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

For a nice description of the Gabor function in a psychophysical context see Visual Pattern Analyzers by Norma Van Surdam Graham starting at page 48.

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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© 1995 Lance Hahn (lance@retina.anatomy.upenn.edu)