Help with luminance, contrast and structure

[Rubiel1]

So, following wiki, I wanted to define luminance ( l ), contrast ( c ) and structure ( s), for that I need the standard deviation: square root of the variance (sigma1_ below). But I also tested the formula $E((X-E(X))^2)$ and it gives me two different results.

Below is the code for $sigma1_= (sigma1_sq)^.5=E(X^2)-E(X)^2$ and $sigma1=E((X-E(X))^2)$ that can be added to here.

    mu1 = F.conv2d(img1, window, padding = window_size//2, groups = channel)
    mu2 = F.conv2d(img2, window, padding = window_size//2, groups = channel)
    mu1_sq = mu1.pow(2)
    mu2_sq = mu2.pow(2)
    mu1_mu2 = mu1*mu2
    sigma1_sq = F.conv2d(img1*img1, window, padding = window_size//2, groups = channel) - mu1_sq
    sigma2_sq = F.conv2d(img2*img2, window, padding = window_size//2, groups = channel) - mu2_sq
    sigma12 = F.conv2d(img1*img2, window, padding = window_size//2, groups = channel) - mu1_mu2
    C1 = 0.01**2
    C2 = 0.03**2
    sigma1 = F.conv2d((img1-mu1).pow(2), window, padding = window_size//2, groups = channel).pow(.5)
    sigma2 = F.conv2d((img2-mu2).pow(2), window, padding = window_size//2, groups = channel).pow(.5)
    sigma1_= sigma1_sq.pow(.5)
    sigma2_= sigma2_sq.pow(.5)
    assert  torch.all(sigma2.eq(sigma2_)) #this returns false
    assert  torch.all(sigma1.eq(sigma1_))

Is there a problem with my code?
Is there any reason to choose one of the two formulas? I assume it has to do with numerical stability.

[lidq92]

@Rubiel1 Your implementation of the second way is wrong. You should be aware of the block-based calculation for SSIM map.
It is not (img1-mu1).pow(2), actually, you need to calculate E[(img1_block_ij-mu1_ij).^2] for all i,j. So the first way is the right way.