三维不等长Arnold变换及其在图像置乱中的应用

3-Dimensional Non-equilateral Arnold Transformation and its Application in Image Scrambling

传统的二维Arnold变换和三维Arnold变换在图像置乱过程中仅能改变图像的像素位置,导致图像置乱效果不理想.为此,利用二维等长Arnold变换构造三维等长Arnold变换的原理,将二维不等长Arnold变换及其反变换进行推广,得到了一种三维不等长Arnold变换及其反变换的算法.该算法将平面图像一一映射为立体空间二值图像,对其像素位置的置乱和恢复间接地改变了平面图像的像素位置和像素值大小;并采用小波多级分解和信息论相结合的方法实现了图像置乱效果的评价.实验结果表明,采用文中算法是可行的,对于图像置乱结果的评价与人的视觉感知基本相符.

The conventional 2D and 3D Arnold transformations are only capable of changing the positions of pixels in process of image scrambling,which bring the effect of image scrambling non-ideal.To address this question,making good use of the principle of constructing 3D equilateral Arnold transformation from 2D equilateral Arnold transformation,a new kind algorithm of 3D non-equilateral Arnold transformation and its anti-transformation is presented by means of extending 2D non-equilateral Arnold transform and its anti-transformation.The algorithm firstly one-to-one maps planar gray image to spatial binary image,then scrambles the positions of pixels in spatial binary image,so that the positions and values of pixels in planar gray image are changed directly,and lastly the image scrambling effect of this algorithm is evaluated by means of combining wavelet multi-decomposition with information theory.The experimental results show that the algorithm proposed in this paper is feasible,and the evaluation of image scrambling results largely consists with human vision.