before watermark embedding, the cover image is transformed through IWT. We have selected the approximate sub band of the integr wavelet transformed cover image for the watermark insertion. Generally watermark embedding only in the approximate sub band reduce the chance of removing or destroying the watermark from the watermarked image. In [27], Wang et al. proposed a 3-level wavelet based intelligent watermarking scheme using particle swarm optimization (PSO) technique. In this scheme, the high sub–bands of the DWT transformed cover image are considered. The coefficents to contains watermark bits are selected randomly from the different sub–bands. Ali & Ahn presented a DWT–SVD based watermarking algorithm where self-adaptive differential evolution algorithm is used during embedding process [1]. Another work is presented by Ali et al was in wavelet domain and SVD domain. In this work the low frequency sub–band is selected and divided into blocks. Again the blocks were SVD transformed and the left and right singular vector matrix are used for watermark embedding using artificial bee colony (ABC) algorithm [2].

In some existing schemes, the watermark bits are embedded directly on the selected coefficients of the cover image. But in the proposed watermarking scheme, instead of embedding the watermark bits directly to the coefficients of the cover image, an indirect method corresponds to a division method is utilized. However watermark embedding only in the low subband increase the chance of removing or destroying the watermark with the attempt of tampering of that portion. Although this proposed method utilize the low sub–band of the transformed cover image, robustness and imperceptibility are strongly achieved through the proposed embedding method and the characteristics of IWT. Also to increase watermarking security, a generated key matrix using logistic is utilized. The intention of the proposed method is to improve the robustness and invisibility of the watermarked image and this scheme is suitable for extract the watermark information in a blind manner.

The rest of the paper is organized as follows. Section 2 describes the related fundamentals for better understanding of the proposed method. Section 3 contains the details of the proposed method. The experimental results and discussion are in Section 4. Section 5 contains the conclusion of the work done in this paper.

2 Preliminaries

2.1 Integer to integer wavelet transform

Due to the multi-resolution characteristic, the conventional wavelet transform is very popular in signal and image processing field. Also it is a very good computational tool to reduce the digital image files with higher compression ratios which helps to storing images using less memory and for transmitting images faster and more reliably. In the Fig. 1, LL sub-band represents the approximation part of the image and LH, HH, HL represents the detail part of the image. But the conventional Wavelet transform is not suitable for truly lossless coding because it gives floating point results for any input sequence which generally create problem for reconstruction of the exact signal or image. Due to this problems, a generalized version of conventional wavelet transform, Integer to Integer Wavelet Transform (IWT) is very popular for lossless coding method. It is also known as the second generation of the wavelet transform. The IWT was introduced by Sweldens (1998). The IWT inherits the multi-resolution characteristics of the conventional wavelet transform and that can map integer input sequence to integer output sequence by rounding off the values of wavelet transformation. Thus as compared to floating point operation they need less storage space and the implementation is faster than the conventional wavelet coefficients. The IWT was constructed by means of lifting scheme. The schematic diagram of the lifting scheme is shown in Fig. 2:

Fig. 1

n-level wavelet transform

Fig. 2

Forward integer wavelet transform

With a lifting scheme, the forward transform is calculated in three steps.

Split

The input sequence is S _j decomposed into an even sequence and odd sequence.

$$\left( \textit{Even}_{j-1},Odd_{j-1}\right) \leftarrow \textit{Split}\left( S_{j}\right)$$

Where

$$\textit{Even}_{j-1} =\left\lbrace \textit{Even}_{j-1,k}= S_{j,2k}\right\rbrace $$

$$Odd_{j-1} =\left\lbrace Odd_{j-1,k}= S_{j,2k+1}\right\rbrace $$

Predict

The numbers from one sequence (generally the odd sequence, O d d _j−1)is predicted on the basis of the other sequence(generally the even sequence, E v e n _j−1 )by the use of correlation between them.The difference, D _j−1between the actual value (O d d _j−1)and the predicted value, P (E v e n _j−1) becomes the wavelet coefficients. The operation of obtaining the differences from the prediction is called the lifting step.

$$D_{j-1}=Odd_{j-1}-P\left( Even_{j-1}\right) $$

Where

$$P_{k}\left( \textit{Even}_{j-1}\right) =\frac{\left( \textit{Even}_{j-1,k}+\textit{Even}_{j-1,k+1}\right) }{2}=\frac{\left( S_{j,2k}+S_{j,2k+1} \right) }{2} $$

