E.g. take Red colour chanel values of four pixels. Lets say they are 100, 101, 102, and 103.
Sum them up, you get 406.
Divide by 4 you get 101, remainder 2.
Because the remainder is 2, the rounding, by adding two befire dividing, produces a final result of 102. The problem is that the actual correct answer is 101.5
Big deal right? Nobody cares! You can't represent the 0.5 anyway, and rounding to the nearest integer beats always rounding down, or always rounding up!
That's all largely true, but well actually the person adding 2 cares enough to at least recognise the problem, but do they know the best solution...
Consider what happens if the majority of the remainders cause rounding to go up. E.g. What if all the pixels were the same colour? Overall the image brightness has changed. Yes it's barely noticeable in most cases, and 99% of people wont care about it, but it's there.
Wouldn't it be better if we took half of those pixels and rounded those down instead? Then the overall brightness would be the same.
Better still, we could add 0, 1, 2, or 3 before dividing by 4 each 1/4th of the time, which helps for the cases where the remainder is odd.
This tends to be done one of several ways:
In a patterened approach - pattern dithering.
In a randomised way, adding anything from 0-3 randomly before the division - random dithering.
Or, where the error term is accumulated as we travel across the pixels in each row - Floyd-Steinberg style dithering.
These are all techniques that subtley increases the quality of the resulting image. It certainly isn't so important in real-time rendering, and it is less important the higher the bit-depth. But when working with say 256-colour images in an image editing program for example, this stuff really makes a difference. Most people will be using an image processing application that will probably happen to use one of the above techniques anyway, so it's all done for you. If you're the one writing such an application, you might need to know this stuff in order to produce images of the same quality as other applications. I just thought I'd share it anyway.
Edited by iMalc, 14 March 2013 - 01:47 AM.
To downsize an image with an even higher quality result, i.e. more true to the orignal image in terms of overall brightness levels, you can perform dithering as well.