The mean filter is the simplest type of low-pass filter; here all the coefficients have identical values. Its characteristics are defined by a kernel width, height and shape. If obvious image deviations occur mostly in only one direction the smoothing can be adjusted by changing the shape of the filter to lie accordingly. When the size of the kernel increases the smoothing effect increases.
When the neighborhood considered is too large blurring and other unwanted effects can appear in the data set.
The selection of Kernel Size and form is a compromise between reduction of noise and a low blurring effect.
Different shapes for the Mean filter can be selected:
- 45 degrees turned rectangle shape
- Circular shape ( = octagonal for smaller kernels).
A Simple 3x3 mean rectangular filter is defined by:
; k = 9
1/k is the scaling factor, which can be applied to avoid general data amplification or damping.
The smoothing effect depends on strongly on the filter kernel size the larger the kernel the larger is the smoothing effect. With large kernel sizes the smoothed value becomes more dependent on values lying further away from the current position. The choice of kernel size is a compromise between a desired noise reduction and keeping the image sharpness.