# How to add noise to color image, so that the MSE becomes square of the standard deviation of the noise?

I have added noise to color image. But when I am calculating the MSE, it is very low compared to the added noise. For std=20, the MSE is below 200. But I think MSE should be close to square of standard deviation of the added random noise(if std=20 then MSE around 400).

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I suspect you are computing the MSE in the wrong way! Can you add your code?

( 2016-06-07 07:42:14 -0500 )edit

//For gray level image

for(int y = 0; y < width; y++){ for(int x = 0; x < height;x++){

        difference = (original.at<double>(x,y) - ref.at<double>(x,y));
sum = sum + difference*difference;
}
}
mse = (float)sum /(width*height);
printf("MSE =%.3f\n",mse);

( 2016-06-07 09:06:42 -0500 )edit

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Here is a Sample Program to reproduce the same!

#include "opencv2/imgproc/imgproc.hpp"
#include "opencv2/highgui/highgui.hpp"

#include <iostream>

using namespace cv;
using namespace std;

bool AddGaussianNoise(const Mat mSrc, Mat &mDst,double Mean=0.0, double StdDev=10.0)
{
if(mSrc.empty())
{
cout<<"[Error]! Input Image Empty!";
return 0;
}
Mat mSrc_16SC;
Mat mGaussian_noise = Mat(mSrc.size(),CV_16SC3);
randn(mGaussian_noise,Scalar::all(Mean), Scalar::all(StdDev));

mSrc.convertTo(mSrc_16SC,CV_16SC3);
addWeighted(mSrc_16SC, 1.0, mGaussian_noise, 1.0, 0.0, mSrc_16SC);
mSrc_16SC.convertTo(mDst,mSrc.type());

return true;
}

double GetPSNR(const Mat& I1, const Mat& I2,double &MSE)
{
Mat s1;
absdiff(I1, I2, s1);       // |I1 - I2|
s1.convertTo(s1, CV_32F);  // cannot make a square on 8 bits
s1 = s1.mul(s1);           // |I1 - I2|^2
Scalar s = sum(s1);         // sum elements per channel
double sse = s.val[0] + s.val[1] + s.val[2]; // sum channels

if( sse <= 1e-10) // for small values return zero
return 0;
else
{
double  mse =sse /(double)(I1.channels() * I1.total());
MSE= mse;
double psnr = 10.0*log10((255*255)/mse);

return psnr;
}
}

int main(int argc, const char* argv[])
{
imshow("Source Image",mScene);

Mat mNoise(mScene.size(),mScene.type());
double Mean=0.0,StdDev=20.0;

imshow("mNoise",mNoise);

double PSNR=0.0,MSE=0.0;

PSNR= GetPSNR(mScene,mNoise,MSE);

cout<< "PSNR : "<<PSNR<<" \n MSE :"<<MSE <<"\n";

waitKey();
return 0;
}

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I am calculating MSE for M-pixel gray level images MSE=1/M ∑_(j=1)^M [ I_target (j)- I_reference (j) ] ^2

where I_target is the degraded image and I_reference is the original image

( 2016-06-07 08:53:16 -0500 )edit

I am getting the same value as yours while considering the three channels.

( 2016-06-07 09:12:46 -0500 )edit

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