Does an image that is scaled down lose more Information when calculating averages of pixels rather than selecting single pixels?
One way to scale down an image is to replace 2x2 pixel blocks with the average of those four pixels, the other way is to just select the top-left pixel (or any other) instead.
Averaging is done by summation and integer division. We reduce the Problem to just scaling 2x2 images down to 1x1 images. For black and white images there are 16 possible images, 15 of those will be black and one will be white thus the entropy of the scaled down image is 0.337 bits. For grayscale images with 5bits per pixel results in 4.2524 bits, with 6bits per pixel we end up at 5.251 bits.
Does averaging really lose more information than just selecting top-left pixels?
I'm aware that you lose some information due to rounding but my calculations don't seem to converge so rounding wouldn't explain everything.