The Gabor Function

The following is an example of a two-dimensional Gabor function which contains horizontal stripes. To make the stripes vertical, exchange X's and Y's. Gabor function may also use sin rather than cos.

                                                         2
                                           -2.77 x (X-Xo)
		f(X,Y) = Amplitude x exp( ---------------- )
                                                  2
                                                Wx
                                                  
                                                        2
                                           -2.77 x (Y-Yo)
		                   x exp( ---------------- )
                                                  2
                                                Wy
                                                  
                                   x cos(2 x pi x f x (Y-Yo)+ p)

• X - horizontal location in space
• Y - vertical location in space
• Amplitude - Peak amplitude of oscillation
• Xo - horizontal midpoint in space
• Yo - vertical midpoint in space
• Wx - full width at half height of horizontal Gaussian
• Wy - full width at half height of vertical Gaussian
• f - frequency of oscillation
• p - phase of oscillation

Click here for a table taken from the above text which describes the relationship between different measures of Gaussian width.

Click here for a table taken from the above text which describes the relationship between the width of a Gaussian function and the width of its Fourier transform

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