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Separable Filters

In the general case, the two-dimensional convolution operation requires (width * height) multiplications for each output pixel. Separable filters are a special case of general convolution in which the filter
displaymath8061
can be expressed in terms of two vectors
displaymath8062
such that for each tex2html_wrap_inline8069
displaymath8063
If the filter is separable, the convolution operation may be performed using only (width + height) multiplications for each output pixel. Equation 9 becomes:
eqnarray2988
To apply the separable convolution, we first apply tex2html_wrap_inline8073 as though it were a width by 1 filter. We then apply tex2html_wrap_inline8079 as though it were a 1 by height filter.



David Blythe
Thu Jul 17 21:24:28 PDT 1997