I am reading a paper, in which the author defines gabor kernels as :
$$ \psi_{\mu,\nu}(x,y)=\frac{\lVert \mathbf{k}_{\mu,\nu} \rVert}{\sigma^{2}}\exp \left(-\frac{\lVert \mathbf{k}_{\mu,\nu}\rVert^{2}\lVert \mathbf{z}\rVert^{2}}{2\sigma^{2}}\right)\times\left[\exp\left(i\mathbf{k}_{\mu,\nu}^{T}\mathbf{z}\right)-\exp\left(-\frac{\sigma^{2}}{2}\right)\right] $$ where $\mu$ and $\nu$ define the orientation and scale of tghe Gabor kernels, respectively, $\mathbf{z}=(x,y)^{T}$, and the wave vector is defined as
$$ \mathbf{k}_{\mu,\nu} = \left(k_{\nu}\cos{\phi_{\mu}},k_{\nu}\sin{\phi_{\mu}}\right)^{T} \quad\text{with}\quad k_{\nu} = \frac{k_{\rm max}}{f^{\nu}}, k_{\rm max}=\frac{\pi}2,f=\sqrt{2},\quad\text{and}\quad\phi_{\mu}=\frac{\pi\mu}{8}$$
Now, I want to plot the graph of this function using matlab to visually see and understand the Gabor filter. I have very basic knowledge in using matlab.
Specifically, I am interested in viewing these Gabor Kernels at single scale $(\nu=0)$ and four orientations $(\mu\in\{0,2,4,6\})$ with $\sigma=1$
Right now I am trying to understand Gabor filters. Any help will be greatly appreciated.
Thanks in advance.