Update

The update step follows the prediction step, where the even values are updated from the input even samples and the updated odd samples. They become the scaling coefficients which will be passed on to the next stage of transform. This is the second lifting step.

$$S_{j-1}=\textit{Even}_{j-1}+U\left( D_{j-1}\right) $$

Where U is the updated operator and defined as follows:

$$U_{k}\left( D_{j-1}\right)=\frac{D_{j-1,k}}{2}=\frac{\left( D_{j-1,k-1}+D_{j-1,k} \right)} {4}+\frac{1}{2} $$

The corresponding inverse transform of IWT is calculated as follows:

$$\textit{Even}_{j-1}\leftarrow S_{j-1} -U\left( D_{j-1} \right) $$

$$Odd_{j-1}\leftarrow D_{j-1} +P\left( \textit{Even}_{j-1} \right) $$

$$S_{j}\leftarrow \textit{Merge}\left( \textit{Even}_{j-1} ,\textit{Odd}_{j-1}\right) $$

In order to achieve multilevel decomposition,the approximation part, (S _j−1,k )is further decomposed into approximate and detail parts using split, predict and update stage and we get S _j,2k and D _j,2k . This process can be repeated n number of times, where n = l o g ₂(N) for the input image of size N × N.

2.2 Logistic mapping

Chaotic signals are a kind of pseudorandom, irreversible and dynamical signals generated by deterministic nonlinear equations, which process good characteristics of pseudorandom sequences .The definition is

$$ x_{n+1}=\mu x_{n}\left( 1-x_{n} \right) $$

(1)

Where x _n ∈ (0,1)is the state of the system for (n = 0, 1, 2,..) and μ ∈ [0,1]. For different values of parameter, μ, the logistic sequence shows different characteristics. For x ∈ (0,1) and μ ∈ [3.57,4], the logistic map shows the chaotic behaviour.

3 Proposed method

This section describes some motivating factors that are used to design a robust and blind watermarking method. In the proposed approach, the authors have considered various test images of size N × N as cover images(C) and a binary logo (W) of size w ×w as watermark. To embed the watermark, a region is selected by applying 1–level IWT on the cover image. As already mentioned, the IWT is an efficient and rapid lifting wavelet transform and its properties are best suited to enhance the robustness and preserve the imperceptibility. Due to this, IWT is very popular in case of digital image watermarking. Also the authors have applied IWT on the cover image to decompose the cover image into four sub-bands, named LL, HL, LH and HH. After 1–level IWT transformation of C, the approximation part i.e. LL sub-band with size N1 × N1 ($N1=\frac {N}{2}$) is used for watermark embedding. In this paper, LL sub-band is termed as CA. Before embedding the watermark, the CA part is decomposed into non-overlapping blocks of size n × n. In the proposed method, the authors consider the block based watermark embedding procedure. To preserve the watermark bit unchanged, a single bit is embedded repeatedly in the selected coefficients of a particular block. Before embedding process some binary key vectors are generated using a division method (explained in the Key Generation phase) for watermark bit embedding. These binary key vectors are generated from a key matrix generated by utilizing the chaotic logistic map. This binary key also utilized to select the coefficients to be embedded in each block. The detail procedure of the proposed method is carried out through three phases as follows:

3.1 Pre-processing phase

This phase again comprises of two parts. In the first part a key matrix of same size as CA is generated from the chaotic logistic map. Here, instead of taking the direct values of initial condition and system parameter, the authors have considers the calculated initial value and system parameter to generate the logistic sequence. The key matrix is used to generate the binary key vectors those are used for watermark embedding. In the next part the detail procedure of required binary key vectors is described.

Key generation using logistic map

• Step 1: Generate a random binary key sequence of l bits long, where l = t ².

• Step 2: Divide the key sequence into blocks of 16-bit each.

  $$K = {\sigma_{1}}{\sigma_{2}}.....{\sigma_{16}}$$

• Step 3: To calculate the initial condition (x ₀) and the system parameter (μ) of the chaotic logistic map, the ASCII key sequence is used. The intermediate values, γ ₁ and γ ₂ are used to calculate the initial condition and γ ₃, γ ₄ are used to calculate the system parameter.

  $${x_{0}} = \bmod \left( {\left( {{\gamma_{1}} + {\gamma_{2}}} \right),2} \right) $$
  $$\mu = \bmod \left( \left( 3.999 + \left( \gamma_{3} + \gamma_{4}\right)\left/1000\right.\right), 1 \right) $$

