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Variance and mean isn't calculated properly

Asked by Sajid Khan on 23 Apr 2013

Hello Everyone,

I am trying to calculate variance and mean of gaussian noise by adding it to uniform image using imnoise function as

image = rgb2gray(im2double(imread('flat_400.jpg')));
image(:,:) = 0.5;
noisy_image = imnoise(image,'gaussian',0,0.8);

and then am trying to calculate mean and variance using

mean_image     = sum(sum(noisy_image))/(size(noisy_image,1)*size(noisy_image,2))
variance = sum(sum((noisy_image - mean_image).^2))/((size(noisy_image,1)*size(noisy_image,2)) - 1)

but the variance and mean are far from the added noise. Can anyone please tell me what's the reason of it?

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Sajid Khan

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2 Answers

Answer by Iman Ansari on 23 Apr 2013
Edited by Iman Ansari on 23 Apr 2013

Hi. Your noise is very large and the output image must be between 0 and 1, so the values greater than 1 became 1 and values less than 0 became zero.

Gaussian noise can be defined:

Mean=0;
Variance=0.8;
Noise=Mean+sqrt(Variance).*randn([256 256]);
mean(Noise(:))
var(Noise(:))

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Iman Ansari
Answer by Sajid Khan on 23 Apr 2013

Well even if I add noise with variance of 0.2 or 0.3, the code provided by me doesn't provide the correct variance and mean.

2 Comments

Jan Simon on 23 Apr 2013

Please post comments in the comment section. Otherwise the connection top the realted message will get lost soon.

Even with a variance of 0.2 the saturation at 0.0 and 1.0 will matter. To narrow the problem down, please try this:

mean_image = mean(noisy_image(:));
var_image  = var(noisy_image(:));
Iman Ansari on 23 Apr 2013

imnoise default variance is 0.01. For this value, the output noise would be became between

[mean-3*sqrt(0.01)   mean-3*sqrt(0.01)]
or 
[mean-0.3  mean+0.3]. 
but for 0.2 ====> [mean-1.3416 mean+1.3416]

http://en.wikipedia.org/wiki/Normal_distribution

Sajid Khan

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