The left column shows the orginal filter as it is passed through a 5-point averager and then a first-difference filter.
The right column starts with the same image, but first passed through the first-difference and then the 5-point averager. Note that the resulting output image from the cascade is the same.

	Start with the same image
	Filter the left with a 5-point averager and the right with a first-difference
	Note the different output images at this point
	Now filter with the "other" filter
	And the final results are the same!