Due to its effectiveness for removing impulse noise and preserving detail features

median filtering has long been a popular tool of filtering algorithm. But in practice

an important issue of applying median filtering is the filtering speed. In this paper

a fast median algorithm based on measure-integral is proposed. A step function is employed to expand the array for median

then the relationship between median and measure-integral is deduced and an algorithm is gained by it. To the question that the compute time of the algorithm increases rapidly when the values of the array or the function range become large

a method of compress the measure space is put forward

which is extended to multi-scale compress method at last. Experiments show that multi-scale space compressed measure-integral based median computation（MCMIM) has higher processing speed and can be combined with most of the earlier improved median filters.