A new robust color image watermarking method for multimedia technology enhanced learning protection

Abstract

In multimedia technology enhanced learning, digital watermarking is an important technique for protecting copyrighted multimedia materials. In this paper, we propose a robust color image watermarking scheme using quaternion geometric Legendre moment invariants (QGLMIs). Firstly, the original image is divided into color image blocks. Then, the Quaternion Discrete Cosine Transform (QDCT) is performed on the color image block. Finally, the digital watermark is embedded into original color image by adaptively modulating the real QDCT coefficients of color image block. For watermark detecting, the LS-SVM correction with low-order QGLMIs is utilized. Experimental results show that the proposed color image watermarking is not only invisible and robust against common image processing operations (especially for color attacks), but also robust against geometrical distortions.

Keywords

Color image watermarking color attacks geometric distortions quaternion geometric Legendre moment invariants

1 Introduction

With the rise of multimedia technologies, investigating the effect of these styles on learners’ intentions to use multimedia for learning has become all the more important [1]. Learning is better with multimedia than with other instructional media because it fosters engagement, motivation and allows discovery learning, distance learning, or multiplying information formats, including dynamic and interactive aspects prompts learners to pay attention to information and to deeply process the learning material. Multimedia can be defined as the presentation of material using both verbal (printed or spoken text) and pictorial forms (audio, image, video, etc.). However, due to the advances of multimedia and internet technologies, digital data can be easily reproduced, manipulated and distributed without any quality degradation, which resulted in strong demand for preventing illegal use of copyrighted data. Digital watermarking is an important technique for copyright protection and integrity authentication in an open network environment [2].

In most of the related applications, the watermark data has to be robust against the “watermark attacks” including common image processing operations and geometric distortions. For still images, the requirement of digital watermark surviving geometrical transformations is necessary since such manipulations as rotation, and scaling are common. Nevertheless, these procedures cause challenging synchronization problems for watermark detection. So, special care has to be taken so that the embedded watermark can survive geometric distortions to achieve the related functionalities in the target application. Nowadays, several approaches that counterattack geometric distortions have been developed. These schemes can be roughly divided into exhaustive search [3, 4], invariant transform [5, 6], geometrical correction [7, 8], and feature-based algorithms [9, 10].

However, most of the existing watermarking schemes mentioned before were designed to mark grayscale images. Color image is more common in our everyday life, and can provide more information than grayscale image, so it is very important to embed the digital watermark into color image for copyright protection. With the introduction of color imaging, some of early grayscale watermarking techniques have been extended to color images. Fu et al. [11] presented an oblivious color image watermarking scheme based on Linear Discriminant Analysis (LDA). The watermark accompanied with a reference is embedded into the RGB channels of color images. The watermark can be correctly extracted under several different attacks. Hussein et al. [12] proposed a non-blind luminance-based color image watermarking technique. Su et al. [13] proposed a state-coding based blind color image watermarking algorithm, in which the R, G, B components of color image watermark are embedded to the Y, Cr and Cb components of color host image respectively. Dejey et al. [14] introduced two color image watermarking using the combined discrete wavelet transform-fan beam transform (DWT-FBT). The two schemes proposed in the combined domain are (i) wavelet fan beam watermarking on luminance and chrominance and (ii) wavelet fan beam watermarking on chrominance alone. Niu et al. [15] described a blind color image watermarking algorithm by using the support vector regression (SVR) and nonsubsampled contourlet transform (NSCT). Chen et al. [16] introduced the quaternion Zernike moments (QZMs) to deal with the color images in holistic manner. It is shown that the QZMs can be obtained from the conventional Zernike moments of each channel. Wang et al. [17] proposed a blind color watermarking method in quaternion Fourier transform domain. For watermark decoding, the pseudo-Zernike moment is utilized. Chen et al. [18] provided a general watermarking framework to illustrate the overall performance gain in terms of imperceptibility, capacity and robustness they can achieve compared to other quaternion Fourier transform based algorithms. The above-mentioned color image watermarking schemes were designed mainly to mark the image luminance component only, which have some disadvantages in varying degrees: (i) they are sensitive to color attacks because of ignoring the significant correlation between different color channels, (ii) they are always not robust to geometric distortions for neglecting the watermark desynchronization.

In this paper, we continue our study in [19]. As noted before, there lacks a detailed discussion regarding the calculation process of the Quaternion Discrete Cosine Transform (QDCT) and the performance of the Quaternion Geometric Legendre Moment Invariants (QGLMIs). Therefore, in this paper, we give a thorough evaluation for the performance of the proposed QGLMIs.

