数字图像的两类非线性变换及其周期性

Two Classes of Nonlinear Transformations for Digital Image and Their Periodicity

研究了 Fibonacci- Q变换及其逆变换的周期性 ,并证明了 Fibonacci变换周期与 Arnold变换周期的关系式 .利用 Fibonacci- Q变换与 Arnold变换之间的内在关系 ,定义了一种新的非线性变换—— A- F变换 ,同时对其变换周期及其逆变换周期进行了研究 ;也给出了这两类变换周期的简洁算法 .由于 A- F变换和 Fibonacci- Q变换与Arnold变换的周期性大相径庭 。

The periodicity of Fibonacci Q transformation and its inverse one is discussed. The periodic relation of Fibonacci Q and Arnold transformation is proved. Using the intrinsic relation between Fibonacci Q and Arnold transformation, a new nonlinear transformation, named A F transformation, is defined. The periodicity of A F transformation and its inverse one is studied. A simple algorithm to work out their periodicity is presented. The periodicity of A F and Fibonacci Q is quite different from that of Arnold, which shows better security in scrambling digital image.