# What are the differences between these two Gabor filter functions

I need to enhance the visibility of veins on dorsal hand vein images in my project. I use two different even-symmetric Gabor filters bank improve vein visibility.

First bank consists of these gabor functions: $$G^\mathit{e}_\mathit{mk}(x,y)=\dfrac{\gamma}{2\pi\sigma^2}\exp\Bigg\{-\frac{1}{2}\left(\dfrac{x_\mathit{\theta}+\gamma^2y_\mathit{\theta}^2}{\sigma^2}\right)\Bigg\}\times \left(\cos(2\pi f_\mathit{0}x_\mathit{\theta})-\exp(-\dfrac{\upsilon^2}{2})\right)$$

Second bank consists of these ones:

$$G^\mathit{e}_\mathit{mk}(x,y)=\exp\Bigg\{-\frac{1}{2}\left(\dfrac{x_\mathit{\theta}+\gamma^2y_\mathit{\theta}^2}{\sigma^2}\right)\Bigg\}\times \cos(2\pi f_\mathit{0}x_\mathit{\theta})$$

where $m$ is the scale index, $k$ is the orientation index, $f_\theta$ is the filter center frequency, $\sigma$ is the standard deviation (often called scale), $\gamma$ is the aspect ratio of the elliptical Gaussian envelope, $\upsilon$ is the factor determining DC response, $x_\theta=(x\cos\theta+y\sin\theta)$ and $y_\theta=(-x\sin\theta+y\cos\theta)$ are rotated versions of the $x$ and $y$ coordinates.

I have coded these filters in MATLAB, I do not have any problem on coding. But I cannot understand the underlying difference between these two gabor functions.

• How is v determined ? – vini Jan 21 '12 at 16:34
• Sorry for late response. $\upsilon=\sqrt{2ln2/\beta}$ where $\beta=(2^{\Delta\omega}-1)/(2^{\Delta\omega}+1)$. $\Delta\omega$ represents the frequency bandwith in octaves which is proposed that there is a significant range in bandwidth ($\Delta\omega(\in [1, 1.5])$) – saglamp Mar 19 '12 at 8:53