The remainder of this paper has been organized as follows. Section 2 presents the QDCT of color images. Section 3 gives our set of QGLMIs. Section 4 contains the description of our watermark embedding procedure. Section 5 covers the details of the watermark detection procedure. The following section gives the experimental results. The final section is the conclusion.

2 Quaternion discrete cosine transform of color image

The representation of color image pixels by pure quaternions has been conceived, and used for color image compression algorithms, color images registration, color image smoothing, and edge detection [20]. Using this representation, a color image f (x, y), sized by X × Y, can be considered as an array of pure quaternion numbers (e.g. with no real parts) $f_{Q} (x, y) = f_{R} (x, y) \cdot i + f_{G} (x, y) \cdot j + f_{B} (x, y) \cdot k$ (1) where f_R (x, y), f_G (x, y) and f_B (x, y) represent respectively the classical red, green and blue components, and i, j, and k are the complex operators.

According to the mentioned concepts in [19], the DQCT transformation pairs of a color image are: $C_{Q} (p, s) = {QDCT}_{Q} [f_{Q} (x, y)]$ (2) $f_{RQ} (x, y) = {IQDCT}_{Q} [C_{Q} (p, s)]$ (3) and they can be computed by the following the steps [21 –23]:

Given a quaternion matrix f_Q (x, y), transform it into the Cayley-Dickson form, i.e. $f_{Q} (x, y) = A (x, y) + B (x, y) \cdot j$ (4)

where A (x, y) and B (x, y) are both complex matrices. Here, A (x, y) = f_R (x, y) · i and B (x, y) = f_G (x, y) + f_B (x, y) · i .

Calculate the DCT of A (x, y) and B (x, y) respectively, the results can be written as DCT_C (A (x, y)) and DCT_C (B (x, y)).

Using DCT_C (A (x, y)) and DCT_C (B (x, y)) to form a full quaternion, i.e.

$\begin{matrix} F_{fQ} (x, y) & = & {DCT}_{C} (A (x, y)) \\ + {DCT}_{C} (B (x, y)) \cdot j \end{matrix}$ (5)

Multiply F_fQ with the quaternion factor μ_Q to obtain the final result, i.e.

$\begin{matrix} C_{Q} (p, s) & = & {QDCT}_{Q} [f_{Q} (x, y)] \\ = & μ_{Q} \cdot F_{fQ} (x, y) \\ = & μ_{Q} \cdot ({DCT}_{C} (A (x, y)) \\ + {DCT}_{C} (B (x, y)) \cdot j) \\ = & μ_{Q} \cdot {DCT}_{C} (A (x, y)) \\ + μ_{Q} \cdot {DCT}_{C} (B (x, y)) \cdot j \\ = & μ_{Q} \cdot {DCT}_{C} (f_{R} (x, y) \cdot i) \\ + μ_{Q} \cdot {DCT}_{C} (f_{G} (x, y) \\ + f_{B} (x, y) \cdot i) \cdot j \\ = & μ_{Q} \cdot {DCT}_{C} (f_{R} (x, y) \cdot i) \\ + μ_{Q} \cdot {DCT}_{C} (f_{G} (x, y) \cdot j \\ + f_{B} (x, y) \cdot k) \\ = & i (μ_{Q} \cdot {DCT}_{C} (f_{R} (x, y)) \\ + j (μ_{Q} \cdot {DCT}_{C} (f_{G} (x, y)) \\ + k (μ_{Q} \cdot {DCT}_{C} (f_{B} (x, y)) \end{matrix}$ (6)

where μ_Q = μ_ii + μ_jj + μ_kk is a unit(pure) quaternion named a quaternionzation factor which meets the constraint that

μ_{Q}^{2} = - 1

Let A (p, s) denote the real part of color image in QDCT domain, C (p, s), D (p, s), and E (p, s) be the three imaginary parts of color image in QDCT domain:

$\begin{matrix} C_{Q} (p . s) & = & A (p, s) + i C (p, s) \\ + j D (p, s) + k E (p, s) \end{matrix}$ (7)

Substitution of μ_Q = μ_ii + μ_jj + μ_kk into Equation (7) leads to $\begin{matrix} A (p, s) & = & - μ_{i} \cdot DCT (f_{R} (x, y)) \\ - μ_{j} \cdot DCT (f_{G} (x, y)) \\ - μ_{k} \cdot DCT (f_{B} (x, y)) \end{matrix}$ (8) $\begin{matrix} C (p, s) & = & μ_{k} \cdot DCT (f_{G} (x, y)) \\ [1 pt] & - μ_{j} \cdot DCT (f_{B} (x, y)) \end{matrix}$ (9) $\begin{matrix} D (p, s) & = & - μ_{k} \cdot DCT (f_{R} (x, y)) \\ [1 pt] & + μ_{i} \cdot DCT (f_{B} (x, y)) \end{matrix}$ (10) $\begin{matrix} E (p, s) & = & μ_{j} \cdot DCT (f_{R} (x, y)) \\ [1 pt] & - μ_{i} \cdot DCT (f_{G} (x, y)) \end{matrix}$ (11)

