Gaussian filter

The Gaussian smoothing filter is used for noise reduction and removing details. The filter is similar to the arithmetic mean filter but it uses a different kernel that represents the shape of a 2 dimensional Gaussian distribution.

Help!:

Please help to code this formula in TeX (<math> </math>)! An example should be provided here in form of an image or textcoded.

<math> G_{2D}(x,y,\sigma)=\frac{1}{\sqrt{2*pi*\sigma^2} <\math>

• In the search engine of the Processing Toolbox, type Smoothing and select Smoothing (gaussian) under Image Filtering of the Orfeo Toolbox.
• Under the Parameters tab, select a single band or a multiband file as input layer.
• Select gaussian from the drop-down list as Smoothing Type.
• Adjust the Radius of a circular element in pixel size.

Figure A: Input image: pansharpend Sentinel-2 composite (RGB=B7,B6,B5), University Göttingen Campus North

Figure B: Output image: Gaussian filtered Sentinel-2 composite (RGB=B7,B6,B5), University Göttingen Campus North