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MathGroup Archive 2008

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Understanding an equation with multiple Summations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg89735] Understanding an equation with multiple Summations
  • From: crd319 at gmail.com
  • Date: Thu, 19 Jun 2008 05:43:59 -0400 (EDT)

I am working on a project which involves comparing two regions of an
image by means of a "G statistic"  The equation I am to use is as
follows:

E_(variable) denotes a Sigma (Summation) with variable as its
condition

ie:
-------
\
/
-------
variable

s,m are two histograms (256x8 2D histograms)
i is a bin number
f_i is the frequency at bin i

The equation, as defined in the paper I'm using, is:

G = 2*( [E_s,m E_i f_i log f_i] -[E_s,m (E_i f_i) log (E_i f_i)] -
[E_i (E_s,m f_i) log (E_s,m f_i) ] +
[(E_s,m E_i f_i) log (E_s,m E_i f_i) ]

I am trying to perform this comparison within a computer program but I
am unsure of the logical flow of it, mostly since there are 3
variables (s,m,i) but only one is explicitly shown to be used.  I am
not familiar with this complex of a problem so if anyone could help my
try and decipher this equation, I would be grateful.


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