| Fractal image compression, as one of the most popular techniques in the image compression fields, has novel decoding method, higher compression ratio. However, along with the deeply research on fractal image compression, the application of fractal coding in many other fields has become more and more widely. Especially in digital watermarking field, many different methods using fractal image coding appeared.In this paper, to solve the problems of the existing fractal image watermarking, three novel watermarking methods are proposed. Furthermore, based on the investigation of fractal image coding parameters, this paper also proposes a new image retrieval method using kernel density estimation of fractal coding parameters.The basic fractal coding method is reviewed. The mathematical basis of fractal coding is described, and the coding process, experimental results are proposed. Digital watermarking techniques, especially based on fractal coding techniques are introduced. For the subsequent fractal coding watermarking research, this paper summarizes the advantages and disadvantages of the existing techniques.The orthogonal fractal coding method is analyzed. Also, to get the effective way for embedding watermarking into fractal coding parameters, it has been proved that one of the parameters would be unchanged in the iterative processing. Experimental results also show that the orthogonal fractal coding method can converge very fast in image decoding.Based on the analysis of orthogonal fractal coding, according to the rules of adaptive multiplication embedding, a formula for watermarking embedding is proposed for embedding gray image as watermarking to the fractal coding image. Because traditional methods can only use 0, 1 sequence as the watermarking, not gray image, so, it is the compensation for the traditional methods.Experimental results also show that this method is feasible, and robust against many attacks. Another blind watermarking method based on fractal coding is proposed. This method can extract watermarking blindly, even if the watermarking is gray image. Based on the quantitative modulation, a formula for watermarking transform is proposed. On the other hand, the collage error of the fractal coding parameters is analyzed. Applied this characteristics into the proposed method, watermarking is much more robust and imperceptible.For image authentication, a fragile digital watermarking method is proposed. This method embeds watermarking into fractal transform, and also embeds fractal coding parameters as watermark into host image. It can not only locate altered areas but also automatically recover the original image through extracting the fractal coding parameters. Also, to reduce the false alarm rate and missed rate, the way for embedding watermarking secondly is proposed. Experimental results show that the proposed method is capable of tamper localization, and effective of automatic recovery.A statistical method, called kernel density estimation, is used for analyzing fractal coding parameters. And then, the fractal signatures are extracted for texture image retrieval. Experimental results show that this method has not only higher retrieval rate but also faster retrieval speed than the existing methods.A brief conclusion is made at the end of this paper. The unresolved problems under the application of fractal coding in watermarking are discussed. The outlook of fractal coding application in digital watermarking and other fields is presented. |