  Where

  $$\begin{array}{l} \gamma_{1} = \left( \sigma_{1}\parallel \sigma_{2}\parallel \sigma_{3} \right)_{10} \left/2^{23}\right.,\\ \gamma_{2} = \left( \sigma_{4}\parallel \sigma_{5}\parallel \sigma_{6} \right)_{10} \left/2^{23}\right.,\\ \gamma_{3} = \left( \sigma_{7}\parallel \sigma_{8}\parallel \sigma_{9} \right)_{10} \left/2^{23}\right.,\\ \gamma_{4} = \left( \sigma_{10}\parallel \sigma_{11}\parallel \sigma_{12} \right)_{10} \left/2^{23}\right. \end{array} $$

• Step 4: Generate a chaotic sequence, a of length l by using the (1).

• Step 5: Reshape the generated chaotic sequence into a square matrix of size t × t.

• Step 6: The matrix is concatenated in raster scan order to generate the matrix K_E M of size CA i.e N1 × N1.

Binary key vectors generation for watermark embedding

This phase generates the binary keys for the individual block of the decomposed CA. The detail procedure is described as follows:

• Step 1: Calculate the difference matrix, D using CA sub–band and K_E M.

  $$D = \left| {CA - K\_EM} \right|$$

• Step 2: Divide the difference matrix, D into the non overlapping blocks, b of size, n × n.

  $$b = \left\{ {{b_{1}},{b_{2}},.....,{b_{\frac{N1^{2}}{n^{2}}}}} \right\}$$

• Step 3: Convert each block into row vector.

  $$d = \left\{ {d_{1\times{n^{2}}},{d_{2\times{n^{2}}}},......,{d_{\frac{N1^{2}}{n^{2}}}\times{n^{2}}}} \right\}$$

For Example

Suppose A is the one of the decomposed block of difference matrix, D.

Then A is converted into row vector as shown below.

• Step 4: Calculate the adjacent differences, A d j_D i f f in each row using the following formula

  For $i=1:2:{\frac {N1^{2}}{n^{2}} }-1$

  $$Adj\_diff(i) = abs({d_{i}} - {d_{i + 1}})$$

Binary Value Generation using Division Method

• Step 5: Take a range, R with minimum value, min and maximum value, max. As we are considering gray test images so m i n = 0 and m a x = 255.

• Step 6: Divide R with r number of divisions to give r slots.

  Then

  $$R = \left\{ {{R_{1}},{R_{2}},.......{R_{r}}} \right\} $$

  Where R ₁ = m i n and R _r = m a x

• Step 7: Then the elements of Binary key vectors, B i n_C A(i) reference to the individual block matrix of CA can be generated from the R and A d j_d i f f(i) as follows:

  $$ Bin\_CA(j) = \left\{ \begin{array}{l} 1\,\,\,\,\,\,\,\,\,\,\,\,if\,{R_{k}} \le \text{Adj\_diff(j)} \le {R_{k + 1}}\\ \,\,\,\,\,\,\,\,\,\,\,\,\,and\,\,\,\bmod (k,2) = = 1\\ \\ 0\,\,\,\,\,\,\,\,\,\,\,if\,{R_{k}} \le \text{Adj\_diff(j)} \le {R_{k + 1}}\\ \,\,\,\,\,\,\,\,\,\,\,\,\,and\,\,\,\bmod (k,2) = = 0 \end{array} \right. $$

  (2)

  Where k = 1 : r and j = 1 : 2 : n ²

For example:

Suppose r = 20, the range can be divided into different slots as shown in Fig. 3.

Fig. 3

Division of a range

The main objective of the generation of the binary key vectors space is to utilize these keys as the reference to the coefficients that are to be modified. The utilization of these reference bits are explained in the next section.

3.2 Watermark embedding phase

This section describes the detail of embedding procedure of watermark of size w × w to the CA part of size N1 × N1. The main objective is to modify the selected coefficients in such a way that the they fall in the same slot as the watermark bit. The detail procedure is described as follows:

Phase 3: watermark embedding

• Step 1: Decompose CA part into non-overlapping blocks of size n × n.

  $$b^{\prime} = \left\{ {{b^{\prime}_{1}},{b^{\prime}_{2}},.....,{b^{\prime}_{\frac{N1^{2}}{n^{2}}}}} \right\} $$

• Step 2: Convert each block into row vectors as follows:

  $$d^{\prime} = \left\{ {d^{\prime}_{1\times{n^{2}}},{d^{\prime}_{2\times{n^{2}}}},......,{d^{\prime}_{\frac{N1^{2}}{n^{2}}}\times{n^{2}}}} \right\} $$

• Step 3: Store the watermark bits in a row vector W ^′.

