about fingerprint quality, How I can calculate the constant of normalizing a summed result

Hello,

I am trying to implement an alogrithm of evaluating fingerprint image quality. This is one of the algorithms presented in a paper, A Novel Measure of Fingerprint Image Quality using Fourier Spectrum.

It is the first one, standard deviation. This is a relatively simple algorithm, but I get a question about normalizing the quality score. I have searched on the internet to find some solutions about normalization, and there is some. But they are used for normalizing a set of data, not for a summed result. Thus, I post this thread. Is there anyone can help me.

The question is that how I can calculate the proper constant of normalizing the summed standard deviation of each block of the fingerprint image. There are two equations described below:

Sk = sqrt( 1/w^2 * sum(G(x,y)-Gk)^2) ) Sstd = 1/c1 * sum(Sk)

Sk is the standard deviation of the kth block and Sstd is said to be the normalized value, c1 is the constant which normalizes the sum of all Sk.

Thanks.