Two-dimensional quaternion linear canonical series for color images

The quaternion-based moments and transforms are among the essential tools for color image processing, and received increasing attention and interest from researchers. In this paper, a novel two-dimensional quaternion linear canonical series (2-D QLCS) for describing color images is introduced. The capabilities of the proposed 2-D QLCS on image representation and reconstruction are analyzed. The proposed 2-D QLCS can be acquired from the common two-dimensional linear canonical transform series (2-D LCTS). The relationships between 2-D QLCS and 2-D LCTS are investigated in detail. Experimental results verify the correctness of the proposed method and show that 2-D QLCS has ideal performance in terms of scale invariance, numerical stabilities and image representation.