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MathGroup Archive 2007

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mutual information of red and green channel

  • To: mathgroup at smc.vnet.net
  • Subject: [mg81274] mutual information of red and green channel
  • From: vickyisai at gmail.com
  • Date: Tue, 18 Sep 2007 00:40:54 -0400 (EDT)

Hello

I am using the following code to calculate mutual information of red
and green channel of an image.

I am calculating Ixy= Sum(i)Sum(j) P(REDi,GREENj) Log[P(REDi,GREENj)/
P(REDi)/P(GREENj)  ]

(that is this formula
http://upload.wikimedia.org/math/c/b/b/cbb518be041b820958181a932a5cd4ff.png
)

I am getting an error of  "Indeterminate expression 0(-=E2=88=9E) encountered.
"

I believe I am getting this because I am taking Probability of Redi
from a histogram that I have computed (value of REDi divided by total
no of pixels ....as my probability of REDi. ame for GREENj
But that histogram has 0 at some places which is leading to divide by
zero.

(i plotted that histogram to check that)

How should I calculated mutual information of red and green channel of
an image.

( I use Mathematica 5.2 and dont have image processing package)
Thank You

Code is below:
--------------------------------------------------------------------------
image=Import["c:/fish.ppm"];
(* Show[image]; *)



part=image[[1,1]];

red=part[[All,All,1]];

histRed=Table[0,{256}];

For[i=1,i<Dimensions[red][[1]],++i,
  For[j=1,j<Dimensions[red][[2]],++j,
    indxr=Floor[red[[i,j]]]+1;
    histRed[[indxr]]=histRed[[indxr]]+1;
    ]
  ]
(* histR=ListPlot[histRed,PlotJoined=EF=94=A2True]; *)

green=part[[All,All,2]];
histGreen=Table[0,{256}];

For[i=1,i<Dimensions[green][[1]],++i,
  For[j=1,j<Dimensions[green][[2]],++j,
    indxg=Floor[green[[i,j]]]+1;
    histGreen[[indxg]]=histGreen[[indxg]]+1;
    ]
  ]
(* histG=ListPlot[histGreen,PlotJoined=EF=94=A2True]; *)


(* Joint Prob. Matrix *)
joinRG=Table[0,{256},{256}];

For[i=1,i<Dimensions[red][[1]],++i,
	For[j=1,j<Dimensions[green][[2]], ++j,
		idx1=Floor[red[[i,j]]]+1;
		idx2=Floor[green[[i,j]]]+1;
		joinRG[[idx1,idx2]]=joinRG[[idx1,idx2]]+1;
	]
]

(*  Ixy= Sum(i)Sum(j) P(xi,yj) Log[P(xi,yj)/P(xi)/P(yj) *)

For[i=1,i<Dimensions[histRed][[1]],++i,
	For[j=1,j<Dimensions[histGreen][[1]],++j,
		Ixy = Ixy + joinRG[[i,j]] / 65536 * Log[2 , ,joinRG[[i,j]] /
histRed[[i]] / histGreen[[j]]   ]
	]
]



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