We may deal with a situation where the intensities in two overlapping image regions and might vary in brightness and contrast. Using those, the variance of an arbitrary rectangular block of pixels can be generated in constant time with 3 products and 9 sums for calculation and 2 products and 6 sums for data access. For a two-dimensional image, both tables can be generated in a single loop with, on average, 1 product and 6 sums for calculation and 5 sums for data access per pixel. The variance of a discrete set of random variables is defined asīoth sums can be generated from two Integral Images over and respectively. Using that table, the mean of an arbitrary rectangular block of pixels can be generated in constant time with 1 product and 3 sums for calculation and 2 products and 6 sums for data access. For a two-dimensional image, the table can be generated in a single loop with, on average, 3~sums for calculation and 5~sums for data access per pixel. The sums can be generated from an Integral Image over.

Let be the set of pixel values in a rectangular block with all pixel values having the same probability, then The mean of a discrete set of random variables is defined as 1.3 Block Matching with Integral Imagesīasic Block Statistics with Integral Images (Summed-Area Tables) Mean.1 Basic Block Statistics with Integral Images (Summed-Area Tables).

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