Invariant domain watermarking using heaviside function of order alpha and fractional Gaussian field

Abstract

Digital image watermarking is an important technique for the authentication of multimedia content and copyright protection. Conventional digital image watermarking techniques are often vulnerable to geometric distortions such as Rotation, Scaling, and Translation (RST). These distortions desynchronize the watermark information embedded in an image and thus disable watermark detection. To solve this problem, we propose an RST invariant domain watermarking technique based on fractional calculus. We have constructed a domain using Heaviside function of order alpha (HFOA). The HFOA models the signal as a polynomial for watermark embedding. The watermark is embedded in all the coefficients of the image. We have also constructed a fractional variance formula using fractional Gaussian field. A cross correlation method based on the fractional Gaussian field is used for watermark detection. Furthermore the proposed method enables blind watermark detection where the original image is not required during the watermark detection thereby making it more practical than non-blind watermarking techniques. Experimental results confirmed that the proposed technique has a high level of robustness.

Fig 1. (a)Watermark consist of random sequence of +1, -1. (b-c) Watermark pattern.

Fig 2. Watermark embedding scheme for the Invariant domain.

Fig 3. Watermark Detection.

Fig 4. Robustness against JPEG compression attack. Five watermarked images are tested for the JPEG compression quality factor ranging from 10 to 90.

Fig 5. Robustness against circular shift Attack. Comparison of the Correlation and Threshold values of five watermarked test images against the circular shift attack.

Fig 6. Circular shift attack operation of 50% image size.

(a) Original image. (b) Pixels at lower half of the image shifted upwards. (c) Circular shift attacked image. Pixels at left half of image shifted towards right hand side of the image.

Fig 7. Robustness against scaling Attack.

(a-d) Comparison of Correlation values of four images after scaling attack of the proposed technique.

Fig 8. Robustness against rotation attack.

The rotated images have also been scaled and cropped. (a-d) Original Test Images, (e-h) Attacked watermarked Test Images: Rotation attack for different values of the angles are taken such as 5, 10, 15 and 30 degree respectively.

Fig 9. Robustness of Proposed Technique against Rotation attacks.

Five watermarked images are tested for the rotation attack. Rotation angle is taken of different values such as 5, 10, 15, 30, 45 and 90 degrees.

Fig 10. Robustness of Proposed Technique against Cropping attack.

(a-c) Original images of size 512×512 pixels. (d) strips 25 and 26 pixels wide were cropped from the bottom and right hand side of the image respectively. The size of the image after cropping attack is 487×486 pixels. (e) strips 54 pixels wide were cropped from the bottom and right hand side of the image. The size of the image after cropping attack is 458×458 pixels. (f) strips 149 pixels wide were cropped from the bottom and right hand side of the image. The size of the image after cropping attack is 363×363 pixels.