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Laplacian of Gaussian Filters

The Laplacian of Gaussian filter (LoG) is a combination of a Laplacian and Gaussian filter where its characteristic is determined by the s parameter and the kernel size as shown in the mathematical expression of the kernel:

Laplacian of Gaussian Filter

 

 

The shape of the filter is defined by from template menu:

Here it is a good idea to set "3D Filter Preview" on in the Output Options so that the shape of the kernel can be monitored in 3D while modifying the kernel parameters:

 

 

Because of the shape Laplacian of Gaussian filters are often called Mexican hat filters.

The kernel size should be selected large enough to contain the negative values otherwise its effect reduces to a Gaussian smoothing filter.

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