I'm currently using a normalized cross correlation(NCC) for measure the degree of similarity between two image. Almost two week studying about how NCC is derived from Cauchy Schwarz inequality but still don't get the answer and why Cauchy Schwarz inequality is used in NCC computation? can someone make explanation about this?
Let say, I want to measure two image f and g.
Cauchy Schwarz inequality
${\iint f \cdot g} \le {\sqrt{ \iint f^2\cdot \iint g^2}}$
from above equation, NCC is expressed
NCC = ${\iint f(x,y) \cdot g(x+u,y+v)dxdy}\over {\sqrt{ \iint f^2(x,y)dxdy \cdot \iint g^2(x+u,y+v)dxdy}}$
The nominator in above equation is cross correlation between two signal but this correlation can't be used to measure the similarity of two signal.
Tha reason behind the cross-correlation is not used for similarity measurement is that it is very sensitive to the local intensity values. That is why we need to normalize this.
For an example, we may refer to this video (starting from 33.46 min).