Then, the IQDCT of Equation (3) can be represented as

$\begin{matrix} f_{RQ} (x, y) & = & {IQDCT}_{Q} [C_{Q} (p, s)] \\ = & μ_{Q} \cdot IDCT (A (p, s)) \\ + i (μ_{Q} \cdot IDCT (C (p, s))) \\ + j (μ_{Q} \cdot IDCT (D (p, s))) \\ + k (μ_{Q} \cdot IDCT (E (p, s))) \end{matrix}$ (12) where IDCT (·) is the real IQDCT of two-dimensional X × Y matrix.

Likewise, Let f_A (x, y) denote the real part of color image in IQDCT domain, f_C (x, y), f_D (x, y), and f_E (x, y) be the three imaginary parts of color image:

$\begin{matrix} f_{RQ} (x, y) & = & f_{A} (x, y) + f_{C} (x, y) \cdot i \\ + f_{D} (x, y) \cdot j + f_{E} (x, y) \cdot k \end{matrix}$ (13)

Substitution of μ_Q = μ_ii + μ_jj + μ_kk into Equation (12) leads to $\begin{matrix} f_{A} (x, y) & = & μ_{i} \cdot IDCT (C (p, s)) \\ + μ_{j} \cdot IDCT (D (p, s)) \\ + μ_{k} \cdot IDCT (E (p, s)) \end{matrix}$ (14) $\begin{matrix} f_{C} (x, y) & = & - μ_{i} \cdot IDCT (A (p, s)) \\ [1 pt] & - μ_{k} \cdot IDCT (D (p, s)) \\ + μ_{j} \cdot IDCT (E (p, s)) \end{matrix}$ (15) $\begin{matrix} f_{D} (x, y) & = & - μ_{j} \cdot IDCT (A (p, s)) \\ [1 pt] & + μ_{k} \cdot IDCT (C (p, s)) \\ - μ_{i} \cdot IDCT (E (p, s)) \end{matrix}$ (16) $\begin{matrix} f_{E} (x, y) & = & - μ_{k} \cdot IDCT (A (p, s)) \\ [1 pt] & - μ_{j} \cdot IDCT (C (p, s)) \\ + μ_{i} \cdot IDCT (D (p, s)) \end{matrix}$ (17)

3 Quaternion geometric Legendre moment invariants

3.1 Quaternion Legendre moments (QLMs) definition

The (p+q)th order QLMs of f_Q (x, y) are given by

$\begin{matrix} {QLM}_{pq} & = & \int_{- 1}^{1} \int_{- 1}^{1} P_{p} (x) P_{q} (y) μ_{Q} f_{Q} (x, y) dxdy, \\ p, q = 0, 1, 2, \dots, \end{matrix}$ (18) where μ_Q is any unit pure quaternion, for example: μ_Q = i , μ_Q = j , μ_Q = k , $μ_{Q} = (\sqrt{2} / 2) i + (\sqrt{2} / 2) k$ , $μ_{Q} = (\sqrt{3} / 3) i + (\sqrt{3} / 3) j + (\sqrt{3} / 3) k$ , etc. P_p (x) is the pth-order orthonormal Legendre polynomial.

Using the orthogonally property of Legendre moments, the image can be approximately reconstructed from a finite number moments of order up to (X, X) as $f_{Q} (x, y) \approx \sum_{x = 0}^{X} \sum_{y = 0}^{X} p_{i} (x) p_{j} (y) μ_{Q} {QLM}_{ij}$ (19)

Figure 1 gives some examples of image reconstruction using QLMs for popular test color image Lena (128*128), Mandrill (256*256), Barbara (512*512). As can be seen from the Fig. 1, the reconstructed images using QLMs show more visual resemblance to the original image.

3.2 Quaternion geometric Legendre moment invariants (QGLMIs)

The geometric transform of a color image consists of rotation, translation and uniform scale transform. Suppose f (x′, y′) is the transformed replica of original image f (x, y). We can use a matrix equation to represent geometric transform as follows: $(\begin{matrix} x^{'} \\ y^{'} \end{matrix}) = α (\begin{matrix} cos φ & sin φ \\ - sin φ & cos φ \end{matrix}) (\begin{matrix} x \\ y \end{matrix}) + (\begin{matrix} Δ x \\ Δ y \end{matrix})$ (20) where α is the scale factor with α > 0, φ is the rotation angle, Δx and Δy are the translation offset along x - axes and y - axes, respectively.

