CSM25 : chi2 test demo

The example below is based on two functions which you should have implemented during exercises:

lsbhide which hides a message in an image and returns a modified image (stegogramme)
chi2stat which calculates the chi2 statistic
chi2p which calculates the probability that the chi2 statistic under the null hypothesis be equal to or higher than the observed value.

To make a test decission, chi2decide may be used.

The demo produces ten plots which are listed below. Random binary messages are embedded, having lengths 10%, 30%, 60% and 100% of capacity. For each stegogramme, and for the covertext, chi2stat and chi2p are plotted.

css1hs@tweek:67$ matlab -nodesktop

                              < M A T L A B >
                  Copyright 1984-2006 The MathWorks, Inc.
                         Version 7.3.0.298 (R2006b)
                              August 03, 2006


  To get started, type one of these: helpwin, helpdesk, or demo.
  For product information, visit www.mathworks.com.

>> path ( '../chi2', path )
>> path ( '..', path )
>>
>> X = imread ( 'image.pnm' ) ;
>>
>> S1 = size ( X )

S1 =

   384   256

>> S = prod(S1)

S =

       98304

>>
>> msg10 = round ( rand ( floor ( 10*S/100 ),1 ) ) ;
>> msg30 = round ( rand ( floor ( 30*S/100 ),1 ) ) ;
>> msg60  = round ( rand ( floor ( 60*S/100 ),1 ) ) ;
>> msg100  = round ( rand ( floor ( S ),1 ) ) ;
>>
>> fplot ( @(a)chi2stat(X,a), [ 100 S ] ) ;
>> print -dpng 'chi2-0.png' ;
>> fplot ( @(a)chi2p(X,a), [ 100 S ] ) ;
>> print -dpng 'p-0.png' ;
>>
>> Y = lsbhide ( X, msg10 ) ;
Message length: 9830.  Image size: 384 x 256 (98304 pixels).
>> fplot ( @(a)chi2stat(Y,a), [ 100 S ] ) ;
>> print -dpng 'chi2-10.png' ;
>> fplot ( @(a)chi2p(Y,a), [ 100 S ] ) ;
>> print -dpng 'p-10.png' ;
>>
>> Y = lsbhide ( X, msg30 ) ;
Message length: 29491.  Image size: 384 x 256 (98304 pixels).
>> fplot ( @(a)chi2stat(Y,a), [ 100 S ] ) ;
>> print -dpng 'chi2-30.png' ;
>> fplot ( @(a)chi2p(Y,a), [ 100 S ] ) ;
>> print -dpng 'p-30.png' ;
>>
>> Y = lsbhide ( X, msg60 ) ;
Message length: 58982.  Image size: 384 x 256 (98304 pixels).
>> fplot ( @(a)chi2stat(Y,a), [ 100 S ] ) ;
>> print -dpng 'chi2-60.png' ;
>> fplot ( @(a)chi2p(Y,a), [ 100 S ] ) ;
>> print -dpng 'p-60.png' ;
>>
>> Y = lsbhide ( X, msg100 ) ;
Message length: 98304.  Image size: 384 x 256 (98304 pixels).
>> fplot ( @(a)chi2stat(Y,a), [ 100 S ] ) ;
>> print -dpng 'chi2-100.png' ;
>> fplot ( @(a)chi2p(Y,a), [ 100 S ] ) ;
>> print -dpng 'p-100.png' ;
>>

Message length	chi2stat	chi2p
0%
10%
30%
60%
100%

CSM25 : chi2 test demo

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