奇异值分解用于图像置乱程度评价研究

Studying on singular value decomposition applied in image scrambling degree evaluation

提出了基于奇异值分解的图像置乱程度评价新方法。首先求置乱前后两图像灰度值差的绝对值矩阵;其次计算灰度差绝对值矩阵与其转置矩阵之积并进行奇异值分解;最后根据所得奇异值构造一个离散概率分布并计算其信息熵作为图像置乱程度评价函数。实验结果表明,所提出的评价方法能够较好地刻画图像的置乱程度,反映了加密次数与置乱程度之间的关系,与人的视觉基本相符。而且对于不同的图像,该评价方法能在一定程度上反映所用的置乱变换在各置乱阶段的效果。

The new image scrambling degree evaluation method based on matrix singular value decomposition is proposed.This paper firstly constructs the absolute value matrix of difference matrix being composed of original matrix and scrambled one.Then the product of gray difference absolute value matrix and its transpose matrix is computed and is decomposed into left orthogonal matrix,diagonal matrix and right orthogoual matrix.Last the discrete probability distribution is defined by means of diagonal element of diagonal matrix,and the information entropy of its probability distribution is computed and acted as the evaluation function of image scrambling degree.Experimental results show that the proposed method is effective to describe the relation between the scrambling effect and the number of iterations in the scrambling techniques,which largely consists with human vision.For different images,when some transformation is used,this evaluation method can reflect to some extent the scrambling effects in each scrambling stage.