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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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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(:))
```

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.

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