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A separable filter in image processing can be written as product of two more simple filters.Typically a 2-dimensional convolution operation is separated into two 1-dimensional filters. This reduces the computational costs on an N × M {\displaystyle N\times M} image with a m × n {\displaystyle m\times n} filter from O {\displaystyle {\mathcal {O}}} down to O ] {\displaystyle {\mathcal {O}}]}.
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