Mean or Average Filter in Image Processing

Average (or mean) filtering is a method of ‘smoothing’ images by reducing the amount of intensity variation between neighboring pixels.

Mean or Average Filter in Image Processing


The average filter works by moving through the image pixel by pixel, replacing each value with the average value of neighboring pixels, including itself.

There are some potential problems:

  • A single pixel with a very unrepresentative value can significantly affect the average value of all the pixels in its neighborhood.
  • When the filter neighborhood straddles an edge, the filter will interpolate new values for pixels on the edge and so will blur that edge. This may be a problem if sharp edges are required in the output.

The following example shows the application of an average filter to a simple one dimensional signal.


A window size of three is used, with one entry immediately preceding and following each entry and following each entry.

Average Filter in Image Processing

For y[1] and y[9], extend the left-most or right most value outside the boundaries of the image

Example: 3 by 3 Mean or Average Filtering in Image Processing


  • Consider the following 3 by 3 average filter:Average Filter in Image Processing
  • We can write it mathematically as

 

Average Filter in Image Processing

2D Average filtering example using a 3 x 3 sampling window:

Keeping border values unchanged

Average Filter in Image Processing

Extending border values outside with values at boundary

Average Filter in Image Processing

Extending border values outside with 0s (Zero-padding)

Average Filter in Image Processing

On the left is an image containing a significant amount of salt and pepper noise. On the right is the same image after processing with an Average filter an Average filter.

Average Filter in Image Processing

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