smoothing/blurring/averaging:

so far, the largest single repository for image processing algorithms i've found is the FAQ for a mailing list:
http://femto.cs.uiuc.edu/faqs/cga-faq.html

whether this is form there or elsewhere (so far i've noted a few but used none) -

corners = ( Noise(x-1, y-1)+Noise(x+1, y-1)+Noise(x-1, y+1)+Noise(x+1, y+1) ) / 16
sides = ( Noise(x-1, y) +Noise(x+1, y) +Noise(x, y-1) +Noise(x, y+1) ) / 8
center = Noise(x, y) / 4

in audio these would be called FIRs or finite impulse response filters, as opposed to IIRs, which i haven't seen much reference to for images yet. the few other filters i've seen for blurring, smoothing, sharpening and edge detection are all based on the adjacent filters, and i suppose performed repeatedly. i'll stop posting now and give myself a chance to code more