Based on this decomposition, we derive a set of QGLMIs, ${QGLMI}_{pq}^{t}$ , ${QGLMI}_{pq}^{s - t}$ and ${QGLMI}_{pq}^{r - s - t}$ that are invariant to translation, uniform scale transform and rotation respectively. They are defined as follows:

$\begin{matrix} {QGLMI}_{pq}^{t} \\ = \sum_{m = 0}^{p} \sum_{n = 0}^{q} \sum_{s = 0}^{m} \sum_{t = 0}^{n} \sum_{i = 0}^{s} \sum_{j = 0}^{t} (\begin{matrix} m \\ s \end{matrix}) (\begin{matrix} n \\ t \end{matrix}) \\ c_{p, m} c_{q, n} d_{s, i} d_{t, j} (- x_{0})^{m - s} (- y_{0})^{n - t} {QLM}_{i, j} \end{matrix}$ (21)

$\begin{matrix} {QGLMI}_{pq}^{s - t} \\ = \sum_{m = 0}^{p} \sum_{n = 0}^{q} \sum_{i = 0}^{m} \sum_{j = 0}^{n} \\ c_{p, m} c_{q, n} d_{m, i} d_{n, j} Γ^{- (m + n + 2)} {QLM}_{ij} \end{matrix}$ (22)

$\begin{matrix} {QGLMI}_{pq}^{r - s - t} \\ = \sum_{m = 0}^{p} \sum_{n = 0}^{q} \sum_{s = 0}^{m} \sum_{t = 0}^{n} \sum_{i = 0}^{s + t} \sum_{j = 0}^{m + n - s - t} (\begin{matrix} m \\ s \end{matrix}) (\begin{matrix} n \\ t \end{matrix}) (- 1)^{t} \\ (cos θ)^{n + s - t} (sin θ)^{m + t - s} \cdot \\ c_{p, m} c_{q, n} d_{s + t, i} d_{m + n - s - t, j} {QLM}_{ij} \end{matrix}$ (23) where $Γ = \sqrt{{QLM}_{00}}$ , $θ = \frac{1}{2} {tan}^{- 1} \frac{2 {QLM}_{11}}{{QLM}_{20} - {QLM}_{02}}$ , x₀ and y₀ are the centroids of x-and y-coordinate are given by $x_{0} = \frac{\sum \sum xf (x, y)}{\sum \sum f (x, y)}, y_{0} = \frac{\sum \sum yf (x, y)}{\sum \sum f (x, y)}$ (24)

By combining ${QGLMI}_{pq}^{t}$ , ${QGLMI}_{pq}^{s - t}$ and ${QGLMI}_{pq}^{r - s - t}$ that are respectively invariant to translation, scale and rotation transform, we can obtain our set of QGLMIs. For a color image f_Q (x, y), we use the following process:

Step 1: Translation invariants ${QGLMI}_{pq}^{t}$ are calculated by Equation (21), where the quaternion Legendre moments QLM_i,j are computed with Equation (18).

Step 2: The combined invariants ${QGLMI}_{pq}^{s - t}$ with respect to translation and scale transform are computed by Equation (22) where the QLM_i,j on the right-hand side of Equation (22) are replace by ${QGLMI}_{pq}^{t}$ computed in step 1.

Step 3: The QGLMIs ( ${QGLMI}_{pq}^{r - s - t}$ ) are calculated by Equation (23) where the QLM_i,j on the right-hand side of Equation (23) are replace by ${QGLMI}_{pq}^{s - t}$ computed in step 2.

3.3 Characteristic analysis of the QGLMIs

QLMs and QGLMIs are well comprehensive characterization and describe the characteristics of the color image. Through a large number of experiments, we proved QGLMIs has better robust performance than QLMs under various common image processing operations (especially for color attacks).

Figure 2 shows the absolute deviation comparison after some common image processing operations of QLMs for the 24-bit color image Lena (512*512). Figure 3 shows the absolute deviation comparison after some common image processing operations of QGLMIs for the 24-bit color image Lena (512*512). It can be seen that the range of the absolute deviation of most QLMs distribute between –1 and 1. By contrast, the range of the absolute deviation of most QGLMIs distribute between –0.1 and 0.1. So, the QGLMIs are more suitable for robust image watermarking than the QLMs.

