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This is work efficient since it does less math; instead of adding 9 values for each pixel (the center pixel and the 8 surrounding it), we add 3 values twice (center and its left and right pixels, then for each of those the partial sum above and below to the center), so we only do 6 adds per pixel.


Notice that the relative efficiency of the two-pass approach increases as the size of the filter support region increases. For example, a 10 x 10 blur implemented in two passes performs 20 adds per pixel (10 adds in each pass) rather than 100.