MIP Mapping is one popular technique for precomputing and performing this prefiltering. MIP is an acronym for the latin phrase multium in parvo, which means "many in a small place". The technique was first described by Lance Williams. The basic idea is to construct a pyramid of images that are prefiltered and resampled at sampling frequencies that are a binary fractions (1/2, 1/4, 1/8, etc) of the original image's sampling.

While rasterizing we compute the index of the decimated image that is sampled at a rate closest to the density of our desired sampling rate (rather than picking the closest one can in also interpolate between pyramid levels).

Computing this series of filtered images requires only a small fraction of addtional storage over the original texture (How small of a fraction?).