In this paper, we propose a geometric correction based robust color image watermarking approach using QGLMIs. The approach embeds the watermark information into original color image in QDCT domain. For watermark decoding, the LS-SVM correction with QGLMIs is utilized, which can effectively improve the approach’s robustness against geometrical distortion.

4 Watermark embedding scheme

Let $\begin{matrix} I & = & {R (x, y), G (x, y), B (x, y)} \\ (0 \leq x < M, 0 \leq y < N) \end{matrix}$ denote a host digital image (color image), and R (x, y) , G (x, y) , B (x, y) are the color component values at position (x, y).

W = {w (i, j) , 0 ≤ i < P, 0 ≤ j < Q} is a binary image to be embedded within the host image. The digital watermark embedding scheme can be summarized as follows.

4.1 Watermark preprocessing

In order to dispel the pixel space relationship of the binary watermark image, and improve the robustness of the whole digital watermark system, watermark scrambling algorithm is used at first. In our watermark embedding scheme, the binary watermark image is scrambled from W to W₁ by using Arnold transform, where $W_{1} = {w (i, j) \in {0, 1}, 0 \leq i < P, 0 \leq j < Q}$

Then, it is divided into watermark blocks W_k of 2×2 bits $\begin{matrix} W_{k} & = & {w_{k} (i, j), 0 \leq i \leq 1, 0 \leq j \leq 1} \\ (k = 1, 2, \dots, P / 2 * Q / 2) \end{matrix}$

4.2 QDCT of color image block

The original color image I is divided into small color image blocks B_k = {b_k (i, j) , 0 ≤ i ≤ 7, 0 ≤ j ≤ 7} (k = 1, 2, ⋯ , M / 8 * N / 8) of 8×8 pixels. The QDCT is performed on the color image block B_k, and a real coefficient matrix A_k and three imaginary coefficient matrices C_k, D_k, E_k are obtained (See Section 2).

From the quaternion representation of color image, we know that the watermarked color image should also be represented in pure quaternion form after IQDCT so as to transmit high-quality watermarked image in RGB color space (or other color space). In order to obtain the pure quaternion representation of watermarked color image, we must ensure f_A (x, y) =0(See Equation (13)). Equation (14) shows that f_A (x, y) have no relation with the real part of color image in QDCT domain, which be denoted by A (p, s). Furthermore, A (p, s) can be simultaneously served by the R, G, B components of the color image f_R (x, y), f_G (x, y) and f_B (x, y) (See Equation (8)), and thus paves the way to process color images in a holistic manner. Therefore, the real part of color image in QDCT domain was selected to be embedded watermarking in this paper.

4.3 Digital watermark embedding

The watermark block W_k with 2×2 watermark bits is embedded into the color image blocks B_k with 8×8 pixels by modifying the real QDCT coefficients block: $\begin{matrix} a_{k}^{'} (i, j) \\ = {\begin{matrix} 2 Δ * round (a_{k} (i, j) / 2 Δ) + Δ / 2 \begin{matrix} \end{matrix} if \begin{matrix} \end{matrix} w_{k} (i, j) = 1 \\ 2 Δ * round (a_{k} (i, j) / 2 Δ) - Δ / 2 \begin{matrix} \end{matrix} if \begin{matrix} \end{matrix} w_{k} (i, j) = 0 \end{matrix} \\ (k = 1, 2, \dots, P / 2 * Q / - 2) (0 \leq i \leq 1, 0 \leq j \leq 1) \end{matrix}$ (25)

where W_k is the digital watermark block, A_k = {a_k (i, j) , 0 ≤ i ≤ 7, 0 ≤ j ≤ 7} is the old real QDCT coefficients block of color image blocks B_k, $A_{k}^{'} = {a_{k}^{'} (i, j), 0 \leq i \leq 7, 0 \leq j \leq 7}$ is the new real QDCT coefficients block, round (·) denotes round operator, Δ is the watermark embedding strength.

4.4 Obtaining the watermarked image

The watermarked color image block $B_{k}^{'}$ can be obtained by performing the IQDCT, in which the new real coefficient matrix $A_{k}^{'}$ is used instead of the old real coefficient matrix A_k. We repeat Sections 4.2–4.3 to embed M * N / 16 * P * Q - 1 copies of digital watermark into other color image blocks. Finally, the watermarked color image I′ can be obtained by combining the watermarked color image blocks.

5 Watermark detection scheme

5.1 Geometric correction with QGLMIs

The standard SVM [24] is solved using quadratic programming methods. However, these methods are often time consuming and are difficult to implement adaptively. LS-SVM is capable of solving both classification and regression problems and is receiving more and more attention because it has some properties that are related to the implementation and the computational method.