• Step 4: The watermark bits of the vector, W ^′ are embedded in the blocks of CA part according to the value of binary vectors B i n_C A(i) to generate the watermarked Image WCA as follows:

The block diagram of the watermark embedding method is shown in Fig. 4.

Fig. 4

Block diagram of the proposed watermark embedding method

3.3 Extraction method

At the receiver end the watermark is detected by the intended recipient from the watermarked image using the same secret key that was used in the embedding method. In the proposed method, instead of sending the whole key ,only the initial value of the logistic map (x ₀) is need to send at the receiver side to generate the required key. The extraction procedure is just the reverse process of embedding procedure and is given as follows:

• Step 1: Generate the key matrix, K_E M from the initial condition (x ₀) of the logistic map.

• Step 2: Calculate the difference matrix, D ^′ using watermarked image, WCA and K_E M.

  $${D^{\prime}} = \left| {WCA - K\_EM} \right|$$

• Step 3: Divide the difference matrix, D ^′ into the non overlapping blocks, b ^′of size, 4 × 4.

  $${b^{\prime}} = \left\{ {{b_{1}}^{\prime},{b_{2}}^{\prime},....,{b_{4096}}^{\prime}} \right\}$$

• Step 4: Convert each block into row vectors, d ^′.

  $$d^{\prime}={d_{1}^{\prime},d_{2}^{\prime},....,d_{4096}^{\prime}}$$

• Step 5: Calculate the adjacent differences, A d j_D i f f ^′ in each block of d ^′.

  $$Adj\_diff = {d_{i}}^{\prime} - {d_{i + 1}}^{\prime}$$

• Step 6: Generate the corresponding binary matrix of A d j_D i f f ^′ i.e. B i n_A d j ^′ using the division method as described above.

• Step 7: Calculate the watermarked vectors, WE that contains watermark bits using the following equation:

  $$WE\,\, = \,\left\{ \begin{array}{l} 0\,\,\,\,\,\,\,\,\,\,\,if\,Bin\_Adj^{\prime}\,\, = \,\,0\\ 1\,\,\,\,\,\,\,\,\,\,\,\,if\,Bin\_Adj^{\prime}\,\, = \,\,1 \end{array} \right.\,\,\,\,\,$$

• Step 8: Extract the watermark bits from WE as follows:

  $$WEX\,(i)\,\, = \,\left\{ \begin{array}{l} 0\,\,\,\,\,\,\,\,\,\,\,\,if\,\max freq\,(WE\,(i))\,\, = \,\,0\\ 1\,\,\,\,\,\,\,\,\,\,\,\,if\,\max freq\,(WE\,(i))\,\, = \,\,1 \end{array} \right.\,\,\,\,\,\,\,\,$$

• Step 9: Reshape WEX into a matrix of size 64 × 64.

The block diagram of the watermark extraction procedure is depicted in Fig. 5.

Fig. 5

Block diagram of the proposed watermark extraction method

4 Experimental results

In the proposed scheme, an embedding process using division method (as discussed in the Section 3.1) is employed where the value of the parameter r (r = number of divisions) is given by the user. In this paper, we have considered the value of r = 20, 30, 40 and 50. For the result analysis, several images of size 512 × 512, given in Fig. 6 and a binary logo of size 64 × 64, given in Fig. 7 are taken as the cover media and watermark respectively.

Fig. 6

Original images: a Lena b Peppers c Houses d Sailboat e Airplane f Goldhill g Couple h Kiel

Fig. 7

Binary logo

The watermark algorithm can be evaluated by considering two important parameters, imperceptibility and robustness (Fig. 8).

Fig. 8

Histogram of original images: a Lena b Peppers c Houses d Sailboat e Airplane f Goldhill g Couple h Kiel

Imperceptibility measurement

The imperceptibility means that the human visual quality of the host image should not be affected much even after watermark embedding. We have generated different sets of watermarked images according to the value of r and are depicted in Figs. 9, 10, 11, and 12.

