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The Gaussian Function

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The Gaussian Function

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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

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