Quaternion Discrete Cosine Transform and its Application in Color Template Matching

Quaternions are the extension of complex numbers and have proved to be a very useful tool for digital color image processing. In this paper, we extend the discrete cosine transform (DCT) to the quaternion field and propose a simple but efficient algorithm to calculate the quaternion discrete cosine transform (QDCT) of a quaternion matrix using its Cayley-Dickson form. Since a color image can be represented by a quaternion matrix, we can apply our novel QDCT to the field of color template matching. Rather than separating a color image into three channel images and processing them respectively as the traditional methods, QDCT can handle color image pixels as vectors and process them in a holistic manner. Experimental results have shown the effectiveness and the promising application future of the proposed QDCT.