Fig. 9

Watermarked images using 20 divisions: a Lena b Peppers c Houses d Sailboat e Airplane f Goldhill g Couple h Kiel

Fig. 10

Watermarked images using 30 divisions: a Lena b Peppers c Houses d Sailboat e Airplane f Goldhill g Couple h Kiel

Fig. 11

Watermarked images using 40 divisions: a Lena b Peppers c Houses d Sailboat e Airplane f Goldhill g Couple h Kiel

Fig. 12

Watermarked images using 50 divisions: a Lena b Peppers c Houses d Sailboat e Airplane f Goldhill g Couple h Kiel

The corresponding watermarked images with different value of r of the Fig. 6 shown in Figs. 9, 10, 11, and 12. There is very low visual degradation of the watermarked images than original images. Also the histograms of the watermarked images in Fig. 13 are similar to the histogram of original images (Fig. 8) which indicate that the proposed watermark algorithm ensures high degree of fidelity.

Fig. 13

Histogram of Watermarked Images: a Lena b Peppers c Houses d Sailboat e Airplane f Goldhill g Couple h Kiel

An alternation to measure the degree of imperceptibility is Peak Signal to Noise Ratio(PSNR) and it can be defined as follows:

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

Wher

$$\text{MSE} =\frac{\sum\limits_{i-1}^{M}\sum\limits_{j-1}^{N} x_{i,j}-\tilde{x}_{i,j} }{M\times{N}} $$

where x _i,j and $\tilde {x}_{i,j}$ denotes the original and encrypted pixel respectively, and the images are of size M × N.

A larger PSNR indicate that the watermarked image more closely resembles the original image meaning that the watermark is more imperceptible. Table 1 shows the calculated PSNR values of the different number of division for the proposed watermarking algorithm. From the Table 1 and the Fig. 14 it shows that the PSNR values are higher than 32 dB and also the PSNR values are improving with the increment of number of divisions.

Table 1 PSNR of the watermarked images with different number of divisions without attack

Fig. 14

Imperceptibility comparision with different number of divisions without attack

Robustness measurement

The robustness of the proposed scheme can be determined in terms of Bit–Error–Rate(BER) and normalized cross correlation(NC) which are measured between the original watermark and extracted watermark (without attack/after applying different types of intended attacks). NC measures the similarities between the original and extracted watermark. For an efficient watermark algorithm the NC values for different test images should be nearly or equal to 1. Generally, N C ≥ 0.75 is acceptable. The BER values should be very less that means they should be nearly or equal to 0.

The NC can be formulated as follows:

$$NC\left( \textit{w},\bar{\textit{w}} \right) = \frac{\sum\limits_{i = 1}^{M} \sum\limits_{j = 1}^{N} \left[ \textit{w}\left( i,j \right) - \mu_{\textit{w}}\right]\, \times \,\left[ \bar{\textit{w}}\left( {i,j} \right) - \mu_{\bar{\textit{w}}}\right]}{\sqrt{\sum\limits_{i = 1}^{M} \sum\limits_{j = 1}^{N} \left[ \textit{w}\left( {i,j} \right) - \mu_{\textit{w}} \right]^{2} \times \sqrt{\sum\limits_{i = 1}^{M}\sum\limits_{j = 1}^{N}\left[ \bar{\textit{w}}\left( {i,j} \right) - \mu_{\bar{\textit{w}}}\right]^{2}}}} $$

Where M and N denote the width and the height of the watermark image, w _i,j and $\bar {\textit {w}}_{i,j}$ denote the original watermark pixel and extracted watermark pixel respectively. μ _w and $\mu _{\bar {\textit {w}}}$ represent the mean of the original watermark and extracted watermark respectively.

The BER can be calculated as follows:

$$ BER=\frac{\textit{Number of error bits}}{\textit{Total bits transmitted}}=\frac{\textit{Number of error bits per second}}{\textit{Data rate per second}} $$

(3)

Table 2 shows the calculated NC and BER values of the proposed scheme. It is observed that the NC values of the extracted watermark of various test images are equal to 1 or nearly equal to 1 and the BER values are also very less which indicate that the extracted watermark is nearly equal to the original watermark. Figures 15 and 16 shows the performance of NC and BER with different number of divisions. Also the robustness can be measured by Tamper Assessment Function(TAF). It is observed by checking the similarity between the original watermark (w) and extracted watemark($\bar {\textit {w}}$). Mathematically it is written as:

$$TAF(\% ) = \frac{1}{{M\times{N}}}\left[ {\sum\limits_{i = 0}^{N - 1} {w \oplus \bar{\textit{w}}} } \right]\, \times \,100 $$

Where M × N is the size of watermark image. The value of TAF shoule be closer to zero for the better result.

