Next: 13.3.3 Convolutions Using the
Up: 13.3.2 The Convolution Operation
Previous: 188.8.131.52 Two-Dimensional Convolutions
In the general case, the two-dimensional convolution operation
(width * height) multiplications for each output pixel.
Separable filters are a special case of general convolution in which
can be expressed in terms of two vectors
such that for each
G[i][j] = Grow[i] * Gcol[j]
If the filter is separable, the convolution operation may be performed
(width + height) multiplications for each output pixel.
Applying the separable filter to Equation15 becomes:
Which can be simplified to:
To apply the separable convolution, first apply Grow as though
it were a width by 1 filter. Then apply Gcol as though it
were a 1 by height filter.