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 particular example of a two-dimensional Gaussian function is
Here the coefficient A is the amplitude, xo,yo is the center and σx, σy are the x and y spreads of the blob. The figure on the right was created using A = 1, xo = 0, yo = 0, σx = σy = 1.
In general, a two-dimensional elliptical Gaussian function is expressed as
where the matrix
is positive-definite.
Using this formulation, the figure on the right can be created using A = 1, (xo, yo) = (0, 0), a = c = 1/2, b = 0.
Read more about this topic: Gaussian Function
Famous quotes containing the word function:
“The mother’s and father’s attitudes toward the child correspond to the child’s own needs.... Mother has the function of making him secure in life, father has the function of teaching him, guiding him to cope with those problems with which the particular society the child has been born into confronts him.”
—Erich Fromm (1900–1980)