The Gaussian Function

A Gaussian function is a function with the following form:

a, b, c and d are arbitrary real constants. The graph of a Gaussian is a characteristic symmetric "bell curve" shape that quickly falls off. 

The parameters:

• a is the height of the curve's peak
• b is the position of the center of the peak
• c (the standard deviation, sometimes called the Gaussian RMS width) controls the width of the "bell"
• d is the value that the function asymptotically approaches far from the peak (in practice d is often set to 0)

Two-dimensional Gaussian function

In two dimensions, the power to which e is raised in the Gaussian function is any negative-definite quadratic form. Consequently, the level sets of the Gaussian will always be ellipses.

• A is the amplitude
• xo,yo is the center
• σx, σy are the x and y spreads of the blob