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Re:Prefix Sums and Their Applications (1993) [pdf] by mturmon on Monday May 26, 2014 @05:41PM (#7801772)
Yes, "Integral Images" would seem to be the two-dimensional extension of the concept discussed in the OP (but the OP does not go there).

People who studied probability are familiar with the 1-dimensional, 2-dimensional, and the general cases, because they are just cumulative distribution functions and the inclusion-exclusion principle (http://en.wikipedia.org/wiki/Inclusion-exclusion_principle) applied to half-spaces.

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