In order to extract accurately digital watermark, we use LS-SVM training model to estimate the geometric transform parameters of watermarked color image, and then correct the watermarked color image according to the estimated parameters for resisting the geometric distortions. The process of correcting watermarked color image based on LS-SVM and QGLMIs is as follows.

5.1.2 Constructing training image

We discuss the familiar geometric distortions including rotation, scaling, and translation etc. In order to obtain the LS-SVM training model, we must construct the training images H^k (k = 0, 1, ⋯ , K - 1). In fact, the training images can be constructed by moving (including X-axis and Y-axis), rotating, and scaling an arbitrary color image. In this paper, we construct the training image samples by moving, rotating and scaling the watermarked color image.

5.1.3 Representative feature vector selection

From the foregoing, we know that the QGLMIs have good robustness against various color attacks, so we select the QGLMIs of color image as representative feature vector for LS-SVM classification. However, we do not need all the QGLMIs in color image geometric correction. Considering that we will discuss global geometric distortions, we select 6 low-order QGLMIs, QLMI₁₃, QLMI₃₁, QLMI₃₃, QLMI₂₅, QLMI₄₃, QLMI₆₁ (we denote them as f_1,3, f_3,1, f_3,3, f_2,5, f_4,3, f_6,1, respectively) as representative feature vector.

5.1.3 LS-SVM training

We firstly select 6 low-order QGLMIs $(f_{1, 3}^{k}, f_{3, 1}^{k}, f_{3, 3}^{k}, f_{2, 5}^{k}, f_{4, 3}^{k}, f_{6, 1}^{k})$ (k = 0, 1, ⋯ , K - 1) of the training color images H^k as representative feature vector, and describe the corresponding geometric transform (X-translation, Y-translation, scaling and rotation) parameters $t_{x}^{k}, t_{y}^{k}, s^{k}, θ^{k}$ (k = 0, 1, ⋯ , K - 1) as the training objective. Here, t_x, t_y, s, θ represent X-direction moving distance,Y-direction moving distance, scaling factor, and rotation angle, respectively.

Then, we can obtain the training samples as following $\begin{matrix} Ω_{k} & = & (f_{1, 3}^{k}, f_{3, 1}^{k}, f_{3, 3}^{k}, f_{2, 5}^{k}, f_{4, 3}^{k}, f_{6, 1}^{k}, t_{x}^{k}, t_{y}^{k}, s^{k}, θ^{k}) \\ (k = 0, 1, \dots, K - 1) \end{matrix}$

For the linear transformation like rotation, scaling, and translation, there is no coupling among the 4 outputs, so we adopt the MIMO system constructed by 4 LS-SVM parallel structures which is with 4 inputs, and the LS-SVM model can be obtained by training.

5.1.4 Watermarked color image correction

Firstly, compute 6 low-order QGLMIs of the watermarked color image I^* ( ${QLMI}_{13}^{*}$ , ${QLMI}_{31}^{*}$ , ${QLMI}_{33}^{*}$ , ${QLMI}_{25}^{*}$ , ${QLMI}_{43}^{*}$ , ${QLMI}_{61}^{*}$ ) and let them be the input vectors.

Then, the actual output $t_{x}^{*}, t_{y}^{*}, s^{*}, θ^{*}$ (geometric transformation parameters) is predicted by using the well trained LS-SVM model.

Finally, correct the geometric distortions of watermarked color image I^* (that is inverse transformation such as rotation angle, translation parameters etc.) by using the obtained geometric transformation parameters $t_{x}^{*}, t_{y}^{*}, s^{*}, θ^{*}$ so that we can get the corrected watermarked image $\hat{I}$ .

Figure 4 shows the geometric correction results for standard image Barbara.

5.2 Watermark extraction

The watermark extraction procedure in the proposed scheme neither needs the original color image nor any other side information. The main steps of watermark extraction can be described as follows.

Firstly, the corrected watermarked color image $\hat{I}$ is divided into small color image blocks ${\hat{B}}_{k}$ of 8×8 pixels ${\hat{B}}_{k} = {{\hat{b}}_{k} (i, j), 0 \leq i \leq 7, 0 \leq j \leq 7}$ ( $k = 1, 2, \dots, \hat{M} / 8 * \hat{N} / 8$ ).

