Correctly samples this image: http://24.media.tumblr.com/33afdde66541395bbb3f9c8818be943a/tumblr_mmd4ozTT2g1qbgkkto1_1280.png (expected "thing.png") and outputs a "1:1" version called "deflate.png" and an explanatory reference called "grid.png"

deflate.py

#!/usr/bin/python

import Image;
import math;

img = Image.open("thing.png");
pixels = img.load();

width = img.size[0];
height = img.size[1];

pixelSize = 7.222222; # this is fiddly bit
halfPixel = math.ceil(pixelSize / 2);

pixelsWide = int(math.floor(width / pixelSize));
pixelsHigh = int(math.floor(height / pixelSize));

# make a new image the size of the deflation
out = Image.new("RGBA", (pixelsWide, pixelsHigh), "white");
newPixels = out.load();

accumX = 0;
accumY = 0;

for y in range(pixelsHigh):
  for x in range(pixelsWide):
		
		# Accumulation is the key
		accumX = accumX + pixelSize;
		accumY = accumY + pixelSize;
		
		# The round function is the lock
		newx = int(round(x * pixelSize) + halfPixel);
		newy = int(round(y * pixelSize) + halfPixel);
		
		# Display
		newPixels[x, y] = pixels[newx, newy];
		pixels[newx, newy] = (255,0,0,255);
		

img.save("grid.png", 'PNG');
out.save("deflate.png", 'PNG');