Conversion from n bands color space to HSI n color space

This paper presents the method to get the equations that transform a color space of n independent primary colors to the HIS _n color system (H: hue, S: saturation, I: intensity); n indicates the number of bands and the shape of the HIS _n space. For n = 3 the structure is a double triangular pyramid, for n 4 it is the structure of the double pyramid tetrangular, and so on.