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Difference of Gaussian(s) is a wavelet function which approximates the Mexican Hat Wavelet by subtracting a wide gaussian from a narrow gaussian, as defined by this formula:


f(x;\mu1,\sigma_1,\sigma_2)
=
rac{1}{\sigma_1\sqrt{2\pi}} \, \exp \left( - rac{(x- \mu)^2}{2\sigma_1^2} ight)- rac{1}{\sigma_2\sqrt{2\pi}} \, \exp \left( - rac{(x- \mu)^2}{2\sigma_2^2} ight).

Images are often Convolved with this function as part of an Edge Detection Algorithm of the same name.