Secondly, the DQCT is performed on the watermarked color image block ${\hat{B}}_{k}$ , and a real coefficient matrix ${\hat{A}}_{k}$ and three imaginary coefficient matrices ${\hat{C}}_{k}$ , ${\hat{D}}_{k}$ , ${\hat{E}}_{k}$ are obtained. (See Section 2)

Thirdly, the watermark block ${\hat{W}}_{k}$ with 2×2 watermark bits are extracted from the real coefficient matrix ${\hat{A}}_{k}$ of the watermarked color image blocks ${\hat{B}}_{k}$ as follow $\begin{matrix} {\hat{w}}_{k} (i, j) \\ = {\begin{matrix} 1 if {\hat{a}}_{k} (i, j) - 2 Δ * round ({\hat{a}}_{k} (i, j) / 2 Δ) > 0 \\ 0 if {\hat{a}}_{k} (i, j) - 2 Δ * round ({\hat{a}}_{k} (i, j) / 2 Δ) \leq 0 \end{matrix} \\ (k = 1, 2, \dots, P / 2 * Q / 2) (0 \leq i \leq 1, 0 \leq j \leq 1) \end{matrix}$ (26)

where ${\hat{W}}_{k} = {{\hat{w}}_{k} (i, j), 0 \leq i \leq 1, 0 \leq j \leq 1}$ is the extracted digital watermark block, ${\hat{A}}_{k} = {{\hat{a}}_{k} (i, j)}$ is the real DQCT coefficients matrix of watermarked color image blocks.

Finally, the digital watermark $\hat{W} = {\hat{w} (i, j), 0 \leq i < P, 0 \leq j < Q}$ can be obtained by the watermark block combination and inverse scrambling operation. Then, the optimal digital watermark W^* can be obtained according to the majority rule.

6 Simulation results

We test the proposed color image watermarking scheme on the popular test images 512×512×24 bit Lena, Barbara, Mandrill, and Peppers, and a 64×64 binary image is used as the digital watermark. The number of training samples is K = 250, the watermark embedding strength is Δ = 40 and the radius-based function (RBF) is selected as the LS-SVM kernel function. Also, the experimental results are compared with schemes in [11 , 26].

Tables 1 and 2 give the LS-SVM estimation performance for geometric transform parameters.

In order to test the robustness of the proposed scheme, we have done extensive experiments. Simulation results, for common image processing operations and geometric distortions. In this study, reliability was measured as the bit error rate (BER) of extracted watermark.

Common image processing operations: Traditional signal processing attacks act on the watermarking system by reducing the watermark energy. Figures 5 and 6 show the visual-perception results and quantitative results for the common image processing operations, which are obtained by the proposed watermarking scheme. Figure 7 shows that our scheme is more robust against average filtering, noise, equalization, blurring, JPEG etc., compared with scheme [11 , 26]. Besides, it can be seen that the watermark message can be entirely extracted (BER = 0) under color attacks, such as light increasing/lowering, contrast increasing/lowering etc.

Geometric distortions: Our scheme can resist RST attacks and it can extract the watermark directly from the corrected watermarked color images, which are corrected with the well trained LS-SVM model. Figure 8 shows a part of the visual-perception results. Figures 9 and 10 show the quantitative results for the geometric distortions, which are covered or missed in the training, respectively. It can be seen that the BER in Fig. 9 is significantly smaller than the BER in Fig. 10. Besides, Fig. 11 verified that our scheme yields better robustness than those in scheme [11, 25, 26].

7 Conclusion

The existing color image watermarking schemes were always designed to mark the image luminance component only, which ignore the significant correlation between different color channels. In this paper, we have proposed a new robust color image watermarking scheme using QGLMIs in QDCT domain. Rather than separating a color image into three channel images and processing them respectively as the traditional methods, QDCT and QGLMIs can handle color image pixels as vectors and process them in a holistic manner. Extensive experiments have indicated that the proposed color image watermarking algorithm is robust to most common image processing operations (especially for color attacks) and geometric distortions, because the efficient QGLMIs based LS-SVM geometric correction is utilized.

In the future, we will extend the proposed watermarking solution to the image retrieval scenario [27], with the goal of addressing the imagery copyright protection and similarity computation problems using a unified framework.

Footnotes

Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grant No. 61272416, 61472171, 61301185 & 61300082, the Foundation of Science and Technology Plan for Higher Education of Liaoning Province of China under Grant No. L2015289, the Program for Liaoning Excellent Talents in University No. LJQ2015006, and Youth Foundation of Liaoning Normal University of China under Grant No. LS2014L016.

References

Vimala

and Chin

G.L.

, Students’ learning styles and their effects on the use of social media technology for learning, Telematics and Informatics33(3) (2016), 808–821.

, Halawani

and Feng

, Multimodal hand and foot gesture interaction for handheld devices, ACM Transactions on Multimedia Computing, Communications, and Applications (TOMM)11(1s) (2014), 10.

, Chang

and Wu

C.C.

