Help with the theory behind a pixelate algorithm?

Question

So say I have an image that I want to "pixelate". I want this sharp image represented by a grid of, say, 100 x 100 squares. So if the original photo is 500 px X 500 px, each square is 5 px X 5 px. So each square would have a color corresponding to the 5 px X 5 px group of pixels it swaps in for...

How do I figure out what this one color, which is best representative of the stuff it covers, is? Do I just take the R G and B numbers for each of the 25 pixels and average them? Or is there some obscure other way I should know about? What is conventionally used in "pixelation" functions, say like in photoshop?

Answer 1

If you want to know about the 'theory' of pixelation, read up on resampling (and downsampling in particular). Pixelation algorithms are simply downsampling an image (using some downsampling method) and then upsampling it using nearest-neighbour interpolation. Note that in code these two steps may be fused into one.

For downsampling in general, to downsample by a factor of n the image is first filtered by an appropriate low-pass filter, and then one sample out of every n is taken. An "ideal" filter to use is the sinc filter, but because of issues with implementing it, the Lanczos filter is often used as a close alternative.

However, for almost all purposes when doing pixelization, using a simple box blur should work fine, and is very simple to implement. This is just an average of nearby pixels.

If you don't need to change the output size of the image, then this means you divide the image into blocks (the big resulting pixels) which are k×k pixels, and then replace all the pixels in each block with the average value of the pixels in that block.

Answer 2

when the source and target grids are so evenly divisible and aligned, most algorigthms give similar results. if the grids are fixed, go for simple averages.

in other cases, especially when resizing by a small percentage, the quality difference is quite evident. the simplest enhancement over simple average is weighting each pixel value considering how much of it's contained in the target pixel's area.

for more algorithms, check multivariate interpolation