Image Representations Based On Complex Number System And Its Application For Image Disguise

The information revolution not only has brought great changes to our lives, but also brought new opportunities and challenges. With the rapid development of computer technology and network bandwidth, pictures and videos are becoming the dominating theme of people’s lives, making it more and more important to the security requirements for the image and video. Image disguise technology is developed in this trend, as an emerging information security technology for the protection of the important image information’s security during transmission in the network.This paper studies the approach of a digital image expressed in the complex plane, establishing the one-to-one correspondence between image and point in the complex plane based on complex bases under positional number system notation. The method of expressing image in the complex plane can be processing an image directly, making an image converted to a complex number, also can divide an image into pieces of small images, making an image converted into a vector of complex numbers; The calculation of the former is magnitude larger, needing to use the large-number operation, whether the latter’s calculation is smaller, the two methods can be selected flexibly according to the application scenario. This method that expressing digital image in the complex plane, can achieve the conversion between different digital images by the mean of calculating the relationship between the vectors in the complex plane, which helps image disguise study using geometrical method. Further, this kind of image expression is applied to digital image disguise.The innovation of this paper is to use the rotation and translation in the complex plane to realize the image disguise, making the targeting image disguised as an irrelevant image to transfer, introducing the classical geometrical method into image processing. The algorithm can disguise simply between two images, also can disguise an image several times, and even to achieve a public image to be decrypted to multiple secret images. In this article we use a series of experiments to verify the feasibility and effectiveness of the algorithm. Experimental results show that when the public image suffers noise pollution during transmission, although the recovery of the image will be slightly affected, but it will still meet the requirements in less precision demand.