Apply mean and standard deviation of an image to another image

Hi I have an image and I calculate the mean and standard deviation like this

   meanint=mean(mean(tmpimg));
   stdint=std(std(tmpimg));

Now I have another image and I try to make it have the same mean and standard deviation as the previous image. That's what I do

   if (meanint2>meanint(1))
        tmpimg = imsubtract(tmpimg,meanint2);
        tmpimg = imadd(tmpimg,meanint);
        tmpimg = imdivide(tmpimg,stdint2);

        tmpimg = immultiply(tmpimg,stdint);
    elseif (meanint2<meanint(1))
        tmpimg = imadd(tmpimg,meanint);
        tmpimg = imsubtract(tmpimg,meanint2);
        tmpimg = immultiply(tmpimg,stdint);
        tmpimg = imdivide(tmpimg,stdint2);
    end

But I don't have the result I want. Does anyone knows why?

Answer 1

[Guillaume]

Really, this can be done with just one operation, with much less error accumulation and chance of truncation (if integer images):

meanreference = mean2(referenceimage);
stdreference = std2(referenceimage);
meantoscale = mean2(imagetoscale);
stdtoscale = std2(imagetoscale);

adjustedimage = imlincomb(stdreference / stdtoscale, imagetoscale, ...
                          meanreference - meantoscale * stdreference / stdtoscale);

If the image is double I wouldn't even bother with the imlincomb:

adjustedimage = meanreference + (imagetoscale - meantoscale) * stdreference / stdtoscale;

[Efstathios Kontolatis]

I searched the documentation and I cannot understand what imlincomb does. Also, what is the ...? The standard deviation is not the same with this process.

[Guillaume]

imlincomb is just a linear combination of images, imlincomb(K1, img, K) as I'm using here, simply does K1 * img + K.

The ellipsis (...) allows you to continue statements on the next line. It is only to make the code more readable, you could have written my example just on one line:

adjustedimage = imlincomb(stdreference / stdtoscale, imagetoscale, meanreference - meantoscale * stdreference / stdtoscale);

[Efstathios Kontolatis]

With this process the standard deviation is not the same

[Guillaume]

Let's see:

>> imagetoscale = uint8(randi([0 100], 200, 100)); %should result in a mean of ~50 and std of ~29
>> referenceimage = uint8(randi([50 254], 100, 100)); %should result in a mean of ~152 and std of ~58.89
>> meantoscale = mean2(imagetoscale)  %you will get slightly different result because of randi
meantoscale = 
      49.923
>> stdtoscale = std2(imagetoscale)  %same
stdtoscale =  
      29.162
>> meanreference = mean2(referenceimage)
meanreference =
      153.34
>> stdreference = std2(referenceimage)
stdreference =
      59.747

So the current mean is 49.923 and standard deviation is 29.162. Target is mean 153.34 and std 59.747.

>> adjustedimage = imlincomb(stdreference / stdtoscale, imagetoscale, meanreference - meantoscale * stdreference / stdtoscale);
>> mean2(adjustedimage)
ans = 
   153.32
>> std2(adjustedimage)
ans = 
   59.759

We achieved 153.32 and 59.759. Considering the number of pixels, that is the same as the reference.

[Efstathios Kontolatis]

OK that's true my fault.

[Adam]

The problem of standard deviation not being the same is that you calculate it wrongly in the code in the question. Mean is a separable operation that you can do as you are doing (though there is no need to do so), std is not.

std2 as Guillaume uses works correctly or as I usually do more generically, just

std( tmpimg(:) )

since it is a statistical operation and the structure of the data in a 2d matrix rather than 1d is not relevant.

Answer 2

[Adam]

tmpimg = imsubtract(tmpimg,meanint2);
tmpimg = imdivide(tmpimg,stdint2);
tmpimg = immultiply(tmpimg,stdint);
tmpimg = imadd(tmpimg,meanint);

seems a more appropriate ordering and gives me the same mean.

[Efstathios Kontolatis]

For which of the two if? Also, the standard deviation is not the same.

[Adam]

I don't see the need for two cases, why is the code different depending whether the mean is greater or smaller?