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

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


Leave a Reply

Your email address will not be published. Required fields are marked *


You may use these HTML tags and attributes: <a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <strike> <strong>