Thank you for your interest in our work. The method you mentioned was first appeared in another paper of Prof. Xiong. Please see the attachment. I think the section 2.6.1 of the attached paper would provide you a more comprehensive explanation.
In this paper, the cross-correlation between two discrete turn angel functions is defined as Equation (4). The variable 'n' represents the shift value and the summation is performed with respect to 'm'. For the two involved waveforms of 'f(.)' and 'g(.)', the result of the cross-correlation depends on the value of 'n'. The minimum of the cross-correlation is obtained when the two waveforms are best aligned. This minimum value is measured as the similarity between two discrete turn angel functions. Please see Equation (5).
I am not sure if I have explained it clearly enough. Please feel free to contact me if you have further questions.