According to my question about separability of Gabor filters in this link, I want now to convolve my image with this separable filter by using the normalized cross correlation operation. Assume my Gabor filter is G
, my image is I
. My Gabor is separated into Low-Pass gaussian filter f(x) and Band-Pass gaussian filter g(y). Therefore the image is convolved with the Gabor using the following equation:
I(x,y)*G(x,y) = (I(x,y)*f(x))*g(y).
But I want to achieve this separable convolution using the normalized cross-correlation operation described below:
Where ^G
is the zero mean, unit normal version of the filter and H(x,y)
represents a filter with all ones and the same size of the Gabor filter.
1) I didn't understand what is ^G
. What should be its value? what it differs from G
?
2) How the normalized cross-correlation is computed for the separable Gabor? I don't know if I use correctly the formula: I(x,y)*f(x)*g(y) / I^2(x,y)*H(x,y)
. I don't think that it's true. because I didn't understand what should be the value of zero mean, unit normal version of the Gabor.