分数微积分用于分形压缩图像嵌入灰度水印

Using fractional calculus to embed gray image as watermark into fractal compressed image

摘要:

传统的基于分形编码的水印技术一般嵌入0,1序列，没有实现灰度图像嵌入。本文在研究正交化分形编码的基础上，利用正交化分形编码参数在迭代过程中的不变性，构造出水印嵌入变换函数，使水印直接嵌入解码参数。分数阶微分序列的引入有效解决了嵌入水印的保密性问题，使得在分形编码的过程中嵌入灰度水印的方法具有了可行性，实现了图像压缩与水印嵌入一体化技术。实验结果表明，水印嵌入对宿主图像的分形编码质量几乎没有影响，水印提取质量良好，且采用分数阶微分序列对灰度水印进行加密效果较好。

Abstract:

For traditional watermarking techniques based on fractal coding, watermarking format is limited to binary sequence 0,1, thus incapable of gray-scale image embedding. In this paper, a novel algorithm feasible for gray-scale watermarking embedding is proposed. To embed watermarking directly into decoding parameters, the host image is encoded with orthogonal fractal coding techniques. Because of the mean-invariant characteristics of fractal encoding parameters during iterations, the watermarking can be embedded into them. On the other hand, fractional calculus pseudo-random sequence has solved the problem that how to enhance the security of embedded watermarking and makes it possible for gray-scale watermark to be embedded during fractal encoding process. Experimental results indicate that proposed algorithm brings little contamination upon the original image，and the extracted watermarking is of good quality. The encryption for gray-scale watermark with fractional differential sequence shows good performance.