Intelligent Automation & Soft Computing DOI:10.32604/iasc.2022.024070 | |

Article |

Contourlet and Gould Transforms for Hybrid Image Watermarking in RGB Color Images

1Department of ECE, Noorul Islam Centre for Higher Education, Kumaracoil, 629180, India

2Department of ECE, Malla Reddy College of Engineering and Technology, Hyderabad, 500001, India

*Corresponding Author: Reena Thomas. Email: reenathomaspaper12@gmail.com

Received: 02 October 2021; Accepted: 03 November 2021

Abstract: The major intention of this work is to introduce a novel hybrid image watermarking technique for RGB color images. This hybrid watermarking algorithm uses two transforms such as Contourlet and Gould transform. The Contourlet transform is used as first stage while the Gould transform is used as second stage. In the watermark embedding phase, the R, G and B channels are transformed using Contourlet transform. The bandpass directional sub band coefficients of Contourlet transformed image are then divided into

Keywords: Contourlet transform; embedding rate; Gould transform; hybrid image watermarking; robustness

Image watermarking [1–3] is a technique where information is hidden on a host image. These watermarking techniques have applications in protecting and verifying the copyright of host image. Today, because to the fast advancement in digital technologies, especially the internet, huge amount of media such as image are transmitted and shared around the world. Protecting and verifying the ownership of the image is a challenging task. Watermarking is an advance solution to ensure the copyright of images. Watermarking system is categorized on the basis of watermark visibility. The watermark will be transparent in a visible watermarking while it is not transparent in an invisible watermarking technique [4–6].

Watermarking can be performed on spatial domain [7–9] as well as frequency domain [10–12]. In spatial domain method, secret data is directly induced on pixel intensities without any transformation in host image pixel intensities. Since the pixel intensities are easily modifiable, these techniques are highly vulnerable to attacks. In a frequency domain scheme, the watermark is induced on the host after applying a transform. These frequency domain methods are more resistant to attacks when compared to spatial domain scheme, because of its less sensitivity to such attacks.

Many researchers are working on image watermarking algorithm [13,14] to improve the performance such as embedding rate, image quality and robustness. The term robustness addresses the capability to recover the watermark even though the image is subjected to various types of spatial attacks. The spatial domain schemes include Histogram Shift [15], Differential Expansion [16] and Predictive Expansion [17]. Frequency domain schemes include transforms such as Discrete Fourier Transform (DFT) [18], Discrete Cosine Transform (DCT) [19] and Discrete Wavelet Transform (DWT) [20]. These transform also uses the decomposition method such as Singular Value Decomposition (SVD) [21], QR Decomposition, Schur Decomposition [22] and LU Decomposition [23].

Initially, the Contourlet transform [24] was proposed using multiscale filtering and block ridgelet transform that works on continuous domain. Later the ridgelet transform was replaced by frequency partitioning and the transform was named as second generation curvelet transform. The Contourlet transform needs an edge detection process and adaptive representation. This Contourlet uses a double filter bank to obtain the sparse representation for smooth contour images. It performs the edge detection process using a transform similar to wavelet. For detecting the Contour segment, it uses a local directional transform.

The multiscale decomposition can be achieved by using Laplacian Pyramid (LP). At each level of Laplacian Pyramid decomposition, a low pass of the original image is generated. In multidirectional filter bank the down sampling the signal

In 2006, Le et al. proposed discrete Gould transform [25]. In this 2D Gould transform a matrix or image

Therefore, the 2D Gould transform for a 2D gray scale image

where

Let f_ij be the pixel in a 2 × 2 subimage in ith row and jth column. In a 2 × 2 subimage the discrete Gould transform coefficients specifies the differencing between the neighbouring pixels. The inverse discrete Gould transform for the transformed image F can be obtained using the relation,

From Eq. (6), if all the Gould coefficients are used for embedding (i.e., all the coefficients are incremented by

3 Proposed Hybrid Watermarking Algorithm

Fig. 2 depicts a detailed flow of embedding process. Let

After embedding the watermark bit

Here,

Input: RGB host image

Output: Watermarked image

Step 1: Separate the channels from the host image

Step 2: Obtain the Contourlet transform for the R channel

Step 3: Subdivided the bandpass directional subband Contourlet coefficients

Step 4: Obtain the Gould transform for the

Step 5: Embed the watermark data

Step 6: Obtain the inverse Gould transform for

Step 7: Merge the

Step 8: Obtain the inverse Contourlet transform for

Step 9: Repeat Step 2 to 8 for G and B channels to obtain

Fig. 3 depicts a detailed flow of extraction process. Let

From the Gould coefficients

The algorithm for watermark embedding is given below,

Input: Watermarked image

Output: Extracted watermark

Step 1: Separate individual channels from the watermarked image

Step 2: Obtain the Contourlet transform for the R channel

Step 3: Subdivided the bandpass directional sub-band Contourlet coefficients to

Step 4: Obtain the Gould transform for the

Step 5: Extract the watermark data

Step 6: Repeat 2nd step through 5th step 5 to extract complete watermark data

MATLAB was used to implement the proposed technique with the four test RGB host images shown in Fig. 4. Each of these host images has a dimension of 512 × 512. The test watermark images are also RGB color images each having a size of

The embedding rate can be calculated as,

Fig. 6 shows the watermarks extracted from different cover images without applying attacks. The robustness of the proposed hybrid watermarking algorithm was tested using the attacks listed in Tab. 1 and Fig. 7 shows the images that are subjected to such attacks.

Figs. 8 and 9 displays the watermarks that have been extracted from the watermarked images that have been applied with attacks listed in Tab. 2. and Fig. 10 shows the watermarked images for the watermark ‘Facebook’ and ‘Apple’.

Tab. 2 shows the PSNR, SSIM, and NCC measurement for the proposed method. The average PSNR was found to be 45 dB. The SSIM and NCC was found to be greater than 0.99. Fig. 11 shows the PSNR for varrying embedding capacity in multiple RGB host images. In all the Host images, the Apple watermark provides a higher PSNR than the Facebook watermark. The NCC (Normalized Cross Correlation) metric gives the robustness of the proposed method when subjected to various attacks. The NCC of the proposed method was compared with existing methods such as Improved Hybrid, Tensor decomposition and LU decomposition. Tab. 3 shows the NCC comparison and the proposed algorithm provides higher values than the existing methods.

This paper introduced a novel hybrid color image watermarking algorithm which uses Contourlet transform and Gould transform. The color image is initially transformed using Contourlet transform and the bandpass directional sub-band coefficients are again transformed using Gould transform. The secret data is induced on the

Acknowledgement: The author with a deep sense of gratitude would thank the supervisor for his guidance and constant support rendered during this research.

Funding Statement: The authors received no specific funding for this study.

Conflicts of Interest: The authors declare that they have no conflicts of interest to report regarding the present study.

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