Sigma filter

The sigma filter is a non-linear filter used in digital image processing and is used to smooth an image function without falsifying or blurring the image edges. In particular, noise features are taken into account with the help of a static analysis. A Gaussian distribution of the noise is assumed for this.

algorithm

1. The standard deviation of the noise in the image background is determined. ${\displaystyle \sigma }$

${\displaystyle \sigma ^{2}={\frac {1}{N}}\cdot \sum _{i=0}^{N}(g_{i}-{\bar {g}})^{2}}$,

where is the number of pixels in the examined image area, the gray value of the -th pixel and the mean gray value in the area ${\displaystyle N}$ ${\displaystyle g_{i}}$ ${\displaystyle i}$ ${\displaystyle {\bar {g}}}$

2. The gray value range to be taken into account in the switching network is determined.

${\displaystyle \{g(x,y)-k\cdot \sigma ,g(x,y)+k\cdot \sigma \}}$

3. The gray value mean value of all pixels in the gray value range of the current switching matrix is ​​then determined.

example

The world's first photo, taken in the early autumn of 1826 by Joseph Nicéphore Nièpce (original)

Filtering using a Sigma filter (7x7)

The world's first photo, taken in the early autumn of 1826 by Joseph Nicéphore Nièpce (original) and its filtering using a Sigma filter (7x7). The differences become clearer when viewed in original size (800x556).