| Wavelets have found wide applications in image processing due to the multiresolution or multiscale analysis property. Lifting scheme is a new method for constructing wavelets and performing wavelet transform. Digital watermarking has recently been proposed as a mean to provide copyright protection of multimedia data against unauthorized uses. A watermark is a digital code containing information of author ID, company logo, product serial number or something else. To be successful, the watermark must be unperceivably and permanently embedded into the data: that is, after any distortion process, it can also be extracted to prove ownership, to recognize the identity of a misappropriate^ to trace the dissemination of the data through the network, or to authenticate the integrity of the data.Wavelets are becoming a key technique in the ongoing source compression standard JPEG-2000.The positive arguments for advocating DWT in image watermarking are: preventing watermark removal by JPEG-2000 lossy compression, reusing previous studies on source coding regarding the visibility of image degradations, and offering the possibility of embedding in the compressed domain. In addition, the multiresolution aspect of wavelets is helpful in managing a good distribution or location of the message in the cover in terms of robustness versus visibility.This paper focuses on wavelets and lifting schemes and their application algorithms for image digital watermarking. The main results are as follow:The lifting scheme of dyadic single wavelet is presented, including the lifting process, lifting factorization of wavelet transform, complexity comparison between the standard wavelet transform and the lifting factorization, and the reversible integer-to-integer lifting wavelet transform.Then the lifting scheme is extended to M band wavelets. The lifting factorization form of M band perfect reconstruction wavelet transform is given. A method for constructing M band wavelet filters using lifting is discussed. After that, the lifting scheme is extended to multiwavelets and of which the lifting factorization is proved. Two algorithms for raising approximation order of multiwavelets utilizing lifting are discussed.For image digital watermarking, the basic requirements, the insertion and detection problem is discussed. A watermarking algorithm based on lifting wavelet transform is proposed, in which the watermark is adaptively embedded into the lowest and middle frequency coefficients according to the local activity of the image. Experimental results show the algorithm is robust to certain common distortions. In addition, a similaralgorithm is presented for inserting a small binary character image into a larger host image.In order to be more robust, a new phase watermarking algorithm is given. The multiscale edge or texture feature of the image is characterized using the edge detection method based on dyadic wavelet transform. The watermark is embedded into the phase components of the multiscale edges. Experimental results show the watermark is very strong.Then the second generation watermarking is discussed. A wavelet domain second generation watermarking method is presented. The feature points of the image are detected from the lowest approximation of the wavelet transform. The watermark is inserted in the wavelet coefficients corresponding to the feature points. If the position of the feature points is stored in a database or in the file head of the watermarked image, the original image is not necessary for watermark detection. This algorithm is more robust than the two given above, especially to JPEG compression. Additionally, a public algorithm based on 3-band lifting wavelet transform is given.Finally, the application of fragile watermarking in image authentication is considered. Utilizing the multiresolution aspect of wavelet transform, an algorithm based on reversible integer-to-integer lifting wavelet transform is proposed. A private key is used to control to embed one watermark bit into one coefficient chose...
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