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Next: 12.3.3 Convolutions Using the Up: 12.3.2 The Convolution Operation Previous: Two-Dimensional Convolutions

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
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can be expressed in terms of two vectors
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such that for each tex2html_wrap_inline11330
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If the filter is separable, the convolution operation may be performed using only (width + height) multiplications for each output pixel. Applying the separable filter to Equation9 becomes:
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Which can be simplified to:
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To apply the separable convolution, first apply tex2html_wrap_inline11334 as though it were a width by 1 filter. Then apply tex2html_wrap_inline11340 as though it were a 1 by height filter.