Abstract
This paper presents a high dynamic range (HDR) image zero watermarking method based on dual tree complex wavelet transform (DT-CWT) and quaternion. In order to be against tone mapping (TM), DT-CWT is used to transform the three RGB color channels of the HDR image for obtaining the low-pass sub-bands, respectively, since DT-CWT can extract the contour of the HDR image and the contour change of the HDR image is small after TM. The HDR image provides a wide dynamic range, and thus, three-color channel correlations are higher than inner-relationships and the quaternion is used to consider three color channels as a whole to be transformed. Quaternion fast Fourier transform (QFFT) and quaternion singular value decomposition (QSVD) are utilized to decompose the HDR image for obtaining robust features, which is fused with a binary watermark to generate a zero watermark for copyright protection. Furthermore, the binary watermark is scrambled for the security by using the Arnold transform. Experimental results denote that the proposed zero-watermarking method is robust to TM and other image processing attacks, and can protect the HDR image efficiently.
Highlights
Since high dynamic range (HDR) imaging is able to capture the wide range of realworld lighting, the HDR image meets the high requirements for image quality and visual perception [1,2,3]
The maximum Normalized cross-correlation (NC) is less than 0.6, which denotes that the zero watermark from one HDR image is distinguishable from those of other images and can prove the uniqueness of a zero watermark
Since most tone mapping (TM) operations preserve the contour information of the image, the three RGB channels are transformed by using dual tree complex wavelet transform (DT-CWT) to extract low-pass sub-bands for the main contour, respectively
Summary
Since high dynamic range (HDR) imaging is able to capture the wide range of realworld lighting, the HDR image meets the high requirements for image quality and visual perception [1,2,3]. By performing SVD and DCT on the expanded matrix, the features representing the main information of the image were extracted to construct a robust zero watermark. A novel zero-watermarking method based on DT-CWT, quaternion fast Fourier transform (QFFT), and quaternion singular value decomposition (QSVD) for the HDR image is presented. When we decompose three color channels of the HDR image by using four-level DT-CWT, three low-pass sub-bands are computed and denoted as F4L,R, F4L,G, and F4L,B, respectively. Considering three low-pass sub-bands of the HDR color image as a whole, the quaternion fast Fourier transform (QFFT) of F4L and its reverse are: K(s, t) = (KR(s, t))i + (KG(s, t))j + (KB(s, t))k (8). Since QFFT and QSVD combine three channels to be transformed, strong correlations of the HDR color image are maintained for robust zero watermarking
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