Table 2 BER and NC of the extracted watermark in different number of division without attack

Fig. 15

NC comparison with different number of divisions

Fig. 16

BER comparison with different number of divisions

From the Table 3 and Fig. 17 it is observed that the values are very less which indicates the similarity of the extracted watermark from the proposed approach with the original watermark.

Table 3 TAF of the watermarked images with different number of divisions without attack

Fig. 17

TAF comparison with different number of divisions

In general during transmission, the watermarked image may be exposed to various attacks on the watermarked images before reaching to the watermark receiver. The attacks include both geometric and non–geometric attacks. Geometric attacks include cropping, resize, rotation, scaling, translation etc and non–geometric attacks include image filtering, averaging, addition of noise, sharpening, brightness, gamma correction compression etc. In the proposed scheme, the watermarked images are verified against both geometric and non–geometric attacks using 20 division, 30 division, 40 division and 50 division. Although in the proposed scheme, number of watermarked images have generated and verified against robustness to various attacks, but as a representative only results of Lena image are presented. The figures below show the watermarked images with attacks and the extracted watermarks are shown below.

Low pass filtering

To prove the robustness against the low pass filtering attacks, gaussian low pass filtering attacks with different sizes are applied on the watermarked images with different value of r. The attacked watermarked images and their corresponding extracted watermarks(logo) with calculated NC and BER values are presented in the following figures.

Gaussian Low-pass Filtering(2 × 2) (Fig. 18).

Fig. 18

Result under Gaussian Low pass filtering (2 × 2) attack and recovered watermark image using a 20 division b using 30 division c using 40 division d using 50 division

Gaussian Low-pass Filtering(3 × 3) (Fig. 19).

Fig. 19

Result under Gaussian Low pass filtering (3 × 3) attack and recovered watermark image using a 20 division b using 30 division c using 40 division d using 50 division

Gaussian Low-pass Filtering(5 × 5) (Fig. 20).

Fig. 20

Result under Gaussian Low pass filtering (5 × 5) attack and recovered watermark image using a 20 division b using 30 division c using 40 division d using 50 division

Gaussian Low-pass Filtering(7 × 7) (Fig. 21).

Fig. 21

Result under Gaussian Low pass filtering(7 × 7) attack and recovered watermark image using a 20 division b using 30 division c using 40 division d using 50 division

From the above figures with the NC and BER values of the extracted logos, it is observed that the proposed method is efficient enough to survive the gaussian low pass filter attack.

Median filtering

Median filtering attack, the center pixel value is modified by the middle value of the sorted pixel values. For the analysis, we have examined the proposed scheme is examined against median filtering attacks with different window sizes.

Median Filtering (3 × 3) (Fig. 22).

Fig. 22

Result under Median filtering(3 × 3) attack and recovered watermark image using a 20 division b using 30 division c using 40 division d using 50 division

Averaging attack

In this type of attack, number of many samples of a precondition data set are inserted with a different secret key or watermark and then are averaged to evaluate the attacked data. If the amount of data set is sufficiently huge, the inserted watermark cannot be discovered any more supposing that it will output zero mean on average (Fig. 23).

Fig. 23

Result under average filtering attack and recovered watermark image using a 20 division b using 30 division c using 40 division d using 50 division

Image noising

One of the common non-geometrical attack is the addition noise. The proposed method is tested for the robustness against salt and pepper noise attack. Salt & ppepper noise is caused during the transmission due to the pixel’s error.

Salt and Pepper noise(var = 0.01) (Fig. 24).

Fig. 24

Result under salt and pepper noise(var=0.01) attack and recovered watermark image using a 20 division b using 30 division c using 40 division d using 50 division

Salt and Pepper noise(var = 0.03) (Fig. 25).

Fig. 25

Result under salt and pepper noise(var=0.03) attack and recovered watermark image using a 20 division b using 30 division c using 40 division d using 50 division

Salt and Pepper noise(var = 0.05) (Fig. 26).

