Quaternion potential functions for a colour image completion method using Markov Random Fields

An exemplar-based algorithm has been proposed recently to solve the Image completion problem by using a discrete global optimisation strategy based on Markov Random Fields. We can apply this algorithm to the task of completing colour images by processing the three colour channels separately and combining the results. However, this approach does not capture the correlations across the colour layers and, thus, may miss out on information important to the completion process. In this paper, we introduce the use of quaternions or hypercomplex numbers in estimating the potential functions for the image completion algorithm. The potential functions are calculated by correlating quaternion image patches based on the recently developed concepts of quaternion Fourier transform and quaternion correlation. Experimental results are presented for image completion which evidence improvements of the proposed approach over the monochromatic model.