Multiple-Action Transform of Quaternion for Color Images

Color image is an important information medium in many multimedia applications. Quaternionic representation (QR), a popular technique for color image processing, is capable of considering the interactions among color channels. However, some commonly used quaternionic operators, such as Clifford translation, rotation, and reflection, only explore the shallow relationships among different color channels. To address this limitation, we propose a simple yet effective operator, named Multiple-Action Transform of Quaternion (MATQ), for color images. MATQ cascades some basic quaternionic operators to form a multiple architecture such that it is able to take account of more complicated relationships among color channels. Three examples of MATQ operators are given and detailedly investigated. Two applications, impulse noise detection and image classification of color images, are provided to show the effectiveness of MATQ. Experiments and comparisons demonstrate that the developed MATQ is a useful tool for color image processing.