Fig. 26

Result under salt and pepper noise(var=0.05) attack and recovered watermark image using a 20 division b using 30 division c using 40 division d using 50 division

Effect of gamma correction

Sometimes watermarked images are enhanced intentionally or unintentionally by power law transformation which may causes the destruction or removal of watermark. The below figures shows the results after the watermarked images are enhanced by gamma correction technique with different gamma value and the recovered watermarks from the enhanced images along with their NC and BER values.

Gamma Correction(gamma = 1) (Fig. 27).

Fig. 27

Result under effect of Gamma Correction(1) and recovered watermark image using a 20 division b using 30 division c using 40 division d using 50 division

Gamma Correction(gamma = 0.75) (Fig. 28).

Fig. 28

Result under effect of Gamma Correction(0.75) and recovered watermark image using a 20 division b using 30 division c using 40 division d using 50 division

Cropping attack

Cropping attack tries to remove some parts of the image with the intention to destroy the embedded watermark.

Cropping(128 × 128 by black) (Fig. 29).

Fig. 29

Result under cropping attack(128 × 128) and recovered watermark image using a 20 division b using 30 division c using 40 division d using 50 division

Cropping(128 × 128 by white) (Fig. 30).

Fig. 30

Result under cropping attack(128 × 128) and recovered watermark image using a 20 division b using 30 division c using 40 division d using 50 division

Cropping(256 × 256 by black) (Fig. 31).

Fig. 31

Result under cropping attack(256 × 256) and recovered watermark image using a 20 division b using 30 division c using 40 division d using 50 division

Cropping(256 × 256 by white) (Fig. 32).

Fig. 32

Result under cropping attack(256 × 256) and recovered watermark image using a 20 division b using 30 division c using 40 division d using 50 division

The watermarked images after cropping attacks and the recovered watermarks along with the NC and BER values are shown above. It is observed that the proposed method can strong enough to survive various types of cropping attacks.

Effect of image resize

In image resizing attack, the size of the image is reduced by different factors and again resize to the original size.

Image resize(512 → 256 →512) (Fig. 33).

Fig. 33

Result under effect of image resize(512$\rightarrow 256\rightarrow$512) and recovered watermark image using a 20 division b using 30 division c using 40 division d using 50 division

Also the robustness of the proposed scheme is observed by considering the different sub-bands of the images which are indicated in Tables 4 and 5 in terms of the NC and BER values.

Table 4 Comparison of NC values with different sub-bands

Table 5 Comparison of BER values with different sub-bands

Comparative analysis

The proposed robust watermarking scheme is based on IWT domain. In the previous section we have shown the efficiency of the proposed method in terms of imperceptibility and robustness to different types of attack by calculating PSNR, NC and BER values. Also the efficiency of the proposed scheme is compared with some existing robust watermarking schemes in transform domain on the basis of NC values before attack and also after applying some image processing attacks on the watermarked images Tables 6, 7, 8, 9, 10, and 11 and Figs. 34, 35, 36, 37, and 38.

Table 6 Comparision of NC values of the proposed method with Kumsawat et al. [13] and Lingamgunta et al. [14]

Table 7 The comparison results with Ansari et al. [3] and Ali & Ahn et al. [1], for common image processing operations (NC)

Table 8 The comparison results with Verma et al. [25], for common image processing operations (NC)

Table 9 The comparison results with Ali et al. [2], for common image processing operations (NC)

Table 10 The comparison results with Thabit et al. [24], for common image processing operations (NC)

Table 11 The comparison results with Wang et al. [27], for common image processing operations (NC)

Fig. 34

The comparison results with Ansari et al. [3] and Ali & Ahn [1], for common image processing operations (NC)

Fig. 35

The comparison results with Verma et al. [25], for common image processing operations (NC)

Fig. 36

The comparison results with Ali et al. [2], for common image processing operations (NC)

Fig. 37

The comparison results with Thabit et al. [24], for common image processing operations (NC)

Fig. 38

The comparison results with Wang et al. [27], for common image processing operations (NC)

Compared with other existing methods, the proposed watermarking algorithm has better robustness against various geometric and non-geometric attacks.

5 Conclusion

In this paper, a novel robust and blind binary watermarking scheme is proposed. The watermark (logo)is embedded in the low sub–band of the IWT transformed cover image. However in the low sub–band portion, the chance of watermark distortion or removal is high. But in the proposed method even after the various types of attacks applied on the watermarked images, the watermark is able to survive with low BER and high NC values. The quality of the watermarked images are also good in terms of perceptibility and PSNR. Also as compared with some existing schemes, the proposed scheme indicate its efficiency with high robustness.