Separable filter - Alchetron, The Free Social Encyclopedia

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 cost of computing the operator.

Examples

1. A two-dimensional smoothing filter is separated in this sample:

1 3 [ 1 1 1 ] ∗ 1 3 [ 1 1 1 ] = 1 9 [ 1 1 1 1 1 1 1 1 1 ]

2. Another two-dimensional smoothing filter with stronger weight in the middle:

1 4 [ 1 2 1 ] ∗ 1 4 [ 1 2 1 ] = 1 16 [ 1 2 1 2 4 2 1 2 1 ]

3. Sobel operator (edge detection)

G x = [ 1 0 − 1 2 0 − 2 1 0 − 1 ] ∗ A = [ 1 2 1 ] ∗ [ + 1 0 − 1 ] ∗ A

This works also for Prewitt operator.

References

Separable filter Wikipedia

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