, Geometrically resilient digital image watermarking by using interest point extraction and extended pilot signals, IEEE Trans on Information Forensics and Security8(12) (2013), 1897–1908.

Valizadeh

and Wang

Z.J.

, Correlation-and-bit-aware spread spectrum embedding for data hiding, IEEE Trans on Information Forensics and Security6(2) (2011), 267–282.

Wang

X.Y.

, Wang

A.L.

and Yong

H.Y.

, A new robust digital image watermarking based on exponent moments invariants in nonsubsampled contourlet transform, Computers and Electrical Engineering40(3) (2014), 942–955.

Mohammad

A.A.

, A new digital image watermarking scheme based on Schur decomposition, Multimedia Tools and Applications59(3) (2012), 851–883.

, Ling

and Zou

, Robust localized image watermarking based on invariant regions, Digital Signal Processing22(1) (2012), 170–180.

Qiu

, Lu

, Deng

and Cai

, A robust blind image watermarking scheme based on template in Lab color space, Communications in Computer and Information Science234 (2011), 402–410.

, Deng

, An

L.L.

and Huang

D.Y.

, Desynchronization attacks resilient image watermarking scheme based on global restoration and local embedding, Neurocomputing106(15) (2013), 42–50.

10.

Tsai

J.S.

, Huang

W.B.

and Kuo

Y.H.

, On the selection of optimal feature region set for robust digital image watermarking, IEEE Trans on Image Processing20(3) (2011), 735–743.

11.

Y.G.

and Shen

R.M.

, Color image watermarking scheme based on linear discriminant analysis, Computer Standard & Interfaces30(3) (2008), 115–120.

12.

Hussein

J.A.

, Luminance-based embedding approach for color image watermarking, Journal of Image, Graphics and Signal Processing4(3) (2012), 49–56.

13.

, Niu

and Liu

, A blind dual color images watermarking based on IWT and state coding, Optic Communication285(7) (2012), 1717–1724.

14.

Dejey

and Rajesh

R.S.

, Robust discrete wavelet-fan beam transforms-based colour image watermarking, IET Image Processing5(4) (2011), 315–322.

15.

Niu

P.P.

, Wang

X.Y.

and Yang

Y.P.

, A novel color image watermarking scheme in nonsampled contourlet-domain, Expert Systems with Applications38(3) (2011), 2081–2098.

16.

Chen

B.J.

, Shu

H.Z.

and Zhang

, Quaternion Zermike moments and their invariants for color image analysis and object recognition, Signal Processing92(2) (2012), 308–318.

17.

Wang

X.Y.

, Wang

C.P.

and Yang

H.Y.

, A robust blind color image watermarking in quaternion Fourier transforms domain, Journal of Systems and Software86(2) (2013), 255–277.

18.

Chen

B.J.

, Coatrieux

and Chen

, Full 4-D quaternion discrete Fourier transform based watermarking for color images, Digital Signal Processing28 (2014), 106–119.

19.

Niu

P.P.

, Wang

X.Y.

and Lu

M.Y.

, Robust color image watermarking using ls-svm correction, Lecture Notes in Computer Science7368 (2012), 290–296.

20.

Todd

A.E.

and Stephen

J.S.

, Hypercomplex Fourier transforms of color images, IEEE Trans on Image Processing16(1) (2007), 22–35.

21.

Jia

, An approach for compressing of multichannel vibration signals of induction machines based on quaternion cosine transform, 2010 International Conference on E-Product E-Service and E-Entertainment (ICEEE2010), Henan, China, 2010, pp. 3976–3979.

22.

Gai

, Sun

Y.F.

and Wang

X.L.

, Color image digital watermarking using discrete quaternion cosine transform, Journal of Optoelectronics Laser20(9) (2009), 1193–1197.

23.

Feng

and Hu

, Quaternion discrete cosine transform and its Application in color template matching, 2008 Congress on Images and Signal Processing (CISP’08), Sanya, China, 2008, pp. 252–256.

24.

Vapnik

, The nature of statistical learning theory, Springer-Verlag, New York, 1995.

25.

Peng

, Wang

and Wang

W.X.

, Image watermarking method in multiwavelet domain based on support vector machines, Journal of Systems and Software83(8) (2010), 1470–1477.

26.

Tsougenis

E.D.

, Papakostas

G.A.

and Koulouriotis

D.E.

, Towards adaptivity of image watermarking in polar harmonic transforms domain, Optics & Laser Technology54(32) (2013), 84–97.

27.

, Shen

and Li

Y.D.

, Learning a hybrid similarity measure for image retrieval, Pattern Recognition46(11) (2013), 2927–2939.