Technique #1 will be:
#1: Copy image to a new image.
#2: Add up all the colors in the mask, divide by 37. Keep this value.
#3: On the new image, average the old color with new color :)

I will place the mask in steps of 5, instead of doing steps of 1... Steps of 1 would blend more.

Lets see what it looks like.
Remember the image we're using is:

Results of Technique #1: 10:51 AM 3/27/02 Yes, there are results!
Compilation of the code resulted in only 1 syntax error. >:)
I'm feelin like a bad ass programmer now >:)

Notice if you will, the grainularity seems to have increased, and the noise decreased. This is exactly what I was hoping it would do. Just for kicks, I'll process it 2x,5x,10x over:
2x:

5x:

10x:

Looks nice. By packing closely resembling colors together and by evening out the colors as a whole, the process is one more step towards completion. The reason it looks blocky is that its processed on big grids for speed.