Hyper-complex number quaternion system-based method for image representation.

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. Except them, other numeral systems for image representation are also worth exploring. Quaternion, as a hyper-complex number mathematical tool, is widely concerned and used in image representation. However, the current mainstream quaternion representation is only applicable to color image representation, and its applicability is limited. Hence, the paper introduces a novel quaternion system-based for image representation, which is suitable not for color image but also for gray-scale image. The representation scheme is a numeral positional system which uses a quaternion as the base, and the method 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,image scrambling and image secret sharing, are demonstrated that the proposed method has an practical research value in image security. [ABSTRACT FROM AUTHOR]