Fractional quaternion cosine transform and its application in color image copy-move forgery detection

In this paper, fractional quaternion cosine transforms (FrQCT) is proposed to generalize the conventional fractional cosine transforms (FrCT) to quaternion signal processing in a holistic manner. Firstly, the new transform FrQCT is defined and the proof of its inverse transform is presented. An efficient discrete implementation method of FrQCT is then proposed, in which the relationship between FrQCT and FrCT of four components is used for a quaternion signal. Finally, a new color image copy-move forgery detection algorithm based on FrQCT and modified PatchMatch matching algorithm is proposed to evaluate the performance of the proposed FrQCT. Experimental results on two public datasets (FAU dataset and GRIP dataset) demonstrate that: (a) the proposed efficient implementation method takes only half the computational time of the direct method; (b) the proposed FrQCT-based forgery detection algorithm can achieve a better performance than some state-of-the-art algorithms, especially in the additional operation case.