What does it mean to get the (MSE) mean error squared for 2 images?

Question

The MSE is the average of the channel error squared.

What does that mean in comparing two same size images?

Answer 1

For two pictures A, B you take the square of the difference between every pixel in A and the corresponding pixel in B, sum that up and divide it by the number of pixels.

Pseudo code:

sum = 0.0
for(x = 0; x < width;++x){
   for(y = 0; y < height; ++y){
      difference = (A[x,y] - B[x,y])
      sum = sum + difference*difference
   }
}
mse = sum /(width*height)
printf("The mean square error is %f\n",mse) 

Answer 2

Conceptually, it would be:

1) Start with red channel
2) Compute the difference between each pixel's gray level value in the two image's red channels pixel-by-pixel (redA(0,0)-redB(0,0) etc for all pixel locations.
3) Square the differences of every one of those pixels (redA(0,0)-redB(0,0)^2
4) Compute the sum of the squared difference for all pixels in the red channel
5) Repeat above for the green and blue channels
6) Add the 3 sums together and divide by 3, i.e, (redsum+greensum+bluesum)/3
7) Divide by the area of the image (Width*Height) to form the mean or average, i.e., (redsum+greensum+bluesum)/(3*Width*Height) = MSE

Note that the E in error is synonymous with difference. So it could be called the Mean Squared Difference. Also mean is the same as average. So it could also be called the Average Squared Difference.

Answer 3

You can have a look at following article: http://en.wikipedia.org/wiki/Mean_squared_error#Definition_and_basic_properties. There "Yi" represents the true values and "hat_Yi" represents the values with which we want to compare the true values.

So, in your case you can consider one image as the reference image and the second image as the image whose pixel values you would like to compare with the first one....and you do so by calculating the MSE which tells you "how different/similar is the second image to the first one"

Answer 4

Check out wikipedia for MSE, it's a measure of the difference between each pixel value. Here's a sample implementation

def MSE(img1, img2):
        squared_diff = (img1 -img2) ** 2
        summed = np.sum(squared_diff)
        num_pix = img1.shape[0] * img1.shape[1] #img1 and 2 should have same shape
        err = summed / num_pix
        return err