A High-dimensional Quaternion System-Based Method for Image Representation

Abstract

For centuries, the decimal number system always was dominant until the advent of digital computers, which brought the binary and other number systems into the spotlight. Nowadays, digital images represented in the computer are often to use the binary form and they are presented the decimal form at the processing end. Except them, other numeral systems for image representation are also worth exploring. In addition, quaternion, as a high-dimensional mathematical tool, is widely used in image processing. However, the current mainstream quaternion representation is only applicable to color image processing, and its applicability is limited. Hence, the paper introduces a novel quaternion numeral system for image representation, which is suitable not for color image but also for grayscale image. The representation scheme converts the traditional two-dimensional array representation of one image into a higher four-dimensional space. Then, some properties of the quaternion can be applied to image analysis and processing. Experiments show that the proposed representation method can retain the essence of the original image reversibly and losslessly. Furthermore, some potential image applications, such as image encryption and image scrambling, are demonstrated that the proposed method has an practical research value in image security.