Image Analysis

and the other recovers the antisymmetric components, given by

$G_a\left(x,y\right)=\sin \left(k_{x}x+k_{y}y\right)\exp \left(-\frac{x^2+y^2}{2{\sigma }^2}\right)\left(5.60\right)$

where kx and ky give the spatial frequency with the strongest response, and σ is referred to as the scale of the filter.

The magnitude distributions of the above two Gabor filters are drawn in Figure 5.17, where kx = ky. Figure 5.17(a) is for the symmetric filter, while Figure 5.17(b) is for the antisymmetric filter.

By rotating and scaling the above two Gabor filters, it is possible to obtain a set of filters with different orientations and bandwidths to compute the Gabor spectrum, as shown in Figure 5.18. In Figure 5.18, each ellipse covers the range determined by the half-peak ...