Re: [WM]: Normalized Correlation

[Cagatay Candan <gte479k@mail.gatech.edu>]

At 10:50 AM 8/14/02 -0400, Joseph O'Ruanaidh wrote:
>However, given that these are BITMAP images we might want to try
HAMMING
>distance. This would be the number of bits that are different. The 
>maximum number of bits they can have in common is N,  the length of the

>vector, so let's divide by N to normalize. Okay that works.
>
>What is the relationship between the two measures?
>The first is based on Euclidean distance (sum of squares)
>
>Look at these tables:
>
>XOR     1     0
>----------------
>1       0     1
>0       1     0
>
>
>x       -1    1
>----------------
>-1       1   -1
>1       -1    1
>I hope you can see that they are isomorphic. If you
>changed all your binary zeros to ones and binary ones to minus ones the

>two distances would be equivalent (different numbers saying exactly the

>same thing).

This is a great observation.  To see the isomorphism more clearly,
please 
have a look at this table:

set_1= { even, odd }  op_1={addition}
set_2= { negative, positive}  op_2={multiplication}

set_1& op_1             %               set_2 & op_2
%%%%%%%%%%%%%%%%%%%%%%%%%%
even+even=  even      %    positive*positive=positive
even+odd =  odd       %     positive*negative=negative
odd+even =  odd       %     negative*positive=negative
odd+odd  =  even      %     negative*negative=positive
%%%%%%%%%%%%%%%%%%%%%%%%%%

The essence of the whole thing is: Both operations map the set elements 
identically. Therefore I may call this operation as binary addition if
that 
is my wish.  And my marsian friend may call it something else if that is

his wish. But his computer and my computer are doing **exact** same
thing 
when we execute this routine. Just we have different labels on it.

best wishes,
cagatay




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