The Increment Gabor Function

The Increment Gabor function differs from the traditional Gabor function by a Gaussian increment. The Gaussian increment is introduced so that the stimulus can be presented in the absence of a background. For further description/discussion see Hahn & Geisler (1995).
The following is an example of a two-dimensional Increment 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
                                   (X-Xo) + (Y-Yo)
	f(X,Y) = Amplitude x exp( ---------------- )
                                              2
                                        2 x  B
                                                  
                 x (1 + sin(2 x pi x f x [(X-Xo)cos(r) + (Y-Yo)sin(r)]+ 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
• f - frequency of oscillation
• p - phase of oscillation
• r - orientation of oscillation
• B - spatial extent parameter defined below

		           ln(c)        w
		     sqrt(------)    ( 2 + 1 )
		             2
		B = -------------- x ---------
		                        w
		       pi x f        ( 2 - 1 )

Back to Models and Math

Back to general retina list

visit(s) to this page.