I am implementing zero order approximation method to calculate Legendre moment of an image. One simple way to calculate moments is directly using loops and calculate the double summation as given in the image-1. Then I read everywhere that kernels are separable, so using this we can do a faster implementation. Someone please elaborate how separability of kernels reduces time complexity in this case.
Later in the paper - the author says the same things (a little difference is that - he has an exact calculation, but still kernel separability is valid in both cases) about a faster implementation as given in the image - 2.
I will be very grateful, if someone can explain this?