图像的排列变换

任何一幅图像的直方图都可以看作是一个多重集合，该多重集由多种可重复使用的颜色组成，而具有该直方图的任意一幅图像就是该多重集上的一个全排列。因此，可以借助于集合论和群论中的一些理论和方法来研究图像的某些性质。本文首先从多重集和置换群的角度讨论了图像和排列之间的相互关系，然后作为应用实例介绍了两种基于排列变换的图像生成方法。

PERMUTATION TRANSFORM OF IMAGES

The histogram of an image can be considered as a multiple set. An image with the histogram is then a complete permutation on the set. Therefore, the theories and methods about multiple set and permutation group can be adopted to study some properties of images. In this paper, the relationships between permutation and image are discussed first, then two permutation transform construction methods are introduced. The constructed permutation transforms are very simple and efficient, and the images generated by them are of complicated structures and various morphologies.