How to find a match between 2 shifted hue histograms?

edit

Hi, i want to implement a feature, which estimate harmonic colors in a image. In the paper Color Harmonization is a visualisation of Harmonic Color templates on the hue wheel:

Each of these templates can be rotated up to 360 degree,too.

Now i search a method to find de best template for my image. Cohen-Or give us a formula,too: , where p is one pixel of the image X, H and S denote the hue and the saturation. He used the arc-lenght metric to callculate the distance between the image and the template /E_t_m(alpha).

I don't know how to find the alpha. (The shiftet template, so i have a good match with my image).

Maybe someone have an idea :)

greetings