Gaussian distribution

The basis function for the generation of kernels (convolution matrices) for image low-pass filtering or smoothing is the Gaussian distribution. The function has the form:

Gaussian function

with parameters x, mean and standard deviation.

Different parameters can lead to different “bell shaped” curves like the following ones:

Gaussian curves

Image taken from http://en.wikipedia.org/wiki/Normal_distribution

Considering that we often will work with Gaussian functions centered at zero (i.e. mean=0), we can simplify the previous formula with the following ones.

One dimension:

1D Gaussian function

Two dimensions:

2D Gaussian function

N dimensions:

ND Gaussian function

 

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