Gaussian filter

Convolution with a Gaussian kernel (also referred to as a Gaussian blur or as a Gaussian filter) is one of the most commonly used filters in image processing. The Gaussian kernel is formed by a matrix that contains the values of a rotationally symmetric Gaussian function

$K_{\mathrm{G}}\left(x,y\mid\sigma\right)=a^{2}\exp{\left(-\frac{x^{2}+y^{2}}{2% \sigma^{2}}\right)}\,.$

Kernel $K_{\mathrm{G}}$ of size $l\times l$ is separable and the vector $\boldsymbol{k}$ (see convolution with separable kernels) can be composed from values $k_{i}\left(x\mid\sigma\right)=a\exp{\left(-\frac{x^{2}}{2\sigma^{2}}\right)}$ , where $i=1,\ldots,l$ , $x=i-\left(l+1\right)/2$ , $l=1+2\left\lceil 3\sigma\right\rceil$ , and is a scaling factor such that $\sum_{i}k_{i}=1$ . Users need to input the standard deviation $\sigma$ .

Threshold for approximate localization of molecules

The threshold value can be specified by users as an expression combining mathematical functions and operators with variables based on the current raw or filtered image. Variables provided by this filter are:

Gauss.I	current raw input image
Gauss.F	corresponding filtered image

Gaussian filter

Threshold for approximate localization of molecules

See also