Separable filter

From Wikipedia, the free encyclopedia
Jump to navigation Jump to search

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 computational costs on an image with a filter from down to . [1]

Examples[edit]

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.

In the examples, there is a cost of 3 multiply accumulate operations for each vector which gives six total (horizontal and vertical). This is compared to the nine operations for the full 3x3 matrix.

References[edit]

  1. ^ "Learning Separable Filters" (PDF). p. 3. Retrieved 2021-01-06.