Separable filter

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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 cost of computing the operator.


1. A two-dimensional smoothing filter:

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

3. The Sobel operator, used commonly for edge detection:

This works also for the Prewitt operator.