3-dimensional non-equilateral Arnold transformation and